text: opencv orthographic projection. AI (Artificial Intelligence) HW/SW Flask Machine Learning (ML) NLP OpenCV…. The sole destination for all your academic queries and an extensive portfolio of all documents (incl Tutorials and Solutions) relevant to your journey at Thapar. Orthographic Projection using Planar Homography. Projectionの設定内容は以下の通りで、 Perspective 透視投影。遠近感の有る(遠くに有るほど小さくなる)描画となる Orthographic 平行投影。遠近感の無い( …. All views expressed on this site are my own and do not represent the opinions of OpenCV. Passive: methods that do not require energy projection …. LEARN NC has been archived soe unc edu Courses EMCC May 10th, 2018 - Gt Gt SUMMER 2018 COURSE. Now I am triyng another technic, using projection map with cone light but I am limited to the “Simple Horizontal FOV”, producing distortions for different distance. Hi everyone! I'm trying to create a program, that I will use to perform some tests. Hi there, just a beginner trying to learn something :)), I want some advises and suggestions on the method used to detect 3d coordinates/ positions of …. Figure 1: The proposed Double Sphere (DS) projection model. An important attribute of the perspective projection, in contrast to the parallel projection…. org or any entity whatsoever with which I have been, . The last step is to multiply by an OpenGL orthographic projection matrix, which maps 2D image points to normalized device coordinates (NDC). The parameters to construct the orthographic projection …. Office Hours: Tue 3:00 - 4:50 pm. Specifically, we will cover the …. inverse returns the inverse of the matrix m. orthographic projections orthographic projection solved. An analytical telecentric projector …. However, it can also be installed separately by using following conda command − conda install -c conda-forge jupyterlab You can …. add_patch () function in axes module of matplotlib library is used to add a Patch to the axes’ patches; return the patch. Lambert Conformal Conic Projection Wikipedia. Geometrical figures are in two dimensions, hence they may be drawn to their actual sizes and shapes on a sheet of paper as it is also in two dimensions. Whereas, in an orthographic projection, objects appear the same no matter the distance from the camera. The coordinates of the vanishing points, in the image plane are V1 =(v1i,v1j)and V2 =(v2i,v2j). What is camera calibration? Camera extrinsics; Perspective projection…. Tips and tricks in CATIA DASSAULT CATIA products FAQ. Note that CoppeliaSim texture coordinates are flipped vertically compared with Pillow and OpenCV and this flag must be true in general. Bitnami Wordpress Directory Path. Imagine we have a three dimensional coordinate system whose origin is at the centre of projection and whose Z axis is along the. Unity is the ultimate game development platform. This model is equivalent to first projecting the world points onto a local fronto-parallel image plane, and then scaling this image using regular perspective projection. duced to perspective matrices, the perspective divide, and how the projection matrix is used to map 3D space onto our 2D screen. The orthographic projection includes the various views of an object i. Your code must be clearly structured and well-commented. In computer vision, homography is a transformation matrix H when applied on a projective plane maps it to another plane (or image). isometric drawing and 3d cubes passy s world of mathematics. This is a tutorial on head pose estimation using OpenCV …. 0 graphics API, there are no dependencies on additional software, operating system version or model-specific hardware. 射影変換行列には主に2種類があって、それぞれ 平行投影変換 (Orthographic projection) と 透視投影変換 (Perspective projection) と呼びます。 平行投影変換 …. head pose estimation using opencv and dlib learn opencv. The function to compute the orthographic projection uses the current transformation parameters. One of the best options is orthographic projection …. LEARN NC has been archived soe unc edu. Pose Estimation using OpenCV and Dlib Learn OpenCV. About opencv open camera black screen I use opencv on VS, use The way to open the camera is always a black screen, and capture. Other projection models Orthographic projection • Special case of perspective projection – Di t f th COP t th PP i i fi itDistance from the COP to the PP is infinite Image World – Also called “parallel projection”: (x, y, z) →(x, y) Other types of projections • Scaled orthographic …. The orthographic projection of the telecentric lens (measurement camera) is modeled by the affine camera. However, once the point P is projected on the image plane, Ps is visible if its x- and y- coordinates are contained within the range [left, rigtht] for x and. And checkout my 4 point OpenCV cv2. Pourquoi ma matrice de projection orthogonale ne fonctionne-t-elle pas ? opengl opencv projection …. The above phenomenon is a consequence of perspective projection, Orthographic Projection: Top View (Optional). We know that in orthographic Projection Projectors (projection vectors) are perpendicular to the projection plane. Spatial projection refers to the …. Computer Graphics Stack Exchange. The word orthographic means “at right angles. corners were automatically detected using OpenCV…. projections perspective camera-matrix unity opencv. { x ′ = x d z y ′ = y d z z ′ = z d z = d. js orthographic projection-matrix. A perspective projection projection (perspective projection) and a front projection (orthographic projection) two kinds. Mapping from the world (3d) to an image (2d) • Can we have a 1-to-1 mapping? • How many possible mappings are there? An optical system defines a particular projection. • there is no shift between camera and image origins. Explore the definition of orthographic projection, different views, measurements, and some examples. Comparison of 3-D surface reconstructions. The idea of the custom layer is to perform an orthographic projection …. Smith, Inverse Rendering of Faces with a 3D Morphable Model, PAMI 2013; Boost system, filesystem, program_options (>=1. mplot3d import Axes3D import numpy as np # create a 21 x 21 vertex mesh xx, yy = np. Figure 1: Applying an OpenCV perspective transform to obtain a “top-down” view of an image. The images gotten from experiments are shown in Fig- ure 2, Figure 6, Figure 7 and Figure 8. ; The course provides foundation in Linear algebra, Python and OpenCV…. The algorithm The OpenCV Library [2] has optimised algorithms for 2D image moment. Cylindrical Equidistant Projection. This projection is useful for "view of globe" or "view from space. 由投影矩阵创建的观察箱(Viewing Box)被称为 平截头体 (Frustum)，每个出现在平截头体范围内的坐标都会最终出现在用户的屏幕上。 将特定范围内的坐标转化到标准化设备坐标系的过程（而且它很容易被映射到2D观察空间坐标）被称之为 投影 (Projection…. 4b is a sketch of the potential resulting 2D projection. Following this, as mentioned in their work, we perform feature matching. In the simplest SFM case the camera can be approximated by . About opencv open camera black screen. Since Y=0 for these points, ignore the second column of the rotation/translation matrix, reducing the projection to a planar homography transform (3x3 matrix). This is what we call an orthographic projection. Projection of a Vector onto a Plane. Isometric Drawing and 3D Cubes Passy s World of Mathematics. 'Orthographic Projections Orthographic Projection Solved May 10th, 2018 September 26th, 2016 - This Is A Tutorial On Head Pose Estimation Using OpenCV C And Python And Dlib We Use SolvePnP And SolvePnPRansac For Pose Estimation' 'Courses EMCC May 10th, 2018 - gt gt SUMMER 2018 COURSE LISTINGS lt lt Students not enrolled in a program at EMCC. Hence, the camera parameters are completely determined by the bounding box of the model's head. using opencv c and python and dlib we use solvepnp and solvepnpransac for pose estimation''Latitude Wikipedia May 9th, 2018 - In geography latitude is a geographic coordinate that specifies the north–south 'Orthographic Projections Orthographic Projection Solved May 10th, 2018 - Development of orthographic projections …. Two oblique projections are well known: Cavalier and Cabinet. 3d transformations projections…. As for the instance association annotation, we gather a team of 40 professional annotators and design a three-stage annotation scheme to obtain reliable annotations in a timely manner. As for the focal length, this article provides some useful information on how to estimate the focal length of a webcam or a cellphone camera. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine. From Deep Learning for Vision Systems by Mohamed Elgendy. Free Downloads for Microsoft Office Office Articles. When creating an orthographic projection matrix we specify the width, height and length of the visible frustum. In Perspective Transformation, we need to provide the points on the image from which want to gather information by changing the perspective. Since a projection plane and a center of projection is used for achieving perspective projection…. OpenFace is a deep-learning-based system built on top of the OpenCV computer vision framework. Most drawing produced and used in industry are Orthographic (Multi-view) drawings. Class Description: Comprehensive introduction to computer vision providing broad coverage including low level vision …. Fringe projection profilometry is a state-of-the-art method in order to characterize the geometry information of three-dimensional (3-D) …. The orthographic projection (also sometimes called oblique projection) is simpler than the other type of projections and learning about it is a good way of apprehending how the perspective projection matrix works. The marker was affixed using removable glue dots. Aloimonos described the approximations of perspective projection based on para-perspective and ortho-perspective projections …. Orthographic projection is a way of showing a three-dimensional (3D) object in two dimensions (2D). (For presentational purposes, the position of projector …. P Projection P Methods of Projection 1. While using perspective projection, the 2D point will be defined as x = X/Z and y = Y/Z. Hardware Setup) How I made a AR Drone Fly itself using Python, OpenCV and PS-Drone with TAG image detection How To Use French Curves How to write like ALL IN ONE Mechanical Drawing Tutorial: Sections by McGraw-Hill Third angle projection, isometric view, Orthographic projection…. Projection To Inverse 2d Matrix 3d. When an image of a scene is captured by a …. Those 3-D lines that are parallel are shownto be automatically …. 1 Orthographic and Perspective Projection. HW 2: (due 4 Feb 2008) Experiement with five different openCV …. Des réunions d'affaires avec des professionnels connectés. Orthographic Projection Solved Examples The Geological Society Of London’s Statement On Climate. The correct method of presenting the three views, in first angle orthographic projection is shown below. Projection Mapping Union Station's History: 0 hour(s) 14 minute(s) Be inspired! Our documentaries follow top professionals as they explain the …. Orthographic Projection • glOrtho(left, right, bottom, top, near, far); • Multiply by a orthographic matrix • left, right • Specify the coordinates for the left and …. words beginning with e words starting with e. models and fitting astropy modeling — astropy v3 0 1. If you calibrated the camera using cv::calibrateCamera, you obtained a camera matrix K a vector of lens distortion coefficients D for your camera and, for each. Perspective Transformation – Python OpenCV. Orthographic projection (sometimes referred to as orthogonal projection, used to be called analemma) is a means of representing three-dimensional objects in two dimensions. Xây dựng ma trận nhân svm tùy chỉnh với opencv…. Camera projection modelsCamera projection mod…. OBJECTIVESWhat are sectional viewsWhy do we draw sectional viewsSections and cutting plane linesHidden lines in sectional …. Today, millions of students across …. javascript - threejs 직교 카메라 - 원근감있는 큐브를 모두 확대. use parallel projection, projection lines are "orthogonal" to the projection plane. The goal of this orthographic projection matrix is to actually remap all coordinates contained within a certain bounding box in 3D space into the canonical viewing …. Hi, I use Citrix Workspace for Chrome to work and until now it worked fine, but know I …. glOrtho(): to produce an orthographic projection (parallel). Now we have 9 degrees of freedom. Modeling Projection Projection is a matrix multiply using homogeneous coordinates: divide by third coordinate and throw it out to get image coords This is known as perspective projection • The matrix is the projection …. The camera must perform an orthographic projection so that it is looking straight at the model with the head contained in the middle $128 \times 128$ square of the rendered image. A 3D perspective projection of an object and line clipping when object is . Let the object be a point set P in 3D. translation (in x and y) and a scaling parameters of the scaled orthographic projection …. Browse other questions tagged c++ opencv computer-vision opencv3. 2D to 1D Orthographic Projection 4. 我已经写了2年的OpenCV，发现仅使用OpenCV RGB图片分割石头真的很难，所以我使用kinect融合扫描地面并得到一个点 Cloud ，其中石头高于地面. The third trivial) transformation for z illustrates how an oblique projection is equivalent to a z axis shear followed by a parallel orthographic projection onto a x-y projection plane. Office Hours: Wednesday 1:30-3:00. This means that we assume there isn't any distortion caused by the distance between the object and the image. ISSN: 2236-3297 SBC Journal on Interactive Systems, volume 5, number 3, 2014 9 In the Perspective Projection, one 3D point on a pyramid of from IR camera. 가까운 거리에 있는 물체는 크게, 멀리 있는 물체는 작게 보이는 …. orthographic projection : 정사 투영 OpenCV 2. , the depth of the scene is \ at", weak-perspective projection is a good approximation of perspective projection. PDF Orthographic Projections. This paper addresses the problem of 3D pose estimation of an object from the visual output of an asynchronous event …. Third angle projection - view from outside the box:. Currently only orthographic projection …. As shown in In this paper, an orthographic projection …. scratch and then generate rendering with opencv, which is not ideal. What exactly is the orthographic projection used by Matlab. An orthographic projection has the viewpoint infinitely far away from any object. The orthographic projection will not modify the size of the objects no matter where the camera is positioned. com/ramsrigouthamg/codes_public/tree/master/opencv/homographyBlog Post :http://ramsrigoutham. Mat normal1 = R1*normal; The distance d can be computed as the dot product between the plane normal and a point on the plane or by computing the plane equation and using the D coefficient: Mat origin (3, 1, CV_64F, Scalar (0)); Mat origin1 = R1*origin + tvec1; double d_inv1 = 1. In orthographic projection, an object appears to be the same size regardless of the depth. Gujar (1988) 3-d objects from 2-d orthographic views—a survey. making a dot by changing the color of appropriate pixel). Perspective projection (how we see "normally") 2. Orthographic Projection; Optical Flow Methods; Orthographic Projection; Image Motion Models; Epipolar Geometry; Essential Matrix; Fundamental Matrix; Normalized 8-point algorithm; Lecture note 3: Homework 1: OpenCV Instructions OpenCV Examples Fundamental Matrix Example: 21 Jan 2008: Computing Optical Flow. Ask Question 6 years ago, it was not possible to set a custom projection matrix, but a workaround using orthographic projection was suggested: see here. Other projection models Orthographic projection • Special case of perspective projection - Di t f th COP t th PP i i fi itDistance from the COP to the PP is infinite Image World - Also called "parallel projection": (x, y, z) →(x, y) Other types of projections • Scaled orthographic - Al ll d Also called "wea k tik perspective". Rules To Be Follow: While forming orthographic drawings following rules should be followed; To top view and front view always form over each other. It's for EDUCATIONAL PURPOSE only. [ Natty] c++ Duplicate OpenGL orthographic projection behaviour without OpenGL By: hamid 1. Embossify is an online design utility service to transform images (jpeg format) into 3D STL …. Learning OpenCV 4 Computer Vision with Python 3: Get to grips with tools, techniques, and algorithms for computer vision and machine learning [3 ed. Computing vector projection onto another vector in Python: # import …. Here is how you can get the appropriate perspective transform. Parameters euclideanToHomogeneous () #include < opencv2/sfm/projection. to cancel the rotation and get the image as if it was acquired by the projection matrix of . The Double Sphere Camera Model. Size of this PNG preview of this SVG file: 553 × 553 pixels. It is also called scaled-orthographic projection. 직교라는 뜻이에요) 아래 그림과 같이 실제 모델 좌표계에서 2D 화면으로 보낼 때 평행선으로 객체가 보내어지면. The breadth and height of an object are shown by side view. Kivy is a full-featured framework for …. Product Launches: 2020 Jeep Wrangler 3. • 2-D Motion: Projection of 3-D motion, depending on 3D object motion and projection …. 在OpenGL中有两个重要的投影变换：正交投影(Orthographic Projection)和透视投影(Perspective Projection)，二者各有对应的变换矩阵。 OPengl、DirectX、OPenCV …. 그리고 A와 [R|t]를 합쳐서 camera matrix 또는 projection matrix라 OpenCV에 있는 solvePnP함수를 이용하면 이러한 계산을 손쉽게 할 수 . The resizeGL method sets the geometric projection used for rasterization. projection = glm::perspective (glm::radians (fov), 800. face3d: Python tools for processing 3D face Introduction This project implements some basic functions related to 3D faces. ENGR1304: Orthographic (Multiview) Projections. An orthographic projection is a system of drawings that represent different sides of an object. Distortion is nil at the center, and increasingly extreme with increasing distance from the center. We identified it from reliable source. Supplementary Experimental Results Orthographic multi-ﬂash 3-D photography. Go to Camera Settings of the Camera Actor and adjust FOV value to your preference. From the menu, choose Plot > 3D : 3D Colormap Surface with Projection. Orthographic projection (also called orthogonal) is the simplest type of projection we'll discuss: it consists of merely projecting points and vectors in a perpendicular fashion onto a plane, as shown in Figure 4. extrinsic/intrinsic camera calibration matrix. • the world and camera coordinate systems are the same. Orthographic projection is the system of projecting the solid object in a complex manner showing each n every dimension in a detailed manner. An orthographic matrix is just like a usual perspective projection matrix, . In these methods of projection a three dimensional object is represented on a projection …. w spencer ph d''Orthographic Projections Orthographic Projection Solved May 10th, 2018 - Development Of Orthographic Projections From Isometric Drawings Solved Examples Given Below Isometric Drawing Pictorial Drawing Orthographic…. python opencv realizes perspective transformation-orthographic projection of the side view. the geological society of london’s statement on climate. The Orthographic Projection …. Topics to be covered by the cs512 course in this semester include: overview of computer vision and related areas, extraction of features from images, probabilistic modeling in images, camera calibration, epipolar geometry estimation, statistical estimation, model reconstruction from images, statistical filtering and tracking in video sequences. courses a to z index Golden West College. There's also a 64-bit version available (for Unity 5 and up). The red circular regions denote the region of potential corner detection in a noisy scene. This Demonstration illustrates the concept of rotating a 2D polygon. /***** * Copyright (C) 2007 by pedromartins * * [email protected] By convention, we say that these points should correspond to the 3D points: (0, 0, 0), (0, 0, 1), (1, 0, 0), and (1, 0, 1). Draw in 3 view Orthographic (Top, Front and Right Side) from the Isometric View – see notes on Orthographic [EDIT] Procedure for drawing in Orthographic Projection. ED-U-II/N2: Using Third Angle Projection Method draw – (a)Front View (b) Top View & (c) Right Hand Side View for the following object. Linear or point-projection perspective (from Latin: perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. The figure is the effect of perspective projection…. Free Downloads For Microsoft Office Office Articles. Orthographic projection •Given camera at constant distance from scene •World points projected along rays parallel to optical access. I cranked open my C++ Microsoft Visual Studio application (with OpenGL and the Oculus SDK for Windows) and implemented some shadows. And that's basically the title of the linked StackExchange question. Although this is an example of perspective projection, the camera is so far from the players (relative to the camera focal length) that they appear to be roughly the same size. 3D->2D transformations (3D projections) Perspective projection; Orthographic projection; Camera calibration. OpenCV: Projection Detailed Description Function Documentation depth () #include < opencv2/sfm/projection. The image below demonstrates the difference between these projections. Point clouds depict objects, terrain or space. projection onto the screen (either orthographic or perspective). The first place to look for basic code to implement basic computer vision algorithms is the OpenCV Library from Intel. Many research groups build on top of the OpenCV code base. Demo #5555530882020 : Test OpenCV Demo #5555500000055 : Tests Demo #555555001111 : Autosimilarities Demo #248 : The Orthographic Projection …. ワールド座標系を正規化デバイス座標系に平行投影 (orthographic projection) する行列を変換行列に乗じます。 引数には、l に表示領域の左端 の位置、r に右端の …. May 9th, 2018 - An Oblique Mollweide Projection Here s what it might look like in an interesting orientation one that neatly depicts the entire Earth on a …. The Qt Quick 2 Spectrogram example demonstrates how to show a polar and cartesian spectrograms and how to utilize orthographic projection to show them …. We will now return to image formation and camera geometry in a bit more detail to determine how one calibrates a camera to determine the relationship between what appears on the image (or retinal) plane and where it is located in the 3D world. 通过对视图坐标系经过投影矩阵(Projection Matrix) 正射投影(Orthographic Projection)：矩阵定义了一个类似立方体的平截头体，指定了一个裁剪空间，每一个在这空间外面的顶点都会被裁剪。 OPengl、DirectX、OPenCV …. Use Unity to build high-quality 3D and 2D games, deploy them across mobile, desktop, VR/AR, …. This permits you to speak precisely what you need your shape to appear to be and removes any miscommunication among you and the man. 2-6, the General Distortion Operator , can directly generate an enlarged output image, which you can scale (or resize) back down so as to merge and super-sample the resulting pixels. If I try to" Use View Settings" with Orthographic Projection…. The graphics pipeline keeps track of the third dimension in the form of. There's a classic book on it: Multiple View Geometry in Computer Vision by Hartley and Zisserman. By generating an orthographic projection for each cascade separately we can now render …. You just need to replace, r and l with t and b (top and bottom). com/2014/06/14/perspective-projection-with-. Instead of using a perspective projection, use an orthographic projection …. Experiment with five different openCV routines. This article explores how to take data within a WebGL project, and project it into the proper spaces to display it on the …. These pages include all of the important …. 测试代码 效果： exe打包 如何配置 Vs2019 编写 C++ 什么是. Matplotlib also allows a 3D scatter plot to. Another role of homogeneous coordinates: Perspective projection •When w≠0, 4D homogeneous coordinate !,",#,Arepresents •Images: libpng, OpenCV…. lambert conformal conic projection …. When creating an orthographic projection …. | There's also the Viz module in OpenCV, but it's quite likely you might have to build your own copy of OpenCV to enable it. Orthographic vs Perspective camera projection in Unity. In any case the affine algorithm from H&Z that we used turned out to be not too suitable, so what fit-model does now is actually estimate an orthographic camera, and then convert the 4x4 ortho matrix into a 3x4 affine matrix. "Learning OpenCV" 책을 번역하면서 사용한 한글 용어를 정리해보았습니다. · An orthographic drawing or orthographic projection is a representation of a three-dimensional-object using several two-dimensional planes. How to reconstruct 3D images from 2D projections. eos/orthographic_camera_esti…. Surface reconstruction is achieved via semiglobal block matching (SGBM) 30 using OpenCV. 3D reconstruction of orthographic projection …. Homograpy transformation maps a point in one plane into a point in another plane, ( x ′ y ′ 1) = H 3 × 3 ( x y 1), where the points X ′ and X are …. The perspective projection case is characteristic of real cameras however, the corresponding equations are difficult to deal with. SUPPORT for all the free codes IS NOT PROVIDED, please DO NOT POST debugging questions. That said, all you need to know is […]. OpenCV: get perspective matrix from translation & rotation. by, for example, performing projections of the 3D model onto a plane (front plane or side plane) using, for example, orthographic projection…. 'orthographic projections orthographic projection solved may 10th, 2018 - development of orthographic projections from isometric drawings solved examples given below isometric drawing pictorial drawing 'HEAD POSE ESTIMATION USING OPENCV AND DLIB LEARN OPENCV SEPTEMBER 26TH, 2016 - THIS IS A TUTORIAL ON HEAD POSE ESTIMATION USING OPENCV C. They are represented by classes THREE. orthographic projection are proposed. How to eliminate odd horizontal lines in orthographic projection …. PARIS achieves this by displaying the orthographic projection of the cancerous Using OpenCV, the KeyDot® is tracked optically with 6 . A set of points where each X, Y, and Z coordinate group represent a single point on a sampled surface. The lightweight marker did not obviously impede the snake’s behavior. In the field of autonomous driving, IPM aids in. Equivalently, the views may be considered to be obtained by rotating the object. orthographic projection 행렬은 정육면체와 같은 절도체 상자를 정의합니다. In Blender when using orthographic projection the objects scale when zooming in on them. An alternative way to simplify the SfM problem is to consider a different projection model. center of projection 투영 중심 orthographic …. The projection of a vector onto a plane is calculated by subtracting the component of which is orthogonal to the plane from. the way in which OpenCV routines do it: R,T. The first entry in the list is (0, 0) indicating the top-left corner. By generating an orthographic projection for each cascade separately we can now render each cascade into different shadow map 0I You can find the Box brush in the Modes Panel under the BSP section, Selecting Single ROI bounding Box in OpenCV …. -Using matrix notation: xh yh zh w = 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 X Y Z 1 -Verify the correctness of the above matrix (homogenize using w=1): x = xh w =Xy= yh w =Y • Properties of orthographic projection …. It makes use of exceptional -dimensional perspectives of the item as opposed to a unmarried 3-dimensional view. This is achieved by setting the positive values of near and far distances into the orthographic projection …. We can virtually enlarge or shrink the clipping volume through the use of a projection matrix, when our clipping volume has the shape of a parallelepiped, or a box, we say that we use an orthographic projection. In Blender when using orthographic projection …. Basically, it's a left-handed co-ordinate viewing cube that is normalized to [-1, 1] in x, y, z. 1 正交投影变换 (Orthographic Projection Transformation) 正交投影是相对简单的一种，坐标的相对位置都不会改变，所有光线都是平行传播，我们只需将 …. The box spans between -1 and 1 on each axis. Orthographic Projection is a way of drawing an 3D object from different directions. Or else you'll just end up with a set of orthographics distorted onto three different planes. the geological society of london's statement on climate. 2D graphics rendering tutorial with PyOpenGL. hpp > Returns the depth of a point transformed by a rigid transform. 모과이의꿈 :: 영상 처리에서 사용되는 용어의 한글화 정리. PerspectiveCamera, which are subclasses of THREE. This is possible because OpenFace uses orthographic projection …. Using these given values I would like to perform perspective transformation to compute an ortographic view of this given image (or its visible part). The following holds true in orthographic drawings: A point appears as a point in any plane of projections. OpenGL 의 Intrinsic matrix 는 4*4 matrix로 3차원 카메라공간 을 3차원 NDT (기준좌표계, 정육면체 모양)에 Projection …. GL_PROJECTION matrix is used for this projection transformation. 여기서 다룰 변환이란 물체의 이동, 크기, 회전 등의 변환 행렬의 결합을 말한다. - Camera view coordinate system: This is the system that has its origin on the camera and the and the Z-axis perpendicular to the image plane. Scaled Orthographic Projection CS4243 Camera Models and Imaging 15 Learning OpenCV. The meaning of ORTHOGRAPHIC PROJECTION is projection of a single view of an object (such as a view of the front) onto a drawing surface in which the lines of projection are perpendicular to the drawing surface. To make it simpler: For Back Projection, you calculate the histogram model of a feature and then use it to find this feature in an image. After taking apart the iPhone 12 Pro Max's new case construction, iFixit was able to investigate the new camera array. Creating a orthographic projection …. The invention discloses a method for performing gait recognition by adopting three-dimensional reconstruction of monocular vision and aims at solving …. focal length (fx, fy) center (cx, sy) The last step is to multiply by an OpenGL orthographic projection …. If it would be possible to create your projection matrix this way so the world coordinate system is nicely placed in the middle of the static platform. Orthographic is a special case of perspective projection…. Head Pose Estimation Using OpenCV And Dlib Learn OpenCV. 我想像这样分割地面上的石头并计算石头的面积:我写了2年的OpenCV，发现仅使用OpenCV RGB图片很难分割石头，所以我使用kinect fusion扫描地面并得到一个点云，其中石头高于地面. Substitute all of the values from the OpenCV matrix to the OpenGL matrices as above. We allow this kind of Camera Projection Matrix graphic could possibly be the most trending topic past we portion it in google benefit or facebook. UAH Global Temperature Update for November 2017 0 36 deg. If you calibrated the camera using cv::calibrateCamera, you obtained a camera matrix K a vector of lens distortion coefficients D for your camera and, for each image that you used, a rotation vector rvec (which you can convert to a 3x3 matrix R using cv::rodrigues, doc. Williams An efficient algorithm for the piecewise linear approximation of planar curves 286--293 E. You can use this to process mesh …. Projecting each of these 3D coordinates into 2D is done by multiplying the 4D vector [x, y, z, 1] with a 4x4 projection …. 📽 "projection" - projected interaction with p5. Remarkable, I was downvoted for answering the question and providing a link to a demonstrations of exactly the feature the question asked - a conversion tool to change from perspective to orthographic. 该程序通过OpenCV实现对Marker的识别和定位，然后通过OpenGL将虚拟物体叠加到摄像头图像下，实现增强现实。 视椎体有两种类型，这涉及到两种投影类型：一种是正交投影（orthographic projection），一种是透视投影（perspective projection…. You might think that orthographic projections are of no use today. Perspective Projection In the methods 2,3 & 4 represent the object by a pictorial view as eyes see it. There's an overhead camera that I've calibrated using OpenCV to . Laser Projector: RayTracer - RayTracer: Laser Projector - Tracer M: Laser Projector …. OpenCV libraries in python, and an Arduino microcontroller connected to servos to control the dart launching and aiming of the robotic system. In the initialize function we start by creating the model, view and projection matrices: 1 glm::mat4 Model, View, Projection; After creation, the above matrices are equal. Application example: If you have a histogram of flesh color (say, a Hue. 2D projection images of the 3D volume are generated. These drawings are formed by projecting the edges of the object perpendicular to the desired planes of projection. camera projection matrix canny computer vision meeting fern Gaussian process highgui histogram of gradient matlab opencv …. In the general case, we have N C cameras { C i } i = 1 N C. University of Waterloo (2018). The idea of this project is to understand mathematical details and terms in the field of computer vision. P C l C r T x l x r e l e r Epipolar Geometry Epipolar line: set of world points that project to same point in left image, when point in left image, when projected to …. The projection matrix is set by the data range of the 3D object. Android Lesson Four Introducing Basic Texturing Learn. Search: Citrix Receiver Add Account. Symbol for 1st Angle Projection Symbol for 3rd Angle Projection. Given a set of 3D points and their corresponding 2D points under orthographic projection, the OnP problem is the determination of the pose . The structure from motion - recovering scene geometry and camera motion from a sequence of images - is an important task and has wide applicability in many tasks, such as navigation and robot manipulation. The reason for using the orthographic projection rather than the perspective projection is that drawings, especially of VTubers, I used a tracker implemented with dlib and OpenCV …. diff (below) for anyone interested, with those changes any camera (tested rgb & semantic) can be made orthographic using the blueprint attributes as follows: camera_bp. In this post, we will explain the image formation from a geometrical point of view. I am looking for python opencv implementation, but if someone at least knows what it is that I need to do/measure to achieve it, it will be super helpful. The PyProcar Python package plots the band structure and the Fermi surface as a function of site and/or s,p,d,f (2D and 3D), projection of atomic orbitals, atoms,. Everything visible is within that box. OE( ¡ ß 7 Ù , !T Z Q< Ö ´ (Perspective Projection) 68OE( ( < 19) 8 , !) 6 0Calibration routine for a telecentric stereo vision syste…. Perspective transformation - OpenCV 3. What is Python 3d To 2d Projection. It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. this way both planes are brought in the same plane containing vp. 가급적이면 모든 용어를 한글 또는 한자어를 이용하여 번역하려고 하였고, 구글링을 통해 그 쓰임이 많은 한글 용어를 우선시 하였습니다. Orthographic Projections Orthographic Head Pose Estimation Using OpenCV And Dlib Learn OpenCV …. Software / Skills: Pytorch, Keras, ROS, OpenCV, PCL, Tensorflow, Linux, Eclipse, Git, Agile - Real-time 2D maps were produced from the orthographic projection …. Orthographic Projection Solved Examples LEARN NC has been archived soe unc edu. Affine cameras • A general affine camera combines the effects of an affine transformation of the 3D space, orthographic projection, and an affine transformation of the image: • Affine projection …. 'head pose estimation using opencv and dlib learn opencv …. Orthographic projection of registered 3. Linear Hough Transform Using Python. I’ll do this by including the img src in a div tag that sets it on top of the Threejs scene. The particular implementation will be bitmap clouds which is one of the simpler methods to …. • If the camera pose is known, we can compute the orthographic …. 윈도우의 크기 조정시 호출되는 reshape 콜백 함수에서 변경된 윈도우 크기의 aspect ratio를 참고하여 orthographic projection를 적용시켜주면 해결 . Custom template-matching scripts (Python, OpenCV) were used to determine the position and orientation of the head. Orthographic Camera Projection matrix. The last step is to multiply by an OpenGL orthographic projection …. So overall, the perspective transformation …. Toledo, Ohio Metropolitan Area. Here is a list of all documented namespace members with links to the namespaces they belong to:. 5; [ Natty] python Modify tick label text By: dopexxx 0. This method can project a quadrilateral picture . 3D Graphics with OpenGL by Examples. A Kinect scans the floor looking for the four corners. Models And Fitting Astropy Modeling — Astropy V3 0 1. python raster coordinate-system openstreetmap opencv. Next in step 214, the processor 130 uses OPENCV …. Datasheets of select parts are available. Orthographic Projection-Itisthe projection of a 3D object onto a plane by a set of parallel rays orthogonal to the image plane. Original file  (SVG file, nominally 553 × 553 pixels, file size: 312 KB) File information. The camera can be approximated by orthographic or …. A 3D scene rendered by OpenGL must be projected onto the computer screen as a 2D image. 3D空間をどのように2Dとして描写するかを設定します。 Projectionには「Perspective」と「Orthographic」があります。 キュー …. The method combines two algorithms; the first algorithm, POS (Pose from Orthography and Scaling) approximates the perspective projection with a scaled orthographic projection …. Here, we are using an Orthographic projection matrix. Note that Matlab and/or octave are languages that start indices at 1 instead of 0 - adjust accordingly. 이 절도체 상자는 이 상자 밖에 있는 vertex들을 clip하는 clipping 공간을 정의합니다. What is Inverse Projection Matrix 2d To 3d. Structure from Motion Introduction to Computer Vision CS223B, Winter 2005 Richard Szeliski. an ability to state and implement the methods of camera Computer Usage: Students use Matlab and Intel OpenCV …. Fig 1: 3D points back-projected from a RGB and Depth image Depth and Inverse Projection. This is such a type of drawing in which Parallel Projection is used for the preparation of the drawing of an object. Words Beginning With E 'Orthographic Projections Orthographic Projection Solved May 10th, 2018 - Development Of Orthographic Projections …. Place the number of this view in the ORTHOGRAPHIC PROJECTION …. But beware, if you use orthographic …. Lecture 5 Cameras, Projection, and Image Formation. The function is based on RQDecomp3x3 (). orthographic projection : 정사 투영 OpenCV (34) Linux (35) Embedded linux (7) Etc. the orthographic view projection of road surfaces using our. 5; [ Natty] python Installing opencv …. Browse The Most Popular 29 Projection Mapping Open Source Projects. Homography examples using OpenCV – Image Alignment. The simplest projection is orthographic projection…. Any of the available plotly # we have to strech it for the opencv …. For a planar object, we can assume Z=0, such that, the problem. Tomasi and Kanade first introduced a factorization method to recover 3D shape of the object and the motion of the camera simultaneously under orthographic projection and obtained accurate results. Perspective Scaled orthographic. Run calibration program (available in OpenCV). (=slower) pixel coordinates calibrated coordinates Linear transformation Pixel coordinates Projection matrix Uncalibrated camera Image plane coordinates Camera extrinsic parameters Perspective projection …. Orthographic Projection is a method of producing dimensioned working drawings or blueprints of 3-D Objects using a series of related 2-D views of the object to communicate the object's length, width and depth. Orthographic Projections OpenCV and Dlib Learn OpenCV. Lambert conformal conic projection Wikipedia. Electrostatic Disinfection Services. It is similar to the projector-enhanced stereo surface reconstruction described previously. com/ramsrigouthamg/codes_public/tree/master/opencv/homographyBlog Post . In the polar aspect, the meridians project as straight lines originating at the pole in the center. DEM or Digital Elevation Model are obtained from interpolated Dense Cloud or 3D Mesh Other Deliverables An Orthophoto Mosaic is an orthographic projection …. I use these functions whenever I need to do a 4 point cv2. Orthographic (Multiview) projections (or orthogonal projection) way to represent 3D objects in 2D. 06-05-ex6: Z軸方向の描画範囲 直交投影では，カ …. The affine3d function described here the transformation in a is A-1SA • i. Several types of projection are available, i. 在视见体中的物体会出现在投影*面上，而在视见体之外的物体不会出现在投影*面上。. 31 shows PosIt from BIAS and PosIt from OpenCV with mean time. Three-Dimensional Coordinates Points in Space Introduction to Vectors Defining the 3D Figure Lights and Camera The Viewport3D and Its Constituents Variations in Code and Markup Fields of View Defining Flat Rectangles Defining "Solid" Figures Balancing Light Sources The Orthographic Projection …. Parallel Projection 평행으로 투영하는 방식을 뜻합니다. Orthographic Projection Solved Examples distorting im v6 examples. Example 3: Orthographic Projection (OGL03Orthographic. Three principle dimensions of an object can be presented only two in each view. For examples of this see the Polaroid Transform. 2D to 1D Perspective Projection 4. Orthographic Projection Solved Examples orthographic projections orthographic projection solved. Here, we define 4 points representing our “top-down” view of the image. Every two objects that have the same size also have the same size in the projection …. Course Descriptions Reynolds Community College. Adjacent view (s) is needed to fulfill the size description. There are two kinds of camera, one using orthographic projection and one using perspective projection. Computer 3D applications count heavily on this principle with a process called ray tracing. To transform between two projections, a homography matrix is required. what is cad amp more frequently asked questions vdci. In the 2D system, we use only two coordinates X and Y but in 3D, an extra coordinate Z is added. The views are produced by using the fundamental concept of Orthographic Projection - the location of the Spectator (the viewer). 11; asked Nov 8, 2021 at 13:50. Release Date: 2020-12-10 // over 1 year ago. is about 60 feet away from the pitcher. Python Examples of mathutils. Omnidirectional and Immersive Systems. Orthographic Projection Suppose d →∞in perspective projection model: Then, we have z →-∞so that -d/z →1 Therefore: (x, y, z) →(x, y) This is called orthographic or "parallel projection Good approximation for telephoto optics Image World. Depth Map from Normal Map •We now have a surface normal, …. Toronto, Canada Area Agile Software Development Lifecycle Process Coop at Crum & Forster Enterprise Design Education University of …. The projector can be placed at an arbitrary position. (Orthographic Projection) • 無限遠のカメラで(≒望遠レンズでズームして) 撮影 • 投影された物体の大きさは遠近に依存しない • OpenGL ではglOrtho() …. perspective transformation opencv. Words Beginning With E Words Starting with E Lambert conformal conic projection …. To obtain perspective projection we project the results of perspective transformation on to a any of the orthographic projection planes say z0 plane. Its first 3 dimensional vectors (3*3 submatrix) contain the rotated X, Y and Z axes. Surface orientation We must understand the geometry of the rays …. 8 Top: We simulate an orthographic projection of a cityscape. It uses multiple views of an object, from points of view rotated about the objects centre through increments of 90 degrees. Regarding the projection matrix: 6 years ago, it was not possible to set a custom projection matrix, but a workaround using orthographic projection …. Write relation between image point, projection matrix, and point in space: Write non-linear relations between coordinates: The math for the calibration procedure follows a recipe that is used in many (most?) problems involving camera …. As there is no applied perspective, lines can be absolutely measured and compared. Orthographic projection • Special case of perspective projection – Distance from the COP to the PP is infinite Image World – Also called “parallel projection”: (x, y, z) → (x, y) Other types of projections • Scaled orthographic – Also called “weak perspective” • Affine projection …. Orthographic Projection Practice Questions ED-U-II/N1: Using First Angle Projection Method draw – (a) Front View (b) Top View (c) Left Hand Side View for the following object. Miscellaneous Transformations and Projections. Computers are an essential part of our lives nowadays. An affine transformation is a type of geometric transformation which preserves collinearity (if a collection of points sits on a line before the transformation, they all sit on a line afterwards) and the ratios of distances between points on a line. If orthographic projection is used, or if no polygon will intersect the near clip plane, we skip this operation. They are formatted to print nicely on most 8 1/2" x 11" inch printers in landscape format. glOrtho() はワールド座標系を正規化デバイス座標系に平行投影 (orthographic projection : 正射影) する行列を変換行列に乗じます。 引数には左 …. Ban đầu được gọi là phép chiếu cầu phẳng (planisphere projection…. For either one of the above projections values of most commonly employed are 45 degrees and 30 degrees. Perspective projection; Orthographic projection; Projective geometry; Vanishing points; Week 2. The orthographic projection (also sometimes called oblique projection) is simpler than the other type of projections and learning about it is a good way of . The system works but is much more complex to set. （3）透视投影：perspective projection GLFrustum::SetPerspective(float fAngle, float fAspect, float fNear, float fFar); 透视投影表示从一个顶点方向看去的视场角 …. 따라서 앞으로 3차원 데이터 분석시에는 orthographic projection을 사용할 것이며, 이 GLFW, OpenCV 를 기본 라이브러리로 활용하여 구현. This course provides the student with a holistic understanding of sensors and how to utilize the data for ML/AI and localization. This is a full project on implementing 3D shadow scanner using OpenCV. The precise projection is defined by two angles and. The window renders a 3D scene with a 3D perspective projection matrix (initialization not shown), then switches to a simple 2D orthographic projection matrix to draw a 2D overlay. 12 “Mixed Reality and tangible interfaces” Interaction speciality – Computer Science Master - University Paris-Saclay Pose with Iteration: POSIT Intuitively: • If you have an orthographic projection, one can compute the camera pose linearly (POS). The project had all the great qualities of having a clear mission, lots of man power, no time constraint and adequate technology ( bricks and mortar ). I have not seen any other examples of fisheye pointing downward, and more than just the 'straight lines' I need the 'orthographic' projection …. Isometric Drawing And 3D Cubes. OpenCV 의 Intrinsic matrix 는 3*3 matrix로 3차원 카메라공간 을 2차원 이미지공간으로 바로 Projection 하고. getPerspectiveTransform using OpenCV. Stereographic Projection is a conformal form of Fisheye Projection where the distance from the centre is not equivalent to the spatial angle. Therefore, the 2D coordinates of that detail on the window are. Goto your myInit function and define your matrix like this. • Projection (3D to 2D) – Orthographic projection • Good for telecentric lenses • Good for long focal length lenses • Good for shallow depth objects (relative to distance to camera) – Scaled orthographic projection …. The technique used for two Dimensional displays of three Dimensional objects is called projection. For example, an orthographic projection of a house typically consists of a top view, or plan, and a front view and one side view (front and side elevations). We shall discuss the orthographic projection in the later example. Creating a orthographic projection from 2D input. Orthographic projection: In the Orthographic Parallel Projection, the Projection is perpendicular to the view plane. Three steps, as described in the code - Setting up the texture to contain our image frame, preparing OpenGL for drawing our texture, and setting up a camera viewpoint (using an orthographic projection …. Machine Learning ใช้ Python และ OpenCV …. orthographic projection은 원근이 있지만 거리가 멀어져도 정면에서는 항상 동일한 크기로 보이게 해줍니다.


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# Proving q-binomial identities

I was wondering if anyone could show me how to prove q-binomial identities? I do not have a single example in my notes, and I can't seem to find any online.

For example, consider: ${a + 1 + b \brack b}_q = \sum\limits_{j=0}^{b} q^{(a+1)(b-j)}{a+j \brack j}_q$

I haven't made much progress on this one, but here's one that I have managed to get something out of: ${2n \brack n}_q = \sum\limits_{k=0}^{n} q^{k^{2}}{n \brack k}_q$

Using the q-binomial theorem from my notes, which is as follows: $(1+qx)(1+q^{2}x)...(1+q^{n}x) = \sum\limits_{k=0}^{n} q^{k(k+1)/2}{n \brack k}_q x^{k}$, I have managed to show that the coefficient of $x^{n}$ is equal to: $\sum\limits_{k=0}^{n} q^{(2k^{2} - 2nk + n^{2} + n)/2} {n \brack k}_q {n \brack n-k}_q$, which is when I was working on the right hand side of the identity. In order to get here, I considered the product of $(1+qx)...(1+q^{n}x)(1+qx)...(1+q^{n}x)$, then tried obtaining the coefficient of $x^n$, as one would in the ordinary binomial proof. I've been trying to mimic the proofs of the regular binomial counterparts of these identities but without much luck.

Help would be appreciated, as I have a midterm exam coming up soon. Thanks :)

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I don’t suppose that by any chance you read German? If you do, take a look at this and at these more extensive notes. –  Brian M. Scott Oct 15 '12 at 5:12
No I don't sadly =( - Just English & French. –  Nizbel99 Oct 15 '12 at 5:14
This is a shame, because the references you've given me look like just what I would need if they were in English. I can't seem to find anything comprehensive like this in English either. –  Nizbel99 Oct 15 '12 at 5:25
You can find a few ideas in answers to this question, this question, and this question. (I’ve not yet had time to look at your actual question.) –  Brian M. Scott Oct 15 '12 at 5:35
Thank you =) - I am taking a look now, although these look a lot more complex than what we've seen in class. I will continue to try and work through this problems as well, in the mean time :) –  Nizbel99 Oct 15 '12 at 5:39

You can prove

$${a + 1 + b \brack b}_q = \sum\limits_{j=0}^{b} q^{(a+1)(b-j)}{a+j \brack j}_q\tag{1}$$ by induction on $b$. Assume $(1)$. Then

\begin{align*} \sum\limits_{j=0}^{b+1} q^{(a+1)(b+1-j)}{a+j \brack j}_q&={a+b+1\brack b+1}_q+\sum\limits_{j=0}^{b} q^{(a+1)(b+1-j)}{a+j \brack j}_q\\ &={a+b+1\brack b+1}_q+q^{a+1}\sum_{j=0}^bq^{(a+1)(b-j)}{a+j\brack j}_q\\ &={a + 1 + b \brack b+1}_q+q^{a+1}{a+1+b\brack b}_q\\ &={a+2+b\brack b+1}_q \end{align*}

by the fundamental recurrence $${n+1\brack k}_q={n\brack k}_q+q^{n-k+1}{n\brack k-1}_q\;.$$ It’s worth mentioning the other fundamental Pascal-like recurrence: $${n+1\brack k}_q=q^k{n\brack k}_q+{n\brack k-1}_q\;.$$

I also found these slides of a talk that I think you might find very useful.

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The slides look very helpful :) Thank you! –  Nizbel99 Oct 15 '12 at 13:04
@user43552: You’re welcome! (I also found them very helpful.) –  Brian M. Scott Oct 15 '12 at 13:05

$\newcommand\gauss[2]{\genfrac[]0{}{#1}{#2}_q}$Here's a straightforward implementation of the method I gave in a hint. The natural combinatorial interpretation of a Gaussian binomial coefficient $\gauss {a+b}b$ is that it counts the lattice paths from the origin to $(a,b)$ (where each step advances one of the two coordinates) with as weight the number of squares above the path, within the rectangle with the origin and $(a,b)$ as diagonally opposite corners. Counting with weight means summing over the indicated set the monomials $q^k$, where $k$ is the weight of the element. (I'm using Cartesian coordinates to tell which side is "above" the path.)

Now $\sum_{j=0}^b\binom{a+j}j$ counts the paths from the origin to one of the points $(a,j)$ for $0\leq j\leq b$, while $\binom{a+1+b}b$ counts the paths from the origin to $(a+1,b)$. Now it is not hard to see why $$\binom{a+1+b}b = \sum_{j=0}^b\binom{a+j}j,$$ as every path from the origin to $(a+1,b)$ there is a unique $j$ for which it contains a step $(a,j)\to(a+1,j)$, and once this $j$ is known, the path is entirely determined by the way it passes from the origin to $(a,j)$, because after arriving at $(a+1,j)$ it has no choice but to go straight up.

Now the Gaussian binomial coefficient $\gauss{a+1+b}b$ on the left tells us we want to attach as weight to such paths the number of squares above it, within the rectangle with sides $a+1$ and $b$. On the right the coefficient $\gauss{a+j}j$ counts the squares above the path within the recatangle with sides $a$ and $j$, and since the path makes a horizontal step $(a,j)\to(a+1,j)$, this number is equal to the number of squares above the (extended) path within the rectangle with sides $a+1$ and $j$. But then the path goes straight up for $b-j$ steps, each of which has $a+1$ squares to its left which are also above the path, and within the rectangle with sides $a+1$ and $b$. So we must multiply the terms coming from $j$ by $q^{(a+1)(b-j)}$ to account for the extra squares counted on the left, and this is exactly what your $q$-formula says.

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Thank you :) - I didn't know about the combinatorial interpretation. It's actually quite helpful for a handful of these identities as well! –  Nizbel99 Oct 15 '12 at 13:05
I might have added, the combinatorial interpretation is often stated in terms of Young diagrams: the part of a $a\times b$ rectangle above a path from its bottom-left to top right corner is a Young diagram with at most $a$ columns and at most $b$ rows, and its size (number of squares) gives the associated weight. See for instance Stanley, Enumerative Combinatorics 1, 1.3.19. –  Marc van Leeuwen Oct 15 '12 at 14:01
+1. If you draw the picture this is a very elegant solution. –  dx7hymcxnpq Oct 19 '12 at 7:23

Your identity follows from this version of Pascal's rule:

$${n \brack k}_q = {n-1 \brack k}_q + q^{n-k} {n-1 \brack k-1}_q.$$

Expanding gives

\begin{align} {a + b + 1 \brack b}_q &= {a+b \brack b}_q + q^{a+1} {a+b \brack b-1}_q \\ &= {a+b \brack b}_q + q^{a+1} \left( {a+b-1 \brack b-1}_q + q^{a+1} {a+b-1 \brack b-2}_q \right) \\ &= \cdots \\ &= \sum_{j=0}^b q^{(b-j)(a+1)} {a+j \brack j}_q. \end{align}

You could of course turn this into a proper proof by induction.

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You can use the $q$-Vandermonde identity to expand the left hand side of your equation

$$\binom{m + n}{k}_{\!\!q} = \sum_{j} \binom{m}{k - j}_{\!\!q} \binom{n}{j}_{\!\!q} q^{j(m-k+j)}\,,$$

$$\max(0, k - m) \le j \le \min(n, k).$$

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## From LaTeX to HTML

The translation of a LaTeX source file into HTML involves of loading tex4ht.sty and *.4ht style files, choosing the desirable options for the translation, compiling the source into dvi code with the native LaTeX engine, and postprocessing the outcome with the tex4ht and t4ht programs (see overview).

The htlatex command loads a script which takes on itself to invoke the different steps of the process, without user intervention. The command assumes the form

htlatex filename "options1" "option2" "options3" "options4"

where the first set of options is for the tex4ht.sty and *.4ht style files, the second set is for the tex4ht postprocessor, the third for the t4ht postprocessor, and the last one is for the LaTeX compiler. For instance,

htlatex filename
This command requests a translation according to the default conditions, which are set to produce HTML transitional 4.0 code.
htlatex filename "html,2,info"
This command is equivalent to the previous one, specifying explicitly the option html for tex4ht.sty instead of doing so implicitly.

In addition, the command requests a break up of the output into separate web pages, in accordance to the two top sectioning levels of the document.

Moreover, it asks for a listing in the log file of the information available for the style files in use. That information, among other things, also introduces additional values available for the first list of options.

htlatex filename "" "dbcs/!"
This command requests the loading of the dbcs branch of Chinese hypertext fonts (on top of those already requested by the default setting).
htlatex filename "foo,frames" "" "-p"
This command requests LaTeX to load a private configuration file, named foo.cfg, and to place the content and table of contents in separate frames. In addition, it asks t4ht not to produce bitmaps for pictures.
htlatex filename "" " -ciso2htf" "" "-translate-file=il2-pl"
This command invokes the LaTeX compiler with the instruction ‘latex -translate-file=il2-plfilename’.

## Available Values for the Options

The fields of option1 should be separated by commas. An ‘info’ field requests a listing in the .log file of many of the the available values. If the list is not empty, it must start with the entry ‘html’, ‘xhtml’, or a name of a private configuration file.

The fields of option2 and options3 should be separated by spaces. The available values can be listed by executing the postprocessors tex4ht.c and t4ht.c, respectively, without arguments (or with wrong sets of arguments).

The first field of option2 should be empty or a subdirectory of ht-fonts (typically augmented with an exclamation mark ‘!’). A space should separate the first field from the second one, also when the first field is empty.

The underlying output formats of available htlatex-like commands are tailored into the commands through fields of option1. The names of these fields are defined in tex4ht.4ht and tex4ht.usr (see General Configuration Files). These values should be of little interest to most users.

Different variants of the htlatex command may be invoked by introducing the commands as arguments to a driver named mk4ht. When provided without arguments, the driver lists the commands it recognizes.

 mk4ht mzlatex filename "html,3" (htlatex filename "html,3,xhtml,mozilla" " -cmozhtf") mk4ht oolatex filename (htlatex filename "xhtml,ooffice" "ooffice/! -cmozhtf" "-coo")

Alternatively, a compilation ‘latex mkht-scripts.4ht’ produces different named scripts of similar functionality.

## XHTML and Unicode

The ‘xhlatex’ command is a variant of the ‘htlatex’ command requesting XHTML output. It consists just of a call to ‘htlatex’ with the entry ‘xhtml’ in the first list of options and ‘-cvalidate’ in the third list. For instance, ‘xhlatex filename’ or ‘htlatex filename "xhtml"’.

To request a Unicode representation of symbols, the first list of options should include the ‘uni-html4’ entry, and the second list should include the ‘-cunihtf’ entry preceded by space. For instance, ‘xhlatex filename "xhtml,uni-html4" " -cunihtf"’.

Unicode representations of symbols in UTF-8 encoding may be requested with the entry ‘-utf8’ added to the second list. For instance, ‘xhlatex filename "xhtml,charset=utf-8" " -cunihtf -utf8"’.

To request expanded usage of unicode values in iso-8859-1 output employ commands similar to

htlatex file "" "iso8859/1/charset/uni/!"

or introduce a similar charset path in tex4ht.env. Otherwise, non iso-8859-1 characters might obtain bitmap representations.

## XHTML with MathML

TeX4ht has different configurations for different modes of output. It is distributed with pre-tailored base configurations for translating LaTeX math into MathML, and extra configurations for adjusting the outcome to Mozilla, MathPlayer, and PMathML CSS. Only presentational MathML is supported.

mzlatex filename
mzlatex filename "html,pmathml"
mzlatex filename "html,mathml-"
mzlatex filename "html,mathplayer"
xhmlatex filename

For XHTML+MathML to be served both by Mozilla and MSIE+MathPlayer use the command line option ‘mathplayer’.

The mzlatex command is a short cut representation for the command ‘htlatex filename "xhtml,mozilla" " -cmozhtf" "-cvalidate"’. It take into account special needs of browsers. The xhmlatex command is a short cut representation for the command ‘htlatex filename "xhtml,mathml" " -cunihtf" "-cvalidate"’; it does not make any compromizes toward browsers.

It might be worthwhile to notice some of the more common sources of problems for MathML. The ‘mathml-’ options asks for a degraded MathML output that sidetracks some of the problems.

## OpenDocument, OpenOffice, and MS Word

A translation for an OpenDocument format can be requested by the ‘\oolatex’ command. The command is a variant of htlatex in which the first list of options holds the entries ‘xhtml,ooffice’, the second list holds the entry ‘-cmozhtf’ preceded by a space, and the third list contains ‘-coo’ (htlatex filename "xhtml,ooffice" "ooffice/! -cmozhtf" "-coo -cvalidate"). The output of a command ‘oolatex filename’ is a zipped file named with a ‘.odt’ extension.

The OpenDocument code employs MathML for formulas, and XSL-FO for formatting. It can be viewed by the OpenOffice word processor which, in turn, can export RTF and other MicroSoft-based formats (see also, Maarten Wisse, “Hacking TeX4ht for XML Output: The Road toward a TeX to Word Convertor”, MAPS 28 (2002), pp. 28-35).

A command of the form ‘htlatex filename "html,word" "symbol/!" "-cvalidate"’ asks for HTML output tuned toward MicroSoft Word. Such a format, however, relies on bitmaps for mathematical formulas.

## DocBook and TEI

The following commands may be used for requesting DocBook and TEI output.

 dbmlatex: htlatex filename "xhtml,docbook-mml" " -cunihtf" "-cdocbk" dblatex: htlatex filename "xhtml,docbook" " -cunihtf" "-cdocbk" teimlatex: htlatex filename "xhtml,tei-mml" " -cunihtf" "-cdocbk" teilatex: htlatex filename "xhtml,tei" " -cunihtf" "-cdocbk"

## JavaHelp

JavaHelp is an online documentation system for use by Java-based applications. Such documents can be produced from LaTeX files through commands similar to ‘jhlatex filename’ for JavaHelp version 2.0.

The above invocation stands for ‘htlatex filename "html,3.2,xml,javahelp,unicode" " -cmozhtf -u10" "-dfilename-doc/ -cjavahelp"’. The ‘-u10’ asks for entity references in base 10—JavaHelp doesn’t seem to support hexadecimal representations. The -cjavahelp invokes the JavaHelp indexer to produce the search database at ‘jobname-doc/jobname-jhs’ with a command similar to ‘java -jar \${HOME}/jh2.0/javahelp/bin/jhindexer.jar -db jobname-doc/jobname-jhs jobname*.html’.

The Java program is to be distributed with the jobname-doc directory.

## Private Configuration Files

The leading entry, in the first list of options of the htlatex-like commands, can equal ‘html’ or ‘xhtml’. If this is not the case, the entry is assumed to be the name of a configuration file. The extension ‘cfg’ is assumed for names of configuration files that are listed without their extension.

A configuration file should take the following form for LaTeX files.

...early definitions...
\Preamble{options}
...definitions...
\begin{document}
...insertions into the header of the html file...
\EndPreamble

It is up to the user to decide the distribution of entries between the \Preamble and the htlatex-like commands.

Example The command ‘htlatex myfile "mycfg,2"’ requests the compilation of a file named myfile.tex, in the presence of a configuration file named mycfg.cfg. The configuration file might have the following content.
\Preamble{html}
\begin{document}
\Css{body { color : red; }}
\EndPreamble
Notes
• Notice that for a LaTeX file the \begin{document} instruction should be present both in the configuration file and the source file.

• Instructions defined within a source file may be redefined in a configuration file. Such a feature enables to keep source files intact for compilation to different formats by different tools.

For instance, a definition of the form \renewcommand\mycommand{...} within a configuration file provided for the following LaTeX source.

\documentclass{...}
\newcommand\mycommand{...}
\begin{document}
Use \mycommand{...}
\end{document}

## Creating Private Command Lines

A htlatex-like script foolatex.bat can be obtained from the compilation under LaTeX of a file similar to the following one.

\def\script{bat}
\input mkht.4ht
\one{,html,next,3}
\two{-ic:\tex4ht\texmf\tex4ht\ht-fonts\#1
-ic:\tex4ht\texmf\tex4ht\ht-fonts\symbol\!}
\three{#1 -dc:\my\dir}
\make{foo}
\end{document}

A call of the form

foolatex filename

is then equivalent to a call of the following form.

htlatex filename "html,next,3" "symbol/!" "-dc:\my\dir"

Scripts obtained in such a manner can embed parameters within their bodies instead of expecting the parameters to be provided in command lines.

Details regarding the available options can be found by compiling under LaTeX a file of the following form.

\input mkht.4ht \end{document}

The compilation requires the ProTex.sty and AlProTex.sty files available at http://www.cse.ohio-state.edu/~gurari/systems.html.

## An Insight into the Commands

Given a LaTeX file

\documentclass{article}
\begin{document}
..................
\end{document}

the ‘htlatex filename’ command produces a call ‘latex filename’ to LaTeX on an implicit file of the following form.

\documentclass{article}
\usepackage{tex4ht}
\begin{document}
..................
\end{document}

Similarly, the command ‘htlatex filename "options"’ produces a call to a ‘latex filename’ command on an implicit file of the following form.

\documentclass{article}
\usepackage[options]{tex4ht}
\begin{document}
..................
\end{document}
The command ‘ht latex filename ’ may be used, instead of the ‘htlatex filename "options"’ command, in cases that the \usepackage instruction is explicitly introduced into the source files.

## A Deeper Insight

From the perspective of TeX4ht, the htlatex-like commands, and the \usepackage, are indirect approaches for getting LaTeX files of the following form. Such files can be explicitly provided for compilations requested through the ‘ht latex filename’ command.

\documentclass{article}
.....
\input tex4ht.sty
.....
\Preamble{options}
.....
\begin{document}
.....
\EndPreamble
..................
\end{document}

## TeX, ConTeXt, and TeXi

Commands similar to those offered for LaTeX are also offered for TeX (dbmtex, dbtex, ht, httex, mztex, ootex, t4ht, teimtex, teitex, tex4ht, xhmtex, xhtex) and TeXi (dbmtexi, dbtexi, httexi, mztexi, ootexi, teimtexi, teitexi, xhmtexi, xhtexi). In the case of TeX, the fragment of code ‘\csname tex4ht\endcsname’ should be introduced by the user into the source file, after the preamble of the file where the document definitions reside (example). In the case of TeXi, such a code fragment is introduced implicitly.

The private configuration files are similar to those of LaTeX, with the instruction ‘\begin{document}’ excluded.

...
\Preamble{options}
...
\begin{document}
...
\EndPreamble
...
The ‘ht tex filename ’ and ‘ht texi filename ’ commands may apply for TeX and TeXi sources that embed such code fragments in their body. The embeded code should replace the ‘\csname tex4ht\endcsname’ fragment in TeX sources, be palces at the strat of the files in TeXi sources, and not include the \begin{document} instruction.

For ConTeXt similar instructions apply with suffixes ‘context’ instead of ‘latex’, ‘tex’, or ‘texi’. For instance, ‘htcontext’ .

## Other Options

• XeTeX files can be compiled with htlatex-like instructions (e.g., htxelatex, htxetex, mzxelatex). Currently only partial support is provided and only TeX-based fonts are handled.
• A jsMath mode of output may be requested with instructions similar to the following one.
htlatex file "xhtml,jsmath" " -cmozhtf"

• The dvipng utility might be activated for bitmap constructions through a request ‘-cdvipng’ in the third options list. For instance,
htlatex file "" "" "-cdvipng"

This utility is reported to produce fast high quality output with much smaller files than other convertors.

• TeX4ht offers also speech output formats.

## Validation

The outcome of the translations should be checked by validators for proper syntax. Typically, with the presence of validators, errors are easy to detect and correct, but they require human intervention.

TeX4ht doesn’t offer a built-in parser to verify the correctness of the outcome. However, external validator(s) can quite easily be integrated into the compilation process.

## Recommendations

To keep with the spirit of LaTeX and hypertext, in which style is assumed to be separated from content, the users are encouraged to avoid inserting TeX4ht code into their source files. Instead, they should place their modifications, to the default settings, within private configuration files to be loaded by htlatex-like commands.

On the other hand, it should be noted that hypertext markings should adhere to strict rules specified by different standards. Consequently, it is strongly advised to check the output obtained from the default configurations, before trying to tailor new ones.


text:
We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Physics

# Staff profile

## Publication details for Professor Ian Smail

Khostovan, A.A., Sobral, D., Mobasher, B., Best, P.N., Smail, I., Matthee, J., Darvish, B., Nayyeri, H., Hemmati, S. & Stott, J.P. (2018). The clustering of H $\beta$ + [O III] and [O II] emitters since z \tilde 5: dependencies with line luminosity and stellar mass. Monthly Notices of the Royal Astronomical Society 478(3): 2999-3015.

### Abstract

We investigate the clustering properties of ∼7000 H β + [O III] and [O II] narrowband-selected emitters at z ∼ 0.8–4.7 from the High-z Emission Line Survey. We find clustering lengths, r0, of 1.5–4.0 h−1 Mpc and minimum dark matter halo masses of 1010.7–12.1 M⊙ for our z = 0.8–3.2 H β + [O III] emitters and r0 ∼ 2.0–8.3 h−1 Mpc and halo masses of 1011.5–12.6 M⊙ for our z = 1.5–4.7 [O II] emitters. We find r0 to strongly increase both with increasing line luminosity and redshift. By taking into account the evolution of the characteristic line luminosity, L⋆(z), and using our model predictions of halo mass given r0, we find a strong, redshift-independent increasing trend between L/L⋆(z) and minimum halo mass. The faintest H β + [O III] emitters are found to reside in 109.5 M⊙ haloes and the brightest emitters in 1013.0 M⊙ haloes. For [O II] emitters, the faintest emitters are found in 1010.5 M⊙ haloes and the brightest emitters in 1012.6 M⊙ haloes. A redshift-independent stellar mass dependency is also observed where the halo mass increases from 1011 to 1012.5 M⊙ for stellar masses of 108.5 to 1011.5 M⊙, respectively. We investigate the interdependencies of these trends by repeating our analysis in a Lline−Mstar grid space for our most populated samples (H β + [O III] z = 0.84 and [O II] z = 1.47) and find that the line luminosity dependency is stronger than the stellar mass dependency on halo mass. For L > L⋆ emitters at all epochs, we find a relatively flat trend with halo masses of 1012.5–13 M⊙, which may be due to quenching mechanisms in massive haloes that is consistent with a transitional halo mass predicted by models.


text:
# Math

how would i express the following fraction with a single denominator

e-4/5 +1

1. 👍
2. 👎
3. 👁
1. e-4/5 +1
5e/5 - 4/5 + 5/5
= (5e+1)/5

1. 👍
2. 👎

## Similar Questions

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text:
106

How do I make a user's browser blink/flash/highlight in the task bar using JavaScript? For example, if I make an AJAX request every 10 seconds to see if the user has any new messages on the server, I want the user to know it right away, even if he is using another application at the time.

Edit: These users do want to be distracted when a new message arrives.

This question is tagged with javascript browser

86

this won't make the taskbar button flash in changing colours, but the title will blink on and off until they move the mouse. This should work cross platform, and even if they just have it in a different tab.

newExcitingAlerts = (function () {
var oldTitle = document.title;
var msg = "New!";
var timeoutId;
var blink = function() { document.title = document.title == msg ? ' ' : msg; };
var clear = function() {
clearInterval(timeoutId);
document.title = oldTitle;
window.onmousemove = null;
timeoutId = null;
};
return function () {
if (!timeoutId) {
window.onmousemove = clear;
}
};
}());

Update: You may want to look at using HTML5 notifications.

55

I've made a jQuery plugin for the purpose of blinking notification messages in the browser title bar. You can specify different options like blinking interval, duration, if the blinking should stop when the window/tab gets focused, etc. The plugin works in Firefox, Chrome, Safari, IE6, IE7 and IE8.

Here is an example on how to use it:

\$.titleAlert("New mail!", {
requireBlur:true,
stopOnFocus:true,
interval:600
});

If you're not using jQuery, you might still want to look at the source code (there are a few quirky bugs and edge cases that you need to work around when doing title blinking if you want to fully support all major browsers).

6

My "user interface" response is: Are you sure your users want their browsers flashing, or do you think that's what they want? If I were the one using your software, I know I'd be annoyed if these alerts happened very often and got in my way.

If you're sure you want to do it this way, use a javascript alert box. That's what Google Calendar does for event reminders, and they probably put some thought into it.

A web page really isn't the best medium for need-to-know alerts. If you're designing something along the lines of "ZOMG, the servers are down!" alerts, automated e-mails or SMS messages to the right people might do the trick.

6

Supposedly you can do this on windows with the growl for windows javascript API:

Your users will have to install growl though.

Eventually this is going to be part of google gears, in the form of the NotificationAPI:

So I would recommend using the growl approach for now, falling back to window title updates if possible, and already engineering in attempts to use the Gears Notification API, for when it eventually becomes available.

6

                var oldTitle = document.title;
var msg = "New Popup!";
var timeoutId = false;

document.title = document.title == msg ? oldTitle : msg;//Modify Title in case a popup

if(document.hasFocus())//Stop blinking and restore the Application Title
{
document.title = oldTitle;
clearInterval(timeoutId);
}
};

if (!timeoutId) {

3

Why not take the approach that GMail uses and show the number of messages in the page title?

Sometimes users don't want to be distracted when a new message arrives.

3

The only way I can think of doing this is by doing something like alert('you have a new message') when the message is received. This will flash the taskbar if the window is minimized, but it will also open a dialog box, which you may not want.

2

You may want to try window.focus() - but it may be annoying if the screen switches around

1

you could change the title of the web page with each new message to alert the user. I did this for a browser chat client and most users thought it worked well enough.

document.title = "[user] hello world";

1

AFAIK, there is no good way to do this with consistency. I was writing an IE only web-based IM client. We ended up using window.focus(), which works most of the time. Sometimes it will actually cause the window to steal focus from the foreground app, which can be really annoying.

0

These users do want to be distracted when a new message arrives.

It sounds like you're writing an app for an internal company project.

You might want to investigate writing a small windows app in .net which adds a notify icon and can then do fancy popups or balloon popups or whatever, when they get new messages.

This isn't overly hard and I'm sure if you ask SO 'how do I show a tray icon' and 'how do I do pop up notifications' you'll get some great answers :-)

For the record, I'm pretty sure that (other than using an alert/prompt dialog box) you can't flash the taskbar in JS, as this is heavily windows specific, and JS really doesn't work like that. You may be able to use some IE-specific windows activex controls, but then you inflict IE upon your poor users. Don't do that :-(

0

function blinkTab() {
const browserTitle = document.title;
let timeoutId;
let message = 'My New Title';

const stopBlinking = () => {
document.title = browserTitle;
clearInterval(timeoutId);
};

const startBlinking = () => {
document.title = document.title  === message ? browserTitle : message;
};

function registerEvents() {
});

});
};

registerEvents();
};

via Javascript


text:
# Propensity score matching after imputation in R with mice

9I have a dataset (500 rows) with missing values in different variables for a propensity score analysis. First I created the propensity score matching by omitting the rows with missing values (about 100 rows) in the variables I used for propensity score calculation, but now I would like to try to impute the missing values with the mice package.

In a first step I imputed the data like this:

impute <- mice(mydata, method =
methods, predictorMatrix =
predictormatrix, m = 5, maxit =
3)
mydata <- complete(impute)

So - as far as I understand - "mydata" now is a new data frame with the imputed values, but it is the first out of 5 different attempts of imputation (because the first attempt is used by default).

Now, as "mydata" is a data frame, I have my "full" data available and can continue with my propensity score matching code:

# matching
match <- matchit(treatment ~ independent1 + independet2 + independent3, data = mydata, method = "nearest")
matched_data <- match.data(match)

# model for outcome by treatment
model <- glm(outcome ~ treatment, data = matched_data, family = binomial(link = "logit"))
publish(model)

So this obviously works if I'm fine with using only the first out of 5 possible imputed datasets (as far as I now "complete" uses the first dataset by default).

Now my question is: I read about the "pool" function, but it seems that in the end I need a regression formula (like seen here https://rdrr.io/cran/mice/man/pool.html at the end of the page > "Example"). My favorite result of the imputed data would be a completed dataset with the same number of rows as before the imputation process (5oo rows) but with imputed values (by all 5 datasets) instead of NAs.

For example:

final_imputed_data <- complete(impute) # don't use the first imputed dataset (out of 5) but all 5

Or do I misunderstand the sense of multiple imputation?

• Is the end goal of this analysis to estimate the propensity scores, or are you going to use the propensity scores as one step in a further analysis? Sep 13, 2021 at 13:05
• After propensity score matching I would like to do further analyses with the matched dataset... Sep 13, 2021 at 13:47

To do multiple imputation with propensity score matching, you should use the MatchThem package, which was designed specifically for this purpose. You need to do the following steps:

1. Multiply impute the data, creating M (e.g., 5) separate datasets with the missing values filled in by estimates of the missing values. mice does this and stores the output in a mids object (which you have called impute). You should use way more than 5 (e.g., 50) imputations, as more is always better.
2. Estimate propensity scores within each imputed dataset and then perform the matching within each imputed dataset. MatchThem does this using the matchthem() function, which uses the same sytnax as matchit() but takes in a mids object instead of a data frame.
3. Assess balance on the matched multiply imputed data. The cobalt package works with matchthem objects (called mimids objects) to assess balance across and within imputed datasets.
4. If balance is achieved, estimate the effect within the imputed datasets. The MatchThem functions with() and pool() (which work similarly to the corresponding functions in mice) do this, correctly incorporating the weights, matching structure, and correction for multiple imputation.

All this is described in the MatchThem paper and documentation. Remember that propensity score matching and multiple imputation are advanced statistical techniques and should only be used by someone with advanced statistical training using these methods.

• What about the problem made you want to use propensity scores? And why use a matching algorithm that discards valid data? Sep 13, 2021 at 13:48
• Hi Noah, thank you for your answer! I read the MatchThem paper you linked here, but I've still got the question, if there is a possibility, to get back a data frame after multiple imputation for further analyses similar to the match.data function, which gives back a full data frame after using matchit(). Sep 14, 2021 at 13:46
• Use the complete() function in MatchThem.
– Noah
Sep 14, 2021 at 14:33
• Hi Noah, thank you again for your response. Could you maybe help me with a code snippet, how to create a "cross section dataset"? If I use complete() with default parameters the FIRST dataset of the 5 will be selected. Is there a way to create a cross section of the different datasets? Does that make sense? Sep 14, 2021 at 18:46
• I mean, I have 5 different datasets - how do I decide, which of them to use for my subsequent analyses? Sep 14, 2021 at 18:53


text:
# Awards

## Awards of Excellence

The Faculty awards Term Distinction to officially recognize students who have attained a high degree of academic excellence.

To be awarded Term Distinction, students must:

• Have at least one alpha/numeric grade in the average.
• Have a minimum term overall average of 80% or higher.
• Have a academic standing for the term of Promoted, Satisfactory, Good, or Excellent.
• Have no marks of incomplete course work (INC), course in progress (IP), missing mark (MM), or under review (UR) or failing grades in the term under consideration for the term Distinction List. When these grades are resolved to alpha/numeric grades, the term’s average will be reviewed for eligibility.

To graduate with Distinction, students must graduate with a cumulative overall average of 80% or higher. To graduate with Dean's Honours, students must graduate with a cumulative overall average of 85% or higher. Students who qualify for both distincitions will graduate with the higher distinction.

## Alumni Gold Medal

An Alumni Gold Medal is presented annually at the spring convocation in recognition of academic excellence of the top graduates from the Faculty of Environment. The award recipient is chosen by the Dean and Associate Dean of Undergraduate Studies based on scholastic achievement.

## Departmental awards for Distinguished Academic Achievement

Awards for Distinguished Academic Achievement are presented annually at spring convocation in recognition of academic excellence of the top graduating student from each academic plan. The award recipient is chosen by the Undergraduate Officer based on scholastic achievement. Normally, these students are considered for, of which one is selected, as the recipient of the Alumni Gold Medal.

## Jack Rosen Memorial Award for Environmental Innovation

This award is presented to the winner of the annual Jack Rosen pitch competition. Students submit ideas for products and services that could help prevent, mitigate, or solve a pressing environmental problem. 10 are selected to pitch their idea to a panel of judges in a competition for the grand prize of $2,000. Up to two additional honourable mention awards of$500 each may be awarded based on merit.


text:
# Glacier flowlines¶

## Centerlines¶

Computing the centerlines is the first task to run after the definition of the local map and topography.

Our algorithm is an implementation of the procedure described by Kienholz et al., (2014). Appart from some minor changes (mostly the choice of certain parameters), we stayed close to the original algorithm.

The basic idea is to find the terminus of the glacier (its lowest point) and a series of flowline “heads” (local elevation maxima). The centerlines are then computed with a least cost routing algorithm minimizing both (i) the total elevation gain and (ii) the distance from the glacier outline:

In [1]: graphics.plot_centerlines(gdir)

The glacier has a major centerline (the longest one), and tributary branches (in this case: two).

At this stage, the centerlines are still not fully suitable for modelling. Therefore, a rather simple procedure converts them to “flowlines”, which now have a regular coordinate spacing (which they will keep for the rest of the workflow). The tail of the tributaries are cut according to a distance threshold rule:

In [2]: graphics.plot_centerlines(gdir, use_flowlines=True)

## Downstream lines¶

For the glacier to be able to grow we need to determine the flowlines downstream of the current glacier geometry:

In [3]: graphics.plot_centerlines(gdir, use_flowlines=True, add_downstream=True)

The downsteam lines area also computed using a routing algorithm minimizing the distance between the glacier terminus and the border of the map as well as the total elevation gain, therefore following the valley floor.

## Catchment areas¶

Each flowline has its own “catchment area”. These areas are computed using similar flow routing methods as the one used for determining the flowlines. Their purpose is to attribute each glacier pixel to the right tributory in order to compute mass gain and loss for each tributary. This will also influence the later computation of the glacier widths).

In [4]: tasks.catchment_area(gdir)

In [5]: graphics.plot_catchment_areas(gdir)

## Flowline widths¶

Finally, the flowline widths are computed in two steps.

First, we compute the geometrical width at each grid point. The width is drawn from the intersection of a line perpendicular to the flowline and either (i) the glacier outlines or (ii) the catchment boundaries:

In [6]: tasks.catchment_width_geom(gdir)

In [7]: graphics.plot_catchment_width(gdir)

Then, these geometrical widths are corrected so that the altitude-area distribution of the “flowline-glacier” is as close as possible as the actual distribution of the glacier using its full 2D geometry:

In [8]: tasks.catchment_width_correction(gdir)

In [9]: graphics.plot_catchment_width(gdir, corrected=True)

Note that a perfect match is not possible since the sample size is not the same between the “1.5D” and the 2D representation of the glacier.

## Implementation details¶

Shared setup for these examples:

import geopandas as gpd
import oggm
from oggm.utils import get_demo_file, gettempdir

cfg.initialize()
cfg.set_intersects_db(get_demo_file('rgi_intersect_oetztal.shp'))
cfg.PATHS['dem_file'] = get_demo_file('hef_srtm.tif')

base_dir = gettempdir('Flowlines_Docs')


text:
# Minimize the standard deviation of the total values of groups of items (optimization?) in r

I am a total novice, but I think what I'm looking for is help with an optimization problem.

I have a set of about 26 items, each with a certain value. I want to distribute these items into 8 groups as equally as possible, having granted that a perfectly equal distribution is not possible because of the individual item values. I think, one way of measuring how equally the items have been divided into groups is by taking the standard deviation of the sums of the values of the items in each group.

Is there a package in R that could help me to minimize the standard deviation of these sums by altering the allotment of items to groups?

FWIW, this is an 'estate division' problem, in which each item has a known value, and no bidding/auctioning can take place.

• I think this is a purely mathematical (optimization) problem rather than a statistical one and as such probably belongs on math.SE rather than here. If you can make it statistical (see th coverage of stats.SE in the FAQ), then it might fit here. If you'd like it moved, you can flag it and a moderator will shift it for you. – Glen_b -Reinstate Monica Feb 18 '13 at 23:54
• (But please don't cross-post) – Glen_b -Reinstate Monica Feb 19 '13 at 0:05
• Do you mean numerically equally as possible, or both numerically and in terms of the number of items? I ask because if the number of items in each group is bounded only between 1 and 19 it seems like the space in which to optimize is kind of huge. – russellpierce Feb 19 '13 at 1:04
• I don't know Glen_b, it seems like just in the identification of the number of possible states (excluding groups that are essentially aliases for each other) which is a sort of precursor to developing an optimization methods is itself a relatively complex problem worthy of CV consideration. – russellpierce Feb 19 '13 at 1:06
• @drnexus thanks for your comment. i mean in terms of 'weights' or 'item values', not in terms of the number of items. so, in the optimal solution, group 1 could have just one item of sufficient value, while the other 7 groups each have, say, 3. – dubhousing Feb 19 '13 at 14:39

There are a variety of measures of evenness of the sums (group-values). For example, one alternative is to try to minimize the difference between the biggest and smallest sum.

Minimizing the standard deviation is the same as minimizing the variance.

However, the mean of the sums is fixed, so minimizing the variance is the same as minimizing the sum of squares of the group-values.

This is getting a bit closer to a 'standard' optimization problem.

It's somewhat related to the Job-shop scheduling problem and a number of other problems.

There are various job-scheduling programs, some of which might be able to work on your problem, but they usually tend to focus on minimizing the maximum completion time (that would correspond to minimizing the largest set, which may not give you a good solution).

From a quick glance it looks like the partitions package in R can generate partitions for you - but unfortunately the number of possible partitions is going to be huge in your case, so you may have to settle for some approximate algorithm (in a similar fashion to some of the bin-packing problems, for example). [Approximate algorithms can often generate very good solutions.]

There may be some value in this:

but it does seem to look mostly at bidding-solutions.

If you have a mixed problem (that is, one which includes divisible assets like cash), your job should be easier.

There might be something to be said for starting with some reasonable solution and using say tabu-search or simulated annealing or something to try to improve it.

If this is a one-off problem can you post the some numbers proportional to the values (it won't affect anything to multiply them by some arbitrary constant like 1.375) - it might help to have something concrete to think about.

• x <- restrictedparts(26,8,include.zero=FALSE) #gives 288 possible item counts for partitioning groups... then there is also the valid permutations of assigning actual assets to the 1:26 ordering... so, there are... a lot of possible allocations. Not very promising. – russellpierce Feb 19 '13 at 1:27
• @drknexus Yes, I calculated a very weak lower bound on the problem size ...and went 'Ack!' -- without some really good way to cut things down, it looks like a pretty large problem. With additional details of the specifics (e.g. if some items will clearly be by themselves or can only be paired with a couple of things), enough of the solution might be "obvious" that the remaining search space is cut way down. – Glen_b -Reinstate Monica Feb 19 '13 at 1:53
• The most obvious constraint is the largest single item. One group will have to be of at least that value. That should cut down a lot of the parameter space as no group can have a combination of items that is substantially less than the value of that single item. – russellpierce Feb 19 '13 at 3:34
• Notably a sum of squares optimization may yield different results than a sum of absolute deviations optimization. It isn't clear that SS is better that abs dev in this context. We could probably toss a lot of options based on individual means being a certain distance from the optimal grand mean of the value of 26 items divided by 8... but testing that condition alone would be time consuming. – russellpierce Feb 19 '13 at 3:49
• @Glen_b Indeed, it is a one-off problem. My grandmother passed away and left behind a lot of valuable jewelry. I will post proportional values later on. – dubhousing Feb 19 '13 at 14:52

This is known as the 'partition problem' and is preferably solved by a dynamic programming approach. You can read about it in Chapter 8.5 of "The Algorithm Design Manual" by Steven Skiena. And you can find an R implementation for minimizing the variance in the thread "optimization challenge" of R-help in January 2010.

EDIT: I'm sorry, I somehow misread the task, assuming the sequence of values would play a role. As a kind of compensation I will show how I would solve this as a multiple knapsack problem, reducing knapsack capacities until no solution is found.

library(adagio)                     # contains a multiple knapsack solver
set.seed(7531)
w <- sample(1:100, 26)              # 26 items used as weights (integers)
p <- rep(1, 26)                     # with equal profits all

t <- 200; k <- rep(t, 8)            # 8 knapsacks with equal capacities
sol <- mknapsack(p, w, k, bck = 1)  # starting with capacity 200
while (all(sol$ksack > 0)) { # diminish capacity until not all t <- t-1; k <- rep(t, 8) # items can be packed Sol <- sol # keep the last feasible solution sol <- mknapsack(p, w, k, bck = -1) } # will take a few seconds to minutes y <- numeric(8) # find weight in each knapsack for (i in 1:8) y[i] <- sum(w[Sol$ksack == i])
y                                   # 161 161 160 161 161 161 159 161

This will not in all cases lead to a solution of smallest variance, but come very close to it.

I would argue that one solution (I cannot prove it is optimal) for such a problem is arranging the items from smallest to largest and then going from there. In such an arrangement the items next to each other will always give the least possible contribution to the overall SD.

I had a similar problem and solved it this way. I did however have the benefit of a constant group size. The method for your problem would still have to evaluate all the possible groups..


text:
$$\require{cancel}$$

# Q1

In the 1925 Michelson-Gale-Pearson experiment, the physicists measured the Sagnac eﬀect due to the earth’s rotation. They laid out a rectangle of sewer pipes with length $$x = 613\: m$$ and width $$y = 339\: m$$, and pumped out the air. The latitude of the site in Illinois was $$41^{\circ}46'$$, so that the eﬀective area was equal to the projection of the rectangle into the plane perpendicular to the earth’s axis. Light was provided by a sodium discharge with $$λ = 570\: nm$$. The light was sent in both directions around the rectangle and interfered, eﬀectively doubling the area. Clever techniques were required in order to calibrate the apparatus, since it was not possible to change its orientation. Calculate the number of wavelengths by which the relative phase of the two beams was expected to shift due to the Sagnac eﬀect, and compare with the experimentally measured result of $$0.230±0.005$$ cycles.

# Q2

The relativistic heavy ion collider RHIC collides counter-rotating beams of gold nuclei at $$9\: \text{GeV/nucleon}$$. If a gold nucleus is approximately a sphere with radius $$6×10^{-15}\: m$$, ﬁnd the maximum angular momentum, in units of $$\hbar$$, about the center of mass for a sideswiping collision. Answer: $$∼ 10^5$$.

# Q3

Show, as claimed section 8.2, that the time-space components of the tensor $$^\star L$$ equal the angular momentum three-vector.


text:
This is problem 23 in Serway physics 7th edition. I can'tfigure out how to solve for the currents in the equations that aregiven on the homework solutions forum. I will rate lifesaver butonly if it shows exactly how to solve the equation for all threecurrents.
Using Kirchhoff's rules (and given 1 =70.0 V, 2 =61.8 V, 3 =79.2 V) calculate the following.

Figure P18.23

(a) Find the current in each resistor shown inFigure P18.23.
 IR1 = mA IR2 = mA IR3 = mA
(b) Find the potential difference between points c andf.
cf = V
Whichpoint is at the higher potential?