projective-geometry | 易学教程

Creating a Cube-based 3-Dimensional Game

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问题 This question was migrated from Mathematics Stack Exchange because it can be answered on Stack Overflow. Migrated 5 years ago . I am trying to create a 3-dimensional game that is based entirely off of cubes of the exact same size. I wanted to learn how to make my own 3-dimensional game using only 2-dimensional game libraries. Currently, the way I am doing is that I have an array storing the locations of all the centers of each cube in the game. Then, when drawing a single cube, I figure out

Back projecting 3D world point to new view image plane

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问题 EDIT: What I have: camera intrinsics, extrinsic from calibration, 2D image and depth map What I need: 2D virtual view image I am trying to generate a novel view(right view) for Depth Image Based Rendering. Reason for this is that only the left image and depth map are available at the receiver which has to reconstruct the right view (see image). I want to know if these steps will give me the desired result or what I should be doing instead, First, by using Camera Calibration toolbox for MATLAB

Computing a projective transformation to texture an arbitrary quad

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问题 I would like to compute a projective transformation to texture an arbitrary quad in webgl (with three.js and shaders if possible/necessary). This is what I want to obtain, taken from this answer. Everything is well described in the post, so I suppose that with a bit of work I could solve the problem. Here is a pseudo-code of the solution: precompute A matrix (should be trivial since texture coordinates are in [0,1] interval) compute B matrix according to the vertex positions (not possible in

Multiple-View Geometry

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问题 I've two images captured from two cameras of same make placed some distance apart, capturing the same scene. I want to calculate the real world rotation and translation among the two cameras. In order to achieve this, I first extracted the SIFT features of both of the images and matched them. I now have fundamental matrix as well as homography matrix . However unable to proceed further, lots of confusion. Can anybody help me to estimate the rotation and translation in between two cameras? I'm

Computing a matrix which transforms a quadrangle to another quadrangle in 2D

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问题 In the figure below the goal is to compute the homography matrix H which transforms the points a1 a2 a3 a4 to their counterparts b1 b2 b3 b4. That is: [b1 b2 b3 b4] = H * [a1 a2 a3 a4] What way would you suggest to be the best way to calculate H(3x3). a1...b4 are points in 2D which are represented in homogeneous coordinate systems ( that is [a1_x a1_y 1]', ...). EDIT : For these types of problems we use SVD, So i would like to see how this can be simply done in Matlab. EDIT : Here is how I

Multiple-View Geometry

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I've two images captured from two cameras of same make placed some distance apart, capturing the same scene. I want to calculate the real world rotation and translation among the two cameras. In order to achieve this, I first extracted the SIFT features of both of the images and matched them. I now have fundamental matrix as well as homography matrix . However unable to proceed further, lots of confusion. Can anybody help me to estimate the rotation and translation in between two cameras? I'm using OpenCV for feature extraction and matching, homography calculations. Jav_Rock If you have the

Computing a matrix which transforms a quadrangle to another quadrangle in 2D

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In the figure below the goal is to compute the homography matrix H which transforms the points a1 a2 a3 a4 to their counterparts b1 b2 b3 b4. That is: [b1 b2 b3 b4] = H * [a1 a2 a3 a4] What way would you suggest to be the best way to calculate H(3x3). a1...b4 are points in 2D which are represented in homogeneous coordinate systems ( that is [a1_x a1_y 1]', ...). EDIT : For these types of problems we use SVD, So i would like to see how this can be simply done in Matlab. EDIT : Here is how I initially tried to solve it using svd (H=Q/P) in Maltlab. Cosider the following code for the given

Is there an algorithm for solving such projection reconstruction geometric problem?

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We have a grid with red squares on it. Meaning we have an array of 3 squares (with angles == 90 deg) which as we know have same size, lying on the same plane and with same rotation relative to the plane they are lying on, and are not situated on same line on plane. We have a projection of the space which contains the plane with squares. We want to turn our plane projection with squares so that we would see it like it's facing us, in general we need a formula for turning each point of that original plane projection so that it would be facing us like on the image below. What formulas can be used

3D Camera coordinates to world coordinates (change of basis?)

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Suppose I have the coordinates X, Y, Z and orientation Rx, Ry, Rz of an object with respect to a camera. In addition, I have the coordinates U, V, W and orientation Ru, Rv, Rw of this camera in the world. How do I transform the position (location and rotation) of the object to its position in the world? It sounds like a change of basis to me, but I haven't found a clear source yet. In fact you have two basis : one relative to the camera, the other is absolute (the world). So you basically want to transform your relative data into absolute data. Location This is the easiest one. You have to

Extract projective homography from two Kinect depth maps

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Given two consecutive 3D point clouds 1 and 2 (not the whole cloud, say 100 points selected from the cloud with OpenCV's GoodFeaturesToMatch), obtained from a Kinect depthmap, I want to compute camera's homography from 1 to 2. I understand that this a projective transform, and it has already been done by many people: here (slide 12) , here (slide 30) and here in what seems to be the classic paper . My problem is that whilst I'm a competent programmer, I haven't got the math or trig skills to turn one of those methods into code. As this is not an easy problem, I offer a large bounty for the