Projection on a plane using a 2*3 matrix

Posted by leipäjuusto on Stack Overflow See other posts from Stack Overflow or by leipäjuusto
Published on 2010-05-21T09:31:45Z Indexed on 2010/05/21 10:00 UTC
Read the original article Hit count: 229

Filed under:

projection

|

matrix

|

plane

|

3d

|

2d

Hello,

I can easily draw the projection of a 3D set of points onto the plane with normal vector (1,1,1), by using the matrix

    (-sqrt(3)/2   sqrt(3)/2   0)
    (-1/2         -1/2        1).

I want to do the same thing, but for a projection onto an arbitrary plane with normal vector (a,b,c) instead of (1,1,1). How to find the matrix?

Thanks in advance!

© Stack Overflow or respective owner

Related posts about projection

Vertex buffer acting strange? [on hold]

as seen on Game Development - Search for 'Game Development'
I'm having a strange problem, and I don't know what could be causing it. My current code is identical to how I've done this before. I'm trying to render a rectangle using VBO and orthographic projection. My results: What I expect: 3x3 rectangle in the top left corner #include <stdio… >>> More
Plane projection and scale causing bluring in silverlight

as seen on Stack Overflow - Search for 'Stack Overflow'
Ok, So I've tried to make an application which relies on images being scaled by an individual factor. These images are then able to be turned over, but the use of an animation working on the ProjectionPlane rotation. The problem comes around when an image is both scaled and rotated. For some reason… >>> More
Map tiling - What kind of projection?

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi. I've taken a large image and divided it in to square tiles (256x256). It is made for google maps also, so the whole image is divided into z_x_y.png (Depending on zoom level). z=0 = 1x1 tile z=1 = 2x2 tilesthe z=2 = 4x4 tiles My imageMap is "flat" and is not based on a sphere like the worldmap… >>> More
Projector Review: HP Notebook Projection Companion

as seen on Internet.com - Search for 'Internet.com'
Got PowerPoints? HP's under-one-pound, palm-sized projector is a computer peripheral that stands out in a crowd, or a conference room. >>> More
Camera for 2.5D Game

as seen on Game Development - Search for 'Game Development'
I'm hoping someone can explain this to me like I'm 5, because I've been struggling with this for hours and simply cannot understand what I'm doing wrong. I've written a Camera class for my 2.5D game. The intention is to support world and screen spaces like this: The camera is the black thing on… >>> More

Related posts about matrix

Find the "largest" dense sub matrix in a large sparse matrix

as seen on Stack Overflow - Search for 'Stack Overflow'
Given a large sparse matrix (say 10k+ by 1M+) I need to find a subset, not necessarily continuous, of the rows and columns that form a dense matrix (all non-zero elements). I want this sub matrix to be as large as possible (not the largest sum, but the largest number of elements) within some aspect… >>> More
How does a template class inherit another template class?

as seen on Stack Overflow - Search for 'Stack Overflow'
I have a "SquareMatrix" template class which inherits "Matrix" template class, like below: SquareMatrix.h: #ifndef SQUAREMATRIX_H #define SQUAREMATRIX_H #include "Matrix.h" template <class T> class SquareMatrix : public Matrix<T> { public: T GetDeterminant(); }; template… >>> More
iPhone OpenGL ES: How do I use gravity vector to correctly transform scene for augmented reality

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying figure out how to get an OpenGL specified object to be displayed correctly according to the device orientation (ie. according to the gravity vector from the accelerometer, and heading from compass). The GLGravity sample project has an example which is almost like this (despite ignoring… >>> More
How do I use the gravity vector to correctly transform scene for augmented reality?

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying figure out how to get an OpenGL specified object to be displayed correctly according to the device orientation (ie. according to the gravity vector from the accelerometer, and heading from compass). The GLGravity sample project has an example which is almost like this (despite ignoring… >>> More
C++ templates - matrix class

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi I'm learning templates in C++ so I decied to write matrix class which would be a template class. In Matrix.h file I wrote #pragma once #include "stdafx.h" #include <vector> using namespace std; template<class T> class Matrix { public: Matrix(); ~Matrix(); GetDataVector(); … >>> More