projective geometry: how do I turn a projection of a rectangle in 3D into a 2D view

Posted by bonomo on Programmers See other posts from Programmers or by bonomo
Published on 2012-11-10T18:11:17Z Indexed on 2012/11/10 23:16 UTC
Read the original article Hit count: 214

Filed under:

3d

|

geometry

So the problem is that I have a 3D projection of a rectangle that I want to turn into 2D. That is I have a photo of a sheet of paper laying on a table which I want to transform into a 2D view of that sheet. So what I need is to get an undistorted 2D image by reverting all the 3D/projection transformations and getting a plain view of the sheet from the top. I happened to find some directions on the subject but they don't suggest an immediate instruction on how this can be achieved. It would be really helpful to get a step-by-step instruction of what needs to be done. Or, alternatively, a link on a resource that breaks it down to little details.

Thank you

© Programmers or respective owner

Related posts about 3d

How to convert videos to 3D format so that I can watch them with 3D glasses

as seen on Super User - Search for 'Super User'
Are there any softwares to convert 2D videos to 3D (preferably XviD avi) so that I can watch them with 3D glasses? No matter if it's freeware or shareware. >>> More
In Email, Image (img) Source (src) Tags are rewritten as relative links. How to fix?

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm working on sending out an html based email, and every time it sends the image src tags and some of the anchor href tags are modified to be relative url's. Update 2: This is happening between when the body of the email is generated and sent and when it arrives in my inbox. Update: I am using… >>> More
WPF 3D - Need help writing conversion methods between 2D and 3D (Point3DToPoint and PointAndZToPoint

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm new to WPF 3D, so I may just be missing something obvious, but how do I convert from 3D to 2D and (for a given z location) from 2D to 3D? Specifically, I need two conversion methods: Point3DToPoint - If I have an (x, y, z) coordinate in the 3D world, how do I determine the (x, y) coordinate… >>> More
3D point on 3D mesh surface

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi All, How can I get a 3D point on 3D mesh surface made up triangulars ? The 3D point may be anywhere on the 3D surface. Thanks. M.Ken >>> More
Matlab 3d volume visualization and 3d overlay

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi, so the question ist pretty much the title. I have a 3d volume loaded as raw data [256, 256, 256] = size(A). It contains only values of zero's and ones, where the 1's represent the structure and 0's the "air". I want to visualize the structure in matlab and then run an algorithm on it and put… >>> More

Related posts about geometry

GLSL check if fragment is on geometry

as seen on Stack Overflow - Search for 'Stack Overflow'
I am currently writing the positions of my geometry to the RGB channels of gl_FragColor and I would like to write 1.0 to the alpha channel if the fragment is part of geometry, and 0.0 if its empty. Is there a simple way to tell if a fragment is geometry or not? Maybe through gl_FragCoord.z? thanks >>> More
In JTS, when I do geometry.buffer(1).buffer(-1), will the resulting geometry be equivalent to the or

as seen on Stack Overflow - Search for 'Stack Overflow'
I was having problems while intersecting two geometries, getting a TopologyException probably due to a rounding error during the operation, then I read this fix and tried a buffer(0) on both input geometries, but still without success. Then I tried geo.buffer(1).buffer(-1) and it worked. Will these… >>> More
Multiple mesh with one geometry and diferent textures. Error

as seen on Stack Overflow - Search for 'Stack Overflow'
I have a loop where I create a multiple Mesh with different geometry, because each mesh has one texture: .... var geoCube = new THREE.CubeGeometry(voxelSize, voxelSize, voxelSize); var geometry = new THREE.Geometry(); for( var i = 0; i < voxels.length; i++ ){ var voxel = voxels[i]; var object; … >>> More
How to read verbose VC++ linker output

as seen on Stack Overflow - Search for 'Stack Overflow'
Trying to debug some linker errors, I turned on /VERBOSE and I'm trying to make sense of the output. It occurs to me that I really don't know how to read it. For example: 1>Compiling version info 1>Linking... 1>Starting pass 1 1>Processed /DEFAULTLIB:mfc80.lib 1>Processed /DEFAULTLIB:mfcs80… >>> More
Drawing a rectangular prism using opengl

as seen on Game Development - Search for 'Game Development'
I'm trying to learn opengl. I did some code for building a rectangular prism. I don't want to draw back faces so I used glCullFace(GL_BACK), glEnable(GL_CULL_FACE);. But I keep getting back faces also when viewing from front and also sometimes when rotating sides are vanishing. Can someone point me… >>> More