I've been wanting to know how to do 3d projections.
Can someone explain how i can use this to find the position for x and y on the 2d plane that is 600 * 600 pixels.
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\$\begingroup\$ What do you mean by "get a position for x and y on a screen?" Are you asking how to get a point on the surface of 3D geometry, or how to project 3D geometry into 2D for rendering? \$\endgroup\$– jzxAug 26, 2015 at 6:13
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\$\begingroup\$ In other words, what would be the output you're looking for? A 3D coordinate? A color? Distance from the camera surface (depth)? \$\endgroup\$– jzxAug 26, 2015 at 6:15
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\$\begingroup\$ I meant the 2d plane that the 3d points are going to be projected onto. \$\endgroup\$– FunshineAug 26, 2015 at 16:45
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2 Answers
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Assuming that you want to compute the position that an arbitrary 3D vertex (x,y,z,1) has on the view plane after the projection: You can use the given parameters to compute a projection matrix:
where f = cotangent(fovy * 0.5)
This is also the matrix that will be set by a call to gluPerspective. Then, you can multiply this matrix with your vertex to obtain the projected vertex position.
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\$\begingroup\$ In the vertex matrix would it contain [x,y,z,1] or just [x,y,z]? \$\endgroup\$– FunshineAug 27, 2015 at 15:39
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\$\begingroup\$ Also what is fovy? Is it the distance to the 2d plane? \$\endgroup\$– FunshineAug 27, 2015 at 15:39
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\$\begingroup\$ @Funshine For some mathematical reasons, the vertex must be a 4D point. You can just add "1" as the last component of the 3D point that you already have. And
fovyis the "Field Of View", in Y-direction. Basically "the (vertical) opening angle" of the view frustum. \$\endgroup\$– Marco13Aug 27, 2015 at 15:43 -
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\$\begingroup\$ Would it be (tan^-1(D/(W/2)))*2 where D is the distance to the 2d plane and W is the width? \$\endgroup\$– FunshineAug 27, 2015 at 16:01
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Generally, you have to use a bunch of matrices. With the traditional OpenGL pipeline, you'd have to mutiply these matrices:
finalMatrix = modelMatrix
*
viewMatrix
*
projectionMatrix
*
viewport.windowMatrix;
To find the position of the vertex on your viewport, just multiply the vertex by the matrix:
onViewportVertex = in3dVertex * finalMatrix;
Of course, this implies that no shader modifies the vertex or the pixel.
answered Aug 28, 2015 at 13:25