Question

I am trying to design an asic graphics processor. I have done extensive research on the topic but I am still kind of fuzzy on how to translate and rotate points. I am using orthographic projection to rasterize the transformed points.

I have been using the following lecture regarding the matrix multiplication (homogenous coordinates)
http://www.cs.kent.edu/~zhao/gpu/lectures/Transformation.pdf

Could someone please explain this a little more in depth to me. I am still somewhat shakey on the algorithm. I am passing a camera (x,y,z) and a camera vector (x,y,z) representing the camera angle, along with a point (x,y,z). What should go where within the matrices to transform the point to the new appropriate location?

Answer 1

Here’s the complete transformation algorithm in pseudocode:

void project(Vec3d objPos, Matrix4d modelViewMatrix,
    Matrix4d projMatrix, Rect viewport, Vec3d& winCoords)
{
    Vec4d in(objPos.x, objPos.y, objPos.z, 1.0);
    in = projMatrix * modelViewMatrix * in;
    in /= in.w; // perspective division
    // "in" is now in normalized device coordinates, which are in the range [-1, 1].

    // Map coordinates to range [0, 1]
    in.x = in.x / 2 + 0.5;    
    in.y = in.y / 2 + 0.5;    
    in.z = in.z / 2 + 0.5;    

    // Map to viewport
    winCoords.x = in.x * viewport.w + viewport.x;    
    winCoords.y = in.y * viewport.h + viewport.y;    
    winCoords.z = in.z;    
}

Then rasterize using winCoords.x and winCoords.y.

For an explanation of the stages of this algorithm, see question 9.011 from the OpenGL FAQ.