Projection Matrix

In the previous article, we discussed the camera transformation which maps a vertex from world space into the camera space. Recall that the camera spans a orthonormal coordinate system with the three vectors \(\vec{u}\), \(\vec{v}\) and \(\vec{w}\), where \(-\vec{w}\) points along the viewing direction. In this section we will deal with the projection of the 3D vertex in camera space into a 2D view plane. In OpenGL, what follows is clipping and mapping to so-called normalized device coordinates which are tightly coupled into the construction of projection matrix. In fact, the pure mathematical construction of the projection matrix is easy. What makes it difficult is the clipping part. (more…)

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