Abstract: From the point of view of geometry, a view frustum culling geometric algorithm is
designed based on projective theory in descriptive geometry. The basic idea is that a proper
computational coordinate system is built, where the space position relation of the view frustum and a
line segment is transformed into the plane position relation of a trapezoid and the line segment by
simple orthographic projection. This geometric dimension reduction method is beneficial to solve
space geometric singular issue. A test sample is designed which includes all kinds of typical position
relations of the view frustum and the line segment to comprehensively evaluate algorithm’s speed and
stability. And especially, there are 78 kinds of geometric singular relations. At last, our view frustum
culling geometric algorithm, classical Liang-Barsky algorithm and a basic algorithm to solvethe
problem of intersection with 6 planes have been implemented on Visual C++ with C program. On the
basement of qualitative analysis, these 3 algorithms have been tested on speed and stability.

Key words: view frustum culling, geometric algorithm, projection theory, geometric singular