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Simple Intersection Tests For Games
by miguel gomez []

October 18, 1999 Article Start Previous Page 7 of 7

A Box-Plane Intersection Test

As you can see from Figure 11, a box-plane intersection test only requires checking whether or not n forms a separating axis.

The box and the plane overlap if the condition

is met, where d is the distance from the center of the box to the plane.

Further Reading

Due to time and space, all of the useful intersection tests could not be described here. Some good polygon algorithms are given in [5] and [6]. References [4] and [8] present unique algorithms for generating and manipulating box trees. Bobic and Lander survey the subject of actual collision detection (determining a point of contact and a surface normal) in [2], [6] and [7], which is definitely an expansive, active area of research. If you plan on employing more advanced collision detection algorithms in your games, you should definitely check out all of the references given below.

Soon after receiving his degree in Physics, Miguel Gomez was lucky enough to land a job as a game programmer. Since then he has programmed physics and graphics for PGA Tour Golf ’96, Hyperblade, Microsoft Baseball 3D, and Destruction Derby 64. He is currently perfecting the collision detection and fluid physics for a kayak racing title at Looking Glass Studios in Redmond. Please send questions and comments to


[1] J. Arvo. A simple method for box-sphere intersection testing. In A. Glassner, editor, Graphics Gems, pp. 335-339, Academic Press, Boston, MA, 1990.

[2] N. Bobic. "Advanced Collision Detection Techniques". Game Developer 6(5):32-42, 1999

[3] M. Gomez. "C++ Data Structures for Rigid-Body Physics". Gamasutra, July 2, 1999

[4] S. Gottschalk, M. C. Lin, and D. Manocha. "OBBTree: A Hierarchical Structure for Rapid Interference Detection." In Proc. SIGGRAPH, pp. 171-180, 1996.

[5] M. Held. "ERIT - A Collection of Efficient and Reliable Intersection Tests". Journal of Graphics Tools, 2(4):25-44, 1997.

[6] J. Lander. "Crashing into the New Year". Game Developer 6(1):21-27, 1999

[7] J. Lander. "When Two Hearts Collide". Game Developer 6(2):19-24, 1999

[8] G. Van den Bergen. "Efficient Collision Detection of Complex Deformable Models Using AABB Trees". Journal of Graphics Tools, 2(4):1-14, 1997.

Article Start Previous Page 7 of 7

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