Cheap well-behaved affine transformation of bounding spheres

A computer system for rendering a scene graph with hierarchical structure, comprising:

• a) a processor for creating a first data structure of an affine transform matrix, and a second data structure of a first bounding sphere having a first radius;
• b) a memory coupled to the processor for storing the first data structure and the second data structure;
• and,
• c) a calculation circuit coupled to said processor for forming an ellipsoid by multiplying said first bounding sphere by said affine transform matrix, calculating the radius of a second bounding sphere, said second radius being at least large enough so that said second bounding sphere would surround the ellipsoid, and rendering the scene graph based on the second bounding sphere.

The computer system of claim wherein:

• said processor further creates a viewer frustum;
• said memory further stores said viewer frustum;
• and,
• said calculation circuit further compares said second bounding sphere with said viewer frustum for intersection.

A computer-readable medium having stored thereon instructions for causing a computer system to render a scene graph with hierarchical structure, said instructions causing the computer system to carry out the steps of:

• a) creating an affine transform matrix;
• b) storing said affine transform matrix in memory;
• c) creating a first bounding sphere having a first radius;
• d) storing said first bounding sphere in memory and forming an ellipsoid by multiplying said first bounding sphere by said affine transform matrix;
• e) calculating a second radius for a second bounding sphere, said second radius being at least large enough so that said second sphere would surround the ellipsoid;
• and
• f) storing said second radius in memory and rendering the scene graph based on the second bounding sphere.