About the Mathematical Utilities

QuickDraw 3D provides a large number of utility functions for operating on basic mathematical objects such as points, vectors, matrices, and quaternions. You can use these utilities to

• set the components of points and vectors
• convert dimensions of points and vectors
• subtract points from points
• calculate distances between points
• determine point-relative ratios
• add and subtract points and vectors
• scale vectors
• determine the lengths of vectors
• normalize vectors
• add and subtract vectors
• determine vector cross products and dot products
• transform points and vectors
• negate vectors
• convert points from Cartesian form to polar or spherical form
• determine affine combinations of points
• manipulate matrices
• set up transformation matrices
• calculate trigonometric ratios
• manipulate quaternions

Many of these functions might be implemented as C language macros. As a result, you should avoid such operations as applying the auto-increment operator (++) to function parameters.

QuickDraw 3D also supplies functions that you can use to manage bounding boxes and spheres for any kind of QuickDraw 3D object.