Mathematics for Computer Graphics

Math & CG

What is Mathematics?

• Mathematics (from Greek máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change

• Mathematics is part of formal science academic field

• Mathematics is closely related to logic

Branches of Mathematics

• Arithmetic

• Algebra

• Geometry

• Logic

• Statistics & probability

• Calculus

• Applied mathematics

– Business & decision theory related applied mathematics

– Engineering and science related applied mathematics

What is Computer Graphics?

• Computer graphics are pictures and movies created using computers - usually referring to image data created by a computer specifically with help from specialized graphical hardware and software

Math + CG Example 1

• Linear algebra

– Basic modeling

– Rasterization

– Lighting

– Collision detection

Math + CG Example 2

• Space partitioning structures

– Quad trees, kD trees, BVHs, etc.

• Any serious real-time rendering system uses these heavily to cut down on the amount of rendering they have to do

– Used for photon mapping & collision detection

Math + CG Example 3

• Splines

– Used heavily in 3D modeling to create more natural looking surfaces

– Spline interpolation is also used in animation, procedural generation and rasterization

Math + CG Example 4

• Signal processing

– Anti aliasing

Math + CG Example 5

• Monte Carlo Integration

– Global illumination

Math + CG Example 6

• Differential Equations

– Simulate any natural phenomenon, such as fluids, crowds, fire and participating media

Is Mathematics Hard?

“It is not that mathematics is hard, just the examinations are made challenging and interesting...”