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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...”
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