Math-Focused Intro to Graphics Programming
Unlock the mathematical secrets behind stunning visuals: a concise course for math-savvy learners eager to dive into the world of computer graphics.
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Linear Algebra Foundations for Graphics
Unit 1: Vectors: The Building Blocks
What is a Vector?
Vector Addition/Subtraction
Scalar Multiplication
Dot Product: Projection
Cross Product: Normals
Unit 2: Matrices: Transforming Space
What is a Matrix?
Matrix Addition
Scalar Multiplication
Matrix Multiplication
Transpose
Unit 3: Points, Lines, and Planes
Points as Vectors
Lines: Parametric Form
Planes: Implicit Equation
Unit 4: Solving Systems of Equations
Linear Systems Refresher
Gaussian Elimination
Geometric Transformations and Coordinate Systems
Unit 1: 2D Transformations
2D Translation Matrices
2D Scaling Matrices
2D Rotation Matrices
2D Shearing Matrices
Combining 2D Transforms
Unit 2: Homogeneous Coordinates
Why Homogeneous Coord?
Homogeneous Translation
Homogeneous Scaling
Homogeneous Rotation
Putting it All Together
Unit 3: 3D Transformations and Coordinate Systems
3D Translation Matrices
3D Scaling Matrices
3D Rotation Matrices
World Coordinates
View Coordinates
Rendering Fundamentals: From Math to Pixels
Unit 1: Rasterization and Pixel Operations
Rasterization Intro
Line Drawing Algorithms
Triangle Rasterization
Clipping
Z-Buffering
Unit 2: Shading Models and Lighting
Intro to Shading
Lambertian Reflectance
Specular Reflection
Ambient Lighting
Normal Vectors
Unit 3: Texturing and Color
Texture Mapping Intro
Bilinear Interpolation
Color Models
Color Theory Basics
Gamma Correction
Curves and Surfaces: Mathematical Representations
Unit 1: Parametric Curves: Bezier Basics
What are Parametric Curves?
Bezier Curves: Intro
Linear Bezier Curves
Quadratic Bezier Curves
Cubic Bezier Curves
Unit 2: Bezier Curves: Properties and Applications
Bezier Curve Equation
Convex Hull Property
Subdivision
Derivatives and Tangents
Bezier in Font Design
Unit 3: Splines and Surfaces
Intro to Splines
B-Splines
NURBS: The Ultimate Spline
Parametric Surfaces
Implicit Surfaces