WebGL and Computer Graphics

4.

Mathematical Foundations for 3D Graphics

4.1.

Vector Mathematics

4.1.1.

Vector Fundamentals

4.1.1.1.

4.1.1.1.1.

Components and Representation

4.1.1.2.

4.1.1.2.1.

Components and Representation

4.1.1.3.

4.1.1.3.1.

Homogeneous Coordinates

4.1.1.3.2.

W Component Significance

4.1.2.

Vector Operations

4.1.2.1.

Vector Addition

4.1.2.1.1.

Component-wise Addition

4.1.2.2.

Vector Subtraction

4.1.2.2.1.

Component-wise Subtraction

4.1.2.3.

Scalar Multiplication

4.1.2.3.1.

Scaling Vectors

4.1.2.4.

4.1.2.4.1.

Calculation Method

4.1.2.4.2.

Geometric Interpretation

4.1.2.5.

4.1.2.5.1.

Calculation Method

4.1.2.5.2.

Geometric Interpretation

4.1.2.5.3.

Right-hand Rule

4.1.2.6.

Vector Normalization

4.1.2.6.1.

Unit Vector Creation

4.1.2.6.2.

Length Calculation

4.2.

Matrix Mathematics

4.2.1.

4.2.1.1.

4.2.1.1.1.

2D Transformation Matrices

4.2.1.2.

4.2.1.2.1.

3D Transformation Matrices

4.2.2.

Matrix Operations

4.2.2.1.

Matrix Multiplication

4.2.2.1.1.

Row-Column Multiplication

4.2.2.1.2.

Non-commutative Property

4.2.2.2.

Matrix Transposition

4.2.2.2.1.

Row-Column Exchange

4.2.2.3.

Matrix Inversion

4.2.2.3.1.

Inverse Matrix Calculation

4.2.2.3.2.

Invertible Matrix Conditions

4.3.

Transformation Mathematics

4.3.1.

Basic Transformations

4.3.1.1.

4.3.1.1.1.

Translation Matrix Construction

4.3.1.1.2.

Translation Vector Application

4.3.1.2.

4.3.1.2.1.

2D Rotation Matrices

4.3.1.2.2.

3D Rotation Matrices

4.3.1.2.3.

Axis-Angle Rotation

4.3.1.2.4.

4.3.1.2.5.

Quaternion Rotation

4.3.1.3.

4.3.1.3.1.

Uniform Scaling

4.3.1.3.2.

Non-uniform Scaling

4.3.1.3.3.

Scaling Matrix Construction

4.3.2.

Composite Transformations

4.3.2.1.

Transformation Order

4.3.2.1.1.

Matrix Multiplication Order

4.3.2.2.

Transformation Concatenation

4.3.2.2.1.

Combined Transformation Matrices

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3. WebGL Rendering Pipeline

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5. 3D Transformations and Projections