Mathematics for Game Development

  1. Specialized Topics
    1. Procedural Noise Functions
      1. Noise Fundamentals
        1. Deterministic Randomness
          1. Spatial Coherence
            1. Frequency and Amplitude
            2. Perlin Noise
              1. Grid-Based Approach
                1. Gradient Vectors
                  1. Interpolation Methods
                    1. Octave Combination
                    2. Simplex Noise
                      1. Simplex Grid
                        1. Gradient Selection
                          1. Performance Advantages
                          2. Noise Variations
                            1. Fractal Noise
                              1. Turbulence
                                1. Ridge Noise
                                  1. Billowy Noise
                                  2. Noise Applications
                                    1. Terrain Generation
                                      1. Height Maps
                                        1. Erosion Simulation
                                          1. Biome Distribution
                                          2. Texture Synthesis
                                            1. Surface Details
                                              1. Material Variation
                                                1. Weathering Effects
                                                2. Environmental Effects
                                                  1. Cloud Generation
                                                    1. Water Simulation
                                                      1. Particle Systems
                                                  2. Graphics Pipeline Mathematics
                                                    1. Coordinate System Transformations
                                                      1. Model Coordinates
                                                        1. World Coordinates
                                                          1. View Coordinates
                                                            1. Clip Coordinates
                                                              1. Screen Coordinates
                                                              2. Model-View-Projection Pipeline
                                                                1. Model Matrix
                                                                  1. Object Transformation
                                                                    1. Local to World Space
                                                                    2. View Matrix
                                                                      1. Camera Transformation
                                                                        1. World to View Space
                                                                          1. Look-At Matrix
                                                                          2. Projection Matrix
                                                                            1. Perspective Projection
                                                                              1. Orthographic Projection
                                                                                1. Projection Parameters
                                                                                2. MVP Matrix Combination
                                                                                  1. Matrix Multiplication Order
                                                                                    1. Vertex Transformation
                                                                                  2. Clipping and Culling
                                                                                    1. View Frustum
                                                                                      1. Clipping Planes
                                                                                        1. Back-Face Culling
                                                                                          1. Occlusion Culling
                                                                                          2. Viewport Transformation
                                                                                            1. Screen Space Conversion
                                                                                              1. Depth Buffer
                                                                                                1. Pixel Coordinates
                                                                                              2. Lighting and Shading Mathematics
                                                                                                1. Light Models
                                                                                                  1. Point Lights
                                                                                                    1. Directional Lights
                                                                                                      1. Spot Lights
                                                                                                        1. Area Lights
                                                                                                        2. Lighting Calculations
                                                                                                          1. Ambient Lighting
                                                                                                            1. Global Illumination Approximation
                                                                                                            2. Diffuse Lighting
                                                                                                              1. Lambert's Law
                                                                                                                1. Surface Normal Importance
                                                                                                                2. Specular Lighting
                                                                                                                  1. Phong Model
                                                                                                                    1. Blinn-Phong Model
                                                                                                                      1. Reflection Vectors
                                                                                                                    2. Advanced Lighting
                                                                                                                      1. Attenuation Models
                                                                                                                        1. Distance-Based Falloff
                                                                                                                          1. Quadratic Attenuation
                                                                                                                          2. Shadow Calculations
                                                                                                                            1. Shadow Mapping
                                                                                                                              1. Ray Tracing
                                                                                                                              2. Global Illumination
                                                                                                                                1. Radiosity
                                                                                                                                  1. Path Tracing
                                                                                                                                2. Shader Mathematics
                                                                                                                                  1. Vertex Shader Operations
                                                                                                                                    1. Position Transformation
                                                                                                                                      1. Normal Transformation
                                                                                                                                        1. Texture Coordinate Manipulation
                                                                                                                                        2. Fragment Shader Operations
                                                                                                                                          1. Color Calculations
                                                                                                                                            1. Texture Sampling
                                                                                                                                              1. Alpha Blending
                                                                                                                                              2. Mathematical Functions in Shaders
                                                                                                                                                1. Built-in Functions
                                                                                                                                                  1. Custom Mathematical Operations

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                                                                                                                                            10. Curves and Splines

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                                                                                                                                            1. Foundational Mathematical Concepts