Computer Graphics

  1. 3D Graphics Pipeline
    1. 3D Coordinate Systems and Spaces
      1. Object Space
        1. Local Coordinate System
          1. Model Coordinates
          2. World Space
            1. Global Coordinate System
              1. World Transformation
              2. View Space
                1. Camera Coordinate System
                  1. View Transformation
                  2. Clip Space
                    1. Projection Transformation
                      1. Homogeneous Clip Coordinates
                      2. Normalized Device Coordinates
                        1. Perspective Division
                          1. NDC Range
                          2. Screen Space
                            1. Viewport Transformation
                              1. Window Coordinates
                            2. 3D Modeling Representations
                              1. Polygon Meshes
                                1. Vertices and Edges
                                  1. Faces and Polygons
                                    1. Mesh Topology
                                      1. Mesh Data Structures
                                        1. Face-Vertex Lists
                                          1. Winged-Edge Structure
                                            1. Half-Edge Structure
                                              1. Vertex-Vertex Lists
                                            2. Parametric Surfaces
                                              1. Bezier Surfaces
                                                1. Tensor Product Surfaces
                                                  1. Control Point Grids
                                                  2. B-Spline Surfaces
                                                    1. Knot Vectors
                                                      1. Surface Continuity
                                                      2. NURBS Surfaces
                                                        1. Rational Basis Functions
                                                          1. Weight Points
                                                        2. Implicit Surfaces
                                                          1. Level Sets
                                                            1. Signed Distance Functions
                                                              1. Metaballs and Blobby Objects
                                                              2. Subdivision Surfaces
                                                                1. Catmull-Clark Subdivision
                                                                  1. Loop Subdivision
                                                                    1. Doo-Sabin Subdivision
                                                                    2. Volumetric Representations
                                                                      1. Voxel Grids
                                                                        1. Octrees
                                                                          1. Distance Fields
                                                                          2. Procedural Modeling
                                                                            1. Fractal Geometry
                                                                              1. L-Systems
                                                                                1. Grammar-Based Modeling
                                                                                  1. Noise-Based Modeling
                                                                                2. 3D Transformations
                                                                                  1. Transformation Matrices in 3D
                                                                                    1. 4x4 Transformation Matrices
                                                                                      1. Homogeneous Coordinates in 3D
                                                                                      2. Basic 3D Transformations
                                                                                        1. 3D Translation
                                                                                          1. 3D Scaling
                                                                                            1. 3D Rotation
                                                                                              1. Rotation about X-axis
                                                                                                1. Rotation about Y-axis
                                                                                                  1. Rotation about Z-axis
                                                                                                    1. Rotation about Arbitrary Axis
                                                                                                    2. 3D Shearing
                                                                                                    3. Composite Transformations
                                                                                                      1. Transformation Concatenation
                                                                                                        1. Transformation Order
                                                                                                          1. Inverse Transformations
                                                                                                          2. Rotation Representations
                                                                                                            1. Euler Angles
                                                                                                              1. Axis-Angle Representation
                                                                                                                1. Quaternions
                                                                                                                  1. Quaternion Mathematics
                                                                                                                    1. Quaternion Rotation
                                                                                                                      1. Quaternion Interpolation
                                                                                                                  2. Camera and Viewing
                                                                                                                    1. Camera Models
                                                                                                                      1. Pinhole Camera Model
                                                                                                                        1. Camera Parameters
                                                                                                                          1. Camera Positioning
                                                                                                                          2. View Matrix Construction
                                                                                                                            1. Look-At Matrix
                                                                                                                              1. Camera Orientation
                                                                                                                                1. Up Vector Calculation
                                                                                                                                2. Projection Transformations
                                                                                                                                  1. Orthographic Projection
                                                                                                                                    1. Parallel Projection
                                                                                                                                      1. Orthographic Matrix
                                                                                                                                      2. Perspective Projection
                                                                                                                                        1. Perspective Matrix
                                                                                                                                          1. Field of View
                                                                                                                                            1. Aspect Ratio
                                                                                                                                              1. Near and Far Planes
                                                                                                                                            2. View Frustum
                                                                                                                                              1. Frustum Definition
                                                                                                                                                1. Frustum Culling
                                                                                                                                                  1. Clipping Planes
                                                                                                                                                2. 3D Clipping
                                                                                                                                                  1. View Frustum Clipping
                                                                                                                                                    1. Plane Equations
                                                                                                                                                      1. Point-Plane Distance
                                                                                                                                                      2. Clipping Algorithms
                                                                                                                                                        1. Sutherland-Hodgman 3D Clipping
                                                                                                                                                          1. Cohen-Sutherland 3D Extension
                                                                                                                                                          2. Homogeneous Clipping
                                                                                                                                                            1. Clipping in Homogeneous Space
                                                                                                                                                              1. Guard Band Clipping

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                                                                                                                                                          3. 2D Graphics Fundamentals

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                                                                                                                                                          5. Lighting and Shading Models