Computer Graphics through Key Mathematics

1 The Processes of Computer Graphics.- Object Model Building.- Depiction of Models.- Conclusion.- 2 Numbers, Counting and Measuring.- Natural Numbers.- Integers.- Rational Numbers.- Real Numbers.- Complex Numbers.- Representations of Number.- The Computer Representation of Number.- Boolean Algebra.- Summary.- 3 Coordinates and Dimension: Representations of Space and Colour.- Cartesian Coordinates.- Defining Space by Equations and Inequalities.- Angles.- Trigonometry and Polar Coordinates.- Dimension.- Coordinate Systems in Three Dimensions.- Colour and its Representation.- Summary.- 4 Functions and Transformations: Ways of Manipulating Space.- Functions as Mappings.- Graphs of Functions.- Transformations in 2D.- Transformations in 3D.- Combining Affine Transformations.- Inversion of Affine Transformations.- Inversion of Functions.- Shape Transformation by Function Change.- Conclusions.- 5 Form from Function: Analysis of Shapes.- The Straight Line.- Drawing General Function Graphs.- Graphs of Polynomials.- Calculus: Differentiation.- Calculus: Integration.- Series Expansions.- Calculus and Animation.- The Exponential Function.- The Conic Sections.- Some Standard 3D Forms and their Equations.- Summary.- 6 Matrices: Tools for Manipulating Space.- Matrices in Computer Graphics.- Definition and Notation.- Forms of Matrices.- Operations on Matrices: Addition.- Operations on Matrices: Multiplication.- The Identity Matrix.- Matrices and Equations.- The Inverse of a Square Matrix.- Matrices, Transformations and Homogeneous Coordinates: Two Dimensions.- Matrices, Transformations and Homogeneous Coordinates: Three Dimensions.- Inverse of a Transformation Matrix.- Perspective Projection.- Computer Implementation of Matrix Methods.- Summary.- 7 Vectors: Descriptions of Spatial Relationships.- Definition of a Vector.- Notation.- Addition of Vectors: The Parallelogram and Triangle Laws.- Multiplication of a Vector by a Scalar.- Examples of Vector Quantities.- Vectors in 2D