| Vector Algebra Survival Kit Some Basic Definitions and Notation Multiplication of a Vector by a Scalar Vector Addition | |
| Position Vectors and Free Vectors | |
| The Vector Equation of a Line Linear Dependence / Independence of Vectors | |
| Vector Bases The Components of a Vector Multiplication of a Vector by a Scalar Vector Addition | |
| Vector Equality Orthogonal, Orthonormal and Right-Handed Vector Bases | |
| Cartesian Bases and Cartesian Coordinates | |
| The Length of a Vector | |
| The Scalar Product of Vectors | |
| The Scalar Product Expresses in Terms of its Components | |
| Properties and Applications of the Scalar Product | |
| The Direction Ratios and Direction Cosines of a Vector | |
| The Vector Product of Two Vectors | |
| The Vector Product Expressed in Terms of its Components | |
| Properties of the Vector Product Triple Produces of Vectors | |
| The Components of a Vector Relative to a Non-orthogonal Basis | |
| The Decomposition of a Vector According to a Basis | |
| The Vector Equation of the Line Revisited | |
| The Vector Equation of the Place | |
| Some Applications of Vector Algebra in Analytical Geometry | |
| Summary of Vector Algebra | |
| Axioms and Rules | |
| A Simple Vector Algebra C Library Matrix Algebra Survival Kit | |
| The Definition of a Matrix | |
| Square Matrices | |
| Diagonal Matrices | |
| The Identity Matrix | |
| The Zero or Null Matrix | |
| The Transpose of a Matrix | |
| Symmetric and Antisymmetric Matrices | |
| Triangular Matrices | |
| Scalar Matrices | |
| Equality of Matrices | |
| Matrix Operations | |
| The Minor of a Matrix | |
| The Determinant of a Matrix | |
| The Computational Rules of Determinants | |
| The Cofactor of an Element of a Matrix and the Cofactor Matrix | |
| The Ajoint Matrix or Adjugate Matrix | |
| The Reciprocal or Inverse of a Matrix | |
| A Theorem on Invertible Matrices and their Determinants | |
| Axioms and Rules of Matrix Inversion | |
| Solving a System of Linear Simultaneous Equations | |
| Orthogonal Matrices | |
| Two Theorems on Vector by Matrix Multiplication | |
| The Row / Column Reversal Matrix | |
| Summary of Matrix Algebra | |
| Axioms and Rules | |
| A Simple Matrix Algebra C Library Vector Spaces or Linear Spaces | |
| The Definition of a Scalar Field | |
| The Definition of a Vector Space | |
| Linear Combinations of Vectors | |
| Linear Dependence and Linear Independence of Vectors | |
| Spans and Bases of a Vector Space | |
| Transformations between Bases | |
| Transformations between Orthonormal Bases | |
| An Alternative Notation for Change of Basis Transformations | |
| Two-Dimensional Transformations | |
| The Definition of a 2D Transformation | |
| The Concatenation of Transformations | |
| 2D Graphics Transformations | |
| 2D Primitive Transformations | |
| 2D Composite Transformations | |
| The Sign of the Angles in Transformations | |
| Some Important Observations | |
| The Matrix Representation of 2D Transformations | |
| The Matrix Representation of Primitive Transformations | |
| Some Transformation Matrix Properties | |
| The Concatenation of Transformation Matrices | |
| Local Frame and Global Frame Transformations | |
| Transformations of the Frame of Reference or Coordinate System | |
| The Viewing Transformation Homogeneous Coordinates | |
| A Simple C Library for 2D Transformations | |
| Two-Dimensional Clipping Clipping a 2D Point to a Rectangular Clipping | |
| Boundary Clipping a 2D Line Segment to a Rectangular Clipping Boundary | |
| The Cohen and Sutherland 2D | |
| Line-Clipping Algorithm | |
| 2D Polygon Clipping | |
| References | |
| Three-Dimensional Transformations Primitive | |
| 3D Transformations | |
| The Global and Local Frames of Reference | |
| Aiming Transformations | |
| Composite Transformations | |
| Local Frame and Global Frame Transformations | |
| Transformations of the Frame of Reference or Coordinate System | |
| References | |
| Viewing and Projection Transformations | |
| The Conceptual Camera Model | |
| The Viewing Transformation | |
| The Projection Transformation | |
| The Projection Transformation | |
| Matrix Parallel Projections | |
| Perspective Projections | |
| The Screen or Device Coordinate System | |
| 3D Line Clipping Perspective Depth | |
| A Simple C Library for 3D Transformations | |
| 3D Rendering Introduction | |
| Rendering Algorithms | |
| Reflection Models and Shading | |
| Techniques Shading Models | |
| References | |
| A1: A Simple Vector Algebra C Library | |
| A2: A Simple Matrix Algebra C Library | |
| A3: A Simple C Library for 2D Transformations | |
| A4: A Simple | |
| Table of Contents provided by Publisher. All Rights Reserved. |
