Title:
Mathematical and computer programming techniques for computer graphics
Personal Author:
Publication Information:
London : Springer-Verlag, 2006
ISBN:
9781852339029
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010107325 | T385 C6545 2006 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Mathematical and Computer Programming Techniques for Computer Graphics introduces the mathematics and related computer programming techniques used in Computer Graphics. Starting with the underlying mathematical ideas, it gradually leads the reader to a sufficient understanding of the detail to be able to implement libraries and programs for 2D and 3D graphics. Using lots of code examples, the reader is encouraged to explore and experiment with data and computer programs (in the C programming language) and to master the related mathematical techniques.
A simple but effective set of routines are included, organised as a library, covering both 2D and 3D graphics - taking a parallel approach to mathematical theory, and showing the reader how to incorporate it into example programs. This approach both demystifies the mathematics and demonstrates its relevance to 2D and 3D computer graphics.
Table of Contents
| 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 |
