Geometric tools for computer graphics
Do you spend too much time creating the building blocks of your graphics applications or finding and correcting errors? Geometric Tools for Computer Graphics is an extensive, conveniently organized collection of proven solutions to fundamental problems that you'd rather not solve over and over...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
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San Francisco, CA :
Morgan Kaufmann
c2003.
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| Edición: | 1st edition |
| Colección: | Morgan Kaufmann series in computer graphics and geometric modeling.
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| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627944906719 |
Tabla de Contenidos:
- 1 Introduction; How to Use This Book; Issues of Numerical Computation; Low-Level Issues; High-Level Issues; A Summary of the Chapters; 2 Matrices and Linear Systems; Introduction; Motivation; Organization; Notational Conventions; Tuples; Definition; Arithmetic Operations; Matrices; Notation and Terminology; Transposition; Arithmetic Operations; Matrix Multiplication; Linear Systems; Linear Equations; Linear Systems in Two Unknowns; General Linear Systems; Row Reductions, Echelon Form, and Rank; Square Matrices; Diagonal Matrices; Triangular Matrices; The Determinant; Inverse; Linear Spaces
- FieldsDefinition and Properties; Subspaces; Linear Combinations and Span; Linear Independence, Dimension, and Basis; Linear Mappings; Mappings in General; Linear Mappings; Matrix Representation of Linear Mappings; Cramer's Rule; Eigenvalues and Eigenvectors; Euclidean Space; Inner Product Spaces; Orthogonality and Orthonormal Sets; Least Squares; Recommended Reading; 3 Vector Algebra; Vector Basics; Vector Equivalence; Vector Addition; Vector Subtraction; Vector Scaling; Properties of Vector Addition and Scalar Multiplication; Vector Space; Span; Linear Independence
- Basis, Subspaces, and DimensionOrientation; Change of Basis; Linear Transformations; Affine Spaces; Euclidean Geometry; Volume, the Determinant, and the Scalar Triple Product; Frames; Affine Transformations; Types of Affine Maps; Composition of Affine Maps; Barycentric Coordinates and Simplexes; Barycentric Coordinates and Subspaces; Affine Independence; 4 Matrices, Vector Algebra, and Transformations; Introduction; Matrix Representation of Points and Vectors; Addition, Subtraction, and Multiplication; Vector Addition and Subtraction; Point and Vector Addition and Subtraction
- Subtraction of PointsScalar Multiplication; Products of Vectors; Dot Product; Cross Product; Tensor Product; The 'Perp' Operator and the ÏPerpÓ Dot Product; Matrix Representation of Affine Transformations; Change-of-Basis/Frame/Coordinate System; Vector Geometry of Affine Transformations; Notation; Translation; Rotation; Scaling; Reflection; Shearing; Projections; Orthographic; Oblique; Perspective; Transforming Normal Vectors; Recommended Reading; 5 Geometric Primitives in 2D; Linear Components; Implicit Form; Parametric Form; Converting between Representations; Triangles; Rectangles
- Polylines and PolygonsQuadratic Curves; Circles; Ellipses; Polynomial Curves; Bezier Curves; B-Spline Curves; NURBS Curves; 6 Distance in 2D; Point to Linear Component; Point to Line; Point to Ray; Point to Segment; Point to Polyline; Point to Polygon; Point to Triangle; Point to Rectangle; Point to Orthogonal Frustum; Point to Convex Polygon; Point to Quadratic Curve; Point to Polynomial Curve; Linear Components; Line to Line; Line to Ray; Line to Segment; Ray to Ray; Ray to Segment; Segment to Segment; Linear Component to Polyline or Polygon; Linear Component to Quadratic Curve
- Linear Component to Polynomial Curve
