Schneider, Philip J. & Eberly, David H., Geometric Tools for Computer Graphics, Morgan Kaufman Publishers, San Francisco 2003

[i][c][1.0.47][r][a]
Schneider, Philip J. & Eberly, David H.
Geometric Tools for Computer Graphics
Morgan Kaufman Publishers
San Francisco 2003
ISBN: 9781558605947

#informatica #geometria
ig01#informatica
ig02#informatica

[i][c] INDICE:

			Foreword
			Figures
			Tables
			Preface
		Chapter 1	Introduction
		1.1	How to Use This Book
		1.2	Issues of Numerical Computations
		1.2.1	Low-Level Issues
		1.2.2	High-Level Issues
		1.3	A Summary of the Chapters
		Chapter 2	Matrices and Linear Systems
		2.1	Introduction
		2.1.1	Motivation
		2.1.2	Organization
		2.1.3	Notational Conventions
		2.2	Tuples
		2.2.1	Definition
		2.2.2	Arithmetic Operations
		2.3	Matrices
		2.3.1	Notation and Terminology
		2.3.2	Transposition
		2.3.3	Arithmetic Operations
		2.3.4	Matrix Multiplication
		2.4	Linear Systems
		2.4.1	Linear Equations
		2.4.2	Linear Systems in Two Unknowns
		2.4.3	General Linear Systems
		2.4.4	Row Reductions, Echelon Form, and Rank
		2.5	Square Matrices
		2.5.1	Diagonal Matrices
		2.5.2	Triangular Matrices
		2.5.3	The Determinant
		2.5.4	Inverse
		2.6	Linear Spaces
		2.6.1	Fields
		2.6.2	Definition and Properties
		2.6.3	Subspaces
		2.6.4	Linear Combinations and Span
		2.6.5	Linear Independence, Dimension, and Basis
		2.7	Linear Mappings
		2.7.1	Mappings in General
		2.7.2	Linear Mappings
		2.7.3	Matrix Representation of Linear Mappings
		2.7.4	Cramer's Rule
		2.8	Eigenvalues and Eigenvectors
		2.9	Euclidean Space
		2.9.1	Inner Product Spaces
		2.9.2	Orthogonality and Orthonormal Sets
		2.10	Least Squares
			Recommended Reading
		Chapter 3	Vector Algebra
		3.1	Vector Basics
		3.1.1	Vector Equivalence
		3.1.2	Vector Addition
		3.1.3	Vector Subtraction
		3.1.4	Vector Scaling
		3.1.5	Properties of Vector Addition and Scalar Multiplication
		3.2	Vector Space
		3.2.1	Span
		3.2.2	Linear Independence
		3.2.3	Basis, Subspaces, and Dimension
		3.2.4	Orientation
		3.2.5	Change of Basis
		3.2.6	Linear Transformations
		3.3	Affine Spaces
		3.3.1	Euclidean Geometry
		3.3.2	Volume, the Determinant, and the Scalar Triple Product
		3.3.3	Frames
		3.4	Affine Transformations
		3.4.1	Types of Affine Maps
		3.4.2	Compossition of Affine Maps
		3.5	Barycentric Coordinates and Simplexes
		3.5.1	Barycentric Coordinates and Subspaces
		3.5.2	Affine Independence
		Chapter 4	Matrices, Vector Algebra, and Transformations
		4.1	Introduction
		4.2	Matrix Representation of Points and Vectors
		4.3	Addition, Subtraction, and Multiplication
		4.3.1	Vector Addition and Subtraction
		4.3.2	Point and Vector Addition and Subtraction
		4.3.3	Subtractions of Points
		4.3.4	Scalar Multiplication
		4.4	Products of Vectors
		4.4.1	Dot Product
		4.4.2	Cross Product
		4.4.3	Tensor Product
		4.4.4	The "Perp" Operator and the "Perp" Dot Product
		4.5	Matrix Representation of Affine Transformations
		4.6	Change-of-Basis/Frame/Coordinate System
		4.7	Vector Geometry of Affine Transformations
		4.7.1	Notation
		4.7.2	Translation
		4.7.3	Rotation
		4.7.4	Scaling
		4.7.5	Reflection
		4.7.6	Shearing
		4.8	Projections
		4.8.1	Orthographic
		4.8.2	Oblique
		4.8.3	Perspective
		4.9	Transforming Normal Vectors
			Recommended Reading
		Chapter 5	Geometric Primitives in 2D
		5.1	Linear Components
		5.1.1	Implicit Form
		5.1.2	Parametric Form
		5.1.3	Converting between Representations
		5.2	Triangles
		5.3	Rectangles
		5.4	Polylines and Polygons
		5.5	Quadratic Curves
		5.5.1	Circles
		5.5.2	Ellipses
		5.6	Polynomial Curves
		5.6.1	Bézier Curves
		5.6.2	B-Spline Curves
		5.6.3	NURBS Curves
		Chapter 6	Distance in 2D
		6.1	Point to Linear Component
		6.1.1	Point to Line
		6.1.2	Point to Ray
		6.1.3	Point to Segment
		6.2	Point to Polyline
		6.3	Point to Polygon
		6.3.1	Point to Triangle
		6.3.2	Point to Rectangle
		6.3.3	Point to Orthogonal Frustum
		6.3.4	Point to Convex Polygon
		6.4	Point to Quadratic Curve
		6.5	Point to Polynomial Curve
		6.6	Linear Components
		6.6.1	Line to Line
		6.6.2	Line to Ray
		6.6.3	Line to Segment
		6.6.4	Ray to Ray
		6.6.5	Ray to Segment
		6.6.6	Segment to Segment
		6.7	Linear Component to Polyline or Polygon
		6.8	Linear Component to Quadratic Curve
		6.9	Linear Component to Polynomial Curve
		6.10	GJK Algorithm
		6.10.1	Set Operations
		6.10.2	Overview of the Algorithm
		6.10.3	Alternatives to GJK
		Chapter 7	Intersection in 2D
		7.01	Linear Components
		7.02	Linear Components and Polylines
		7.3	Linear Components and Quadratic Curves
		7.3.1	Linear Components and General Quadratic Curves
		7.3.2	Linear Components and Circular Components
		7.4	Linear Components and Polynomial Curves
		7.4.1	Algebraic Method
		7.4.2	Polyline Approximation
		7.4.3	Hierarchical Bounding
		7.4.4	Monotone Decomposition
		7.4.5	Rasterization
		7.5	Quadratic Curves
		7.5.1	General Quadratic Curves
		7.5.2	Circular Components
		7.5.3	Ellipses
		7.6	Polynomial Curves
		7.6.1	Algebraic Method
		7.6.2	Polyline Approximation
		7.6.3	Hierarchical Bounding
		7.6.4	Rasterization
		7.7	The Method of Separating Axes
		7.7.1	Separation by Projection onto a Line
		7.7.2	Separation of Stationary Convex Polygons
		7.7.3	Separation of Moving Convex Polygons
		7.7.4	Intersection Set for Stationary Convex Polygons
		7.7.5	Contact Set for Moving Convex Polygons
		Chapter 8	Miscellaneous 2D Problems
		8.1	Circle through Three Points
		8.2	Circle Tangent to Thre Lines
		8.3	Line Tangent to a Circle at a Given Point
		8.4	Line Tangent to a Circle through a Given Point
		8.5	Lines Tangent to Two Circles
		8.6	Circle through Two Points with a Given Radius
		8.7	Circle through a Point and Tangent to a Line with a Given Radius
		8.8	Circles Tangent to Two Lines with a Given Radius
		8.9	Circles through a Point a Tangent to a Circle with a Given Radius
		8.10	Circles Tangent to a Line and a Circle with a Given Radius
		8.11	Circles Tangent to Two Circles with a Given Radius
		8.12	Line Perpendicular to a Given Line through a Given Point
		8.13	Line between and Equidistant to Two Points
		8.14	Line Parallel to a Given Line at a Given Distance
		8.15	Line Parallel to a Given Line at a Given Vertical (Horizontal) Distance
		8.16	Lines Tangent to a Given Circle and Normal to a Given Line
		Chapter 9	Geometric Primitives in 3D
		9.1	Linear Components
		9.2	Planar Components
		9.2.1	Planes
		9.2.2	Coordinate System Relative to a Plane
		9.2.3	2D Objects in a Plane
		9.3	Polymeshes, Polyhedra, and Polytopes
		9.3.1	Vertex-Edge-Face Tables
		9.3.2	Connected Meshes
		9.3.3	Manifold Meshes
		9.3.4	Closed Meshes
		9.3.5	Consistent Ordering
		9.3.6	Platonic Solids
		9.4	Quadric Surfaces
		9.4.1	Three Nonzero Eigenvalues
		9.4.2	Two Nonzero Eigenvalues
		9.4.3	One Nonzero Eigenvalue
		9.5	Torus
		9.6	Polynomial Curves
		9.6.1	Bézier Curves
		9.6.2	B-Spline Curves
		9.6.3	NURBS Curves
		9.7	Polynomial Surfaces
		9.7.1	Bézier Surfaces
		9.7.2	B-Spline Surfaces
		9.7.3	NURBS Surfaces
		Chapter 10	Distance in 3D
		10.1	Introduction
		10.2	Point to Linear Component
		10.2.1	Point to Ray or Line Segment
		10.2.2	Point to Polyline
		10.3	Point to Planar Component
		10.3.1	Point to Plane
		10.3.2	Point to Triangle
		10.3.3	Point to Rectangle
		10.3.4	Point to Polygon
		10.3.5	Point to Circle or Disk
		10.4	Point to Polyhedron
		10.4.1	General Problem
		10.4.2	Point to Oriented Bounding Box
		10.4.3	Point to Orthogonal Frustum
		10.5	Point to Quadric Surface
		10.5.1	Point to General Quadric Surface
		10.5.2	Point to Elipsoid
		10.6	Point to Polynomial Curve
		10.7	Point to Polynomial Surface
		10.8	Linear Components
		10.8.1	Lines and Lines
		10.8.2	Segment/Segment, Line/Ray, Line/Segment, Ray/Ray, Ray/Segment
		10.8.3	Segment to Segment, Alternative Approach
		10.9	Linear Component to Triangle, Rectangle, Tetrahedron, Oriented Box
		10.9.1	Linear Component to Triangle
		10.9.2	Linear Component to Rectangle
		10.9.3	Linear Component to Tetrahedron
		10.9.4	Linear Component to riented Bounding Box
		10.10	Line to Quadric Surface
		10.11	Line to Polynomial Surface
		10.12	GJK Algorithm
		10.13	Miscellaneous
		10.13.1	Distance betwen Line and Planar Curve
		10.13.2	Distance between Line and Planar Solid Object
		10.13.3	Distance between Planar Curves
		10.13.4	Geodesic Distance on Surfaces
		Chapter 11	Intersection in 3D
		11.01	Linear Components and Planar Components
		11.1.1	Linear Components and Planes
		11.1.2	Linear Components and Triangles
		11.1.3	Linear Components and Polygons
		11.1.4	Linear Component and Disk
		11.2	Linear Components and Polyhedra
		11.3	Linear Components and Polyhedra
		11.3.1	General Quadric Surfaces
		11.3.2	Linear Components and a Sphere
		11.3.3	Linear Components and an Ellipsoid
		11.3.4	Linear Components and Cylinders
		11.3.5	Linear Components and a Cone
		11.4	Linear Components and Polynomial Surfaces
		11.4.1	Algebraic Surfaces
		11.4.2	Free-Form Surfaces
		11.5	Planar Components
		11.5.1	Two Planes
		11.5.2	Three Planes
		11.5.3	Triangle and Plane
		11.5.4	Triangle and Triangle
		11.6	Planar Components and Polyhedra
		11.6.1	Trimeshes
		11.6.2	General Polyhedra
		11.7	Planar Components and Quadratic Surfaces
		11.7.1	Plane and General Quadric Surface
		11.7.2	Plane and Sphere
		11.7.3	Plane and Cylinder
		11.7.4	Plane and Cone
		11.7.5	Triangle and Cone
		11.8	Planar Components and Polynomial Surfaces
		11.8.1	Hermite Curves
		11.8.2	Geometry Definitions
		11.8.3	Computing the Curves
		11.8.4	The Algorithm
		11.8.5	Implementation Notes
		11.9	Quadric Surfaces
		11.9.1	General Intersection
		11.9.2	Ellipsoids
		11.10	Polynomial Surfaces
		11.10.1	Subdivision Methods
		11.10.2	Lattice Evaluation
		11.10.3	Analytic Methods
		11.10.4	Marching Methods
		11.11	The Method of Separating Axes
		11.11.1	Separation of Stationary Convex Polyhedra
		11.11.2	Sepaaration of Moving Convex Polyhedra
		11.11.3	Intersection Set for Stationary Convex Polyhedra
		11.11.4	Contact Set for Moving Convex Polyhedra
		11.12	Miscellaneous
		11.12.1	Oriented Bounding Box and Orthogonal Frustum
		11.12.2	Linear Component and Axis-Aligned Bounding Box
		11.12.3	Linear Component and Oriented Bounding Box
		11.12.4	Plane and Axis-Aligned Bounding Box
		11.12.5	Plane and Oriented Bounding Box
		11.12.6	Axis-Aligned Bounding Boxes
		11.12.7	Oriented Bounding Boxes
		11.12.8	Sphere and Axis-Aligned Bounding Box
		11.12.9	Cylinders
		11.12.10	Linear Component and Torus
		Chapter 12	Miscellaneous 3D Problems
		12.1	Projection of a Point onto a Plane
		12.2	Projection of a Vector onto a Plane
		12.3	Angle between a Line and a Plane
		12.4	Angle between Two Planes
		12.5	Plane Normal to a Line and through a Given Point
		12.6	Plane through Three Points
		12.7	Angle between Two Lines
		Chapter 13	Computational Geometry Topics
		13.1	Binary Space-Partitioning Trees in 2D
		13.1.1	BSP Tree Representation of a Polygon [ di Philip J. Schneider ]
		13.1.2	Minimum Splits versu Balanced Splits
		13.1.3	Point in Polygon Using BSP Trees
		13.1.4	Partitioning a Line Segment by a BSP Tree
		13.2	Binary Space-Partitioning Trees in 3D
		13.2.2	Minimum Splits versus Balanced Trees
		13.2.3	Point in Polyhedron Using BSP Trees
		13.2.4	Partitioning a Line Segment by a BSP Tree
		13.2.5	Partitioning a Convex Polygon by a BSP Tree
		13.3	Point in Polygon
		13.3.1	Point in Triangle
		13.3.2	Point in Convex Polygon
		13.3.3	Point in General Polygon
		13.3.4	Faster Point in General Polygon
		13.3.5	A Grid Method
		13.4	Point in Polyhedron
		13.4.1	Point in Tetrahedron
		13.4.2	Point in Convex Polyhedron
		13.4.3	Poin tin General Polyhedron
		13.5	Boolean Operations on Polygons
		13.5.1	The Abstract Operations
		13.5.2	The Two Primitive Operations
		13.5.3	Boolean Operations Using BSP Trees
		13.5.4	Other Algorithms
		13.6	Boolean Operations on Polyhedra
		13.6.1	Abstract Operations
		13.6.2	Boolean Operations Using BSP Trees
		13.7	Convex Hulls
		13.7.1	Convex Hulls in 2D
		13.7.2	Convex Hulls in 3D
		13.7.3	Convex Hulls in Higher Dimensions
		13.8	Delaunay Triangulation
		13.8.1	Incremental Construction in 2D
		13.8.2	Incremental Construction in general Dimensions
		13.8.3	Construction by Convex Hull
		13.9	Polygon Partitioning
		13.9.1	Visibility Graph of a Simple Polygon
		13.9.2	Triangulation
		13.9.3	Triangulation by Horizontal Decomposition
		13.9.4	Convex Partitioning
		13.10	Circumscribed and Inscribed Balls
		13.1001	Circumscribed Ball
		13.1002	Inscribed Ball
		13.11	Minimum Bounds for Point Sets
		13.1101	Minimum-Area Rectangle
		13.1102	Minimum-Volume Box
		13.1103	Minimum-Area Circle
		13.1104	Minimum-Volume Sphere
		13.1105	Miscellaneous
		13.12	Area and Volume Measurements
		13.1201	Area of a 2D Polygon
		13.1202	Area of a 3D Polygon
		13.1203	Volume of a Polyhedron
		Appendix A	Numerical Methods
		A.1	Solving Linear Systems
		A.1.1	Special Case: Solving a Triangular System
		A.1.2	Gaussian Elimination
		A.2	Systems of Polynomials
		Appendx B	Trigonometry
		Appendix C	Basic Formulas for Geometric Primitives
			References
			Index
			About the Authors

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