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Vectors and Matrices for Geometric and 3D Modeling [Mīkstie vāki]

  • Formāts: Paperback / softback, 272 pages, height x width: 280x216 mm
  • Izdošanas datums: 30-Nov-2020
  • Izdevniecība: Industrial Press Inc.,U.S.
  • ISBN-10: 0831136553
  • ISBN-13: 9780831136550
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Vectors and Matrices for Geometric and 3D ModelingPalielināt
  • Formāts: Paperback / softback, 272 pages, height x width: 280x216 mm
  • Izdošanas datums: 30-Nov-2020
  • Izdevniecība: Industrial Press Inc.,U.S.
  • ISBN-10: 0831136553
  • ISBN-13: 9780831136550
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780831136550.html
Keywords:
Vectors are perhaps the most important mathematical objects used in modeling and animation. They have the properties of magnitude and direction, and provide visual understanding of model construction and analysis. Matrices are natural and hardworking partners of vectors.
This work presents lessons on vectors and matrices in geometric and 3D modeling&;the mathematics at the foundation of computer graphics applications. The lessons appear as chapters, generally organized from introductory to more complex topics. Within each chapter, there is a similar order of elementary-to-advanced discussion. 
Here are topics that are usually published in briefer form in more advanced texts as part of their supporting mathematics. In this work, vectors and matrices are the main subjects. This text offers an easier-to-understand introduction to the main ideas behind vectors and matrices, stripped of formalism, and leading directly to geometric modeling. It demonstrates the relationships between vectors, matrices, basis vectors and barycentric coordinates, all of which are not usually seen in ordinary texts. This text also discusses how these concepts are applied to produce curves and surfaces, and how they facilitate the analysis of spatial relationships. 
For those readers beginning studies in geometric and 3D modeling, animation, CGI, or CAD/CAM, this work serves as an introduction to vectors and matrices, and provides a good start to understanding how they are applied. For instructors, this book can be a primary text or supplement to more advanced or specialized texts on geometric and 3D modeling.
           
Features
  • More than 150 illustrations support visual understanding of the content.
  • 100+ exercises and extended solutions enhance the classroom environment.
  • A comprehensive range of topics offers an in-depth look at the math underlying 3D modeling and animation courses.
  • Linear algebra and calculus are not prerequisites.
Acknowledgments xi
Preface xiii
1 Vectors PDQ
1(10)
1.1 A Very Brief Overview
1(1)
1.2 With Comments Added
2(2)
1.3 And What Follows
4(1)
1.4 Backstory: The Very Short Version
5(1)
1.5 Notation Motivation
6(5)
Vectors
6(2)
Matrices
8(1)
Indexing
9(1)
Curves and Surfaces
9(2)
2 The Visual Vector
11(12)
2.1 Directed Line Segment
11(3)
2.2 Free and Fixed Vectors
14(1)
2.3 Vector Addition
15(2)
2.4 Vector Components
17(1)
2.5 Vector Multiplication
18(3)
2.6 A Geometry Problem
21(1)
2.7 The Idea of a Vector as a Displacement
22(1)
3 The Algebraic Vector
23(28)
3.1 There's a Vector in Your Coordinate System
23(2)
3.2 Form and Equality
25(1)
3.3 Magnitude and Direction
26(4)
Magnitude
27(1)
Direction
28(1)
Unit Vectors
29(1)
3.4 Addition and Subtraction
30(1)
3.5 Products of Vectors
31(5)
Scalar Product
32(1)
Vector Product
33(2)
Scalar Triple Product
35(1)
Vector Triple Product
35(1)
3.6 Functions and Derivatives
36(1)
3.7 Linear Vector Spaces
37(2)
3.8 Vector Equations
39(1)
3.9 Quaternions
40(4)
3.10 Geometry Problems
44(2)
Problem 1 The Law of Sines
44(1)
Problem 2 The Area of a Triangle
45(1)
Problem 3 A Property of Triangles
45(1)
3.11 Exercises
46(5)
4 Matrix Basics
51(12)
4.1 Equality and Order
51(1)
4.2 Row and Column Matrices
52(1)
4.3 Transpose of a Matrix
53(1)
4.4 Addition and Subtraction
54(1)
4.5 Multiplication
55(3)
4.6 Partitioning a Matrix
58(2)
4.7 Summary of Matrix Properties
60(1)
4.8 Exercises
60(3)
5 Special Matrices
63(16)
5.1 Identity Matrix
63(1)
5.2 Diagonal Matrix
64(1)
5.3 Trace of a Matrix
65(1)
5.4 Symmetric Matrix
66(1)
5.5 Orthogonal Matrix
66(1)
5.6 Inverse of a Matrix
67(1)
5.7 Collinear Vectors, Eigenvalues, and Eigenvectors
68(3)
5.8 Similar Matrices
71(1)
5.9 Determinants
72(2)
5.10 Summary of Determinant Properties
74(1)
5.11 Exercises
75(4)
6 Basis Vectors
79(10)
6.1 Oblique Coordinate Systems
79(1)
6.2 Basis Vector Basics
80(2)
6.3 Change of Basis
82(2)
6.4 Reciprocal Basis Vectors
84(2)
6.5 Orthogonal Basis Vectors and Matrices
86(1)
6.6 Frames
86(3)
7 Barycentric Coordinate Systems
89(10)
7.1 Origins
89(1)
7.2 Barycentric Coordinates
89(1)
7.3 Relative to Two Points
90(2)
7.4 Relative to a Triangle
92(4)
7.5 Relative to a Tetrahedron
96(1)
7.6 Generalized Barycentric Coordinates
97(2)
8 Translation and Rotation
99(26)
8.1 Translation
99(5)
8.2 Rotation in the Plane
104(4)
8.3 Rotation in Space
108(2)
8.4 Rotation about an Arbitrary Axis
110(4)
8.5 Eigenvectors and Equivalent Rotations
114(1)
8.6 Rotation and Quaternions
115(1)
8.7 Combining Translation and Rotation
116(5)
8.8 Kinematics
121(2)
8.9 Exercises
123(2)
9 More Transformations
125(32)
9.1 Translation
125(1)
9.2 Rotation
126(1)
9.3 Scaling
127(6)
9.4 Shear
133(2)
9.5 Reflection
135(4)
9.6 Inversion
139(3)
9.7 Projection
142(6)
9.8 Sweep Transformations
148(7)
Translational Sweep
150(1)
Generalized Translational Sweep
150(3)
Rotational Sweep
153(1)
Translation with Deformation Sweep
154(1)
9.9 Exercises
155(2)
10 Vector-Defined Geometric Objects I
157(22)
10.1 Points
157(1)
10.2 Lines
158(4)
Line Through a Point and Parallel to a Vector
158(3)
Line Defined by Two Points
161(1)
10.3 Planes
162(2)
Through a Point and Parallel to Two Independent Vectors
162(1)
Three-Point Definition
163(1)
Point on the Plane and the Unit Normal to It
163(1)
Normal Vector from the Origin to the Plane
164(1)
10.4 Polygons
164(5)
Definition of a Polygon
164(1)
Properties of Polygons
165(2)
Convex Hull of a Polygon
167(1)
Triangles: A Very Special Polygon
168(1)
Data Structure for Polygons
168(1)
10.5 Polyhedra
169(7)
Definition of a Polyhedron
169(1)
Properties of Polyhedra
170(1)
Convex Hull of a Polyhedron
171(1)
Connectivity Matrix
171(2)
Data Structure for Polyhedra
173(1)
Euler's Formula for Simple Polyhedra
174(1)
Euler's Formula for Nonsimple Polyhedra
174(2)
10.6 Exercises
176(3)
11 Vector-Defined Geometric Objects II
179(22)
11.1 Curve-Defining Functions
179(3)
11.2 Bezier Curves
182(2)
11.3 Local Properties of a Curve
184(9)
11.4 Global Properties of a Curve
193(2)
11.5 Surface-Defining Functions
195(1)
11.6 Local Properties of a Surface
196(2)
11.7 Global Properties of a Surface
198(3)
12 Spatial Relationships
201(16)
12.1 Distance
201(1)
12.2 Minimum Distances
202(6)
Minimum Distance Between a Point and a Curve
203(1)
Minimum Distance Between a Point and a Plane
203(1)
Minimum Distance Between a Point and a Surface
204(1)
Minimum Distance Between Two Curves
205(1)
Minimum Distance Between a Curve and a Plane
205(1)
Minimum Distance Between a Curve and a Surface
206(1)
Minimum Distance Between Two Surfaces
207(1)
12.3 Line Intersections
208(4)
Intersection of Two Lines
208(1)
Intersection of a Line and a Plane
209(1)
Intersection of a Line and a Curve
210(1)
Intersection of a Line and a Surface
211(1)
12.4 Plane Intersections
212(2)
Intersection of Two Planes
212(1)
Intersection of a Plane and a Curve
213(1)
Intersection of a Plane and a Surface
214(1)
12.5 Curve Intersections
214(3)
Intersection of Two Curves
214(1)
Intersection of a Curve and a Surface
215(2)
Solutions
217(30)
Chapter 3 The Algebraic Vector
217(7)
Chapter 4 Matrix Basics
224(3)
Chapter 5 Special Matrices
227(6)
Chapter 8 Translation and Rotation
233(4)
Chapter 9 More Transformations
237(3)
Chapter 10 Vector-Defined Geometric Objects I
240(7)
Index 247
Michael E. Mortenson does independent research and writes on topics in geometric and 3D modeling. He is a former research scientist with a major aerospace corporation, and the author of several successful textbooks, including Geometric Modeling, Third Edition, Mathematics for Computer Graphics Applications, 2e, Geometric Transformations for 3D Modeling, 2e, and 3D Modeling, Animation, and Rendering: An Illustrated Lexicon. These works have garnered over 2400 citations. He is a graduate of the UCLA School of Engineering.