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E-raamat: Making Images with Mathematics

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Making Images with MathematicsSuurem pilt
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This textbook teaches readers how to turn geometry into an image on a computer screen. This exciting journey begins in the schools of the ancient Greek philosophers, and describes the major events that changed peoples perception of geometry. The readers will learn how to see geometry and colors beyond simple mathematical formulas and how to represent geometric shapes, transformations and motions by digital sampling of various mathematical functions.Special multiplatform visualization software developed by the author will allow readers to explore the exciting world of visual immersive mathematics, and the book software repository will provide a starting point for their own sophisticated visualization applications.







Making Images with Mathematics serves as a self-contained text for a one-semester computer graphics and visualization course for computer science and engineering students, as well as a reference manual for researchers and developers.

Arvustused

This book is intended for computer science and engineering students and computer graphics practitioners. It can also be used by teachers as a reference material for a one-semester course of computer graphics and visualization. The book is self-contained and presents the theory in a very accessible way with many visual examples. (Agniezka Lisowska, zbMATH 1483.68003, 2022)

1 From Ancient Greeks to Pixels
1(24)
1.1 Drawing with Computer
1(5)
1.1.1 How We See the World
1(1)
1.1.2 Displaying Images
2(1)
1.1.3 Computer Monitors
3(2)
1.1.4 Storing Images in Computers
5(1)
1.2 From "Earth Measuring" to Computer Graphics
6(4)
1.2.1 Evolution of Geometry
6(2)
1.2.2 Computer Graphics and Beyond
8(2)
1.3 We Need Digits to Draw with Computer
10(9)
1.3.1 2D Cartesian Coordinates
11(1)
1.3.2 Polar Coordinates
11(3)
1.3.3 3D Cartesian Coordinates
14(1)
1.3.4 Cylindrical Coordinates
15(1)
1.3.5 Spherical Coordinates
16(1)
1.3.6 Visualization Pipeline
16(3)
1.4 Geometric Algebra
19(3)
1.4.1 Geometric Modeling
19(1)
1.4.2 Rendering Geometry to Images
20(1)
1.4.3 Mathematical Functions in Geometric Modeling
20(2)
1.5 Summary
22(1)
References
23(2)
2 Geometric Shapes
25(60)
2.1 Sampling Geometry
25(1)
2.2 Points
26(1)
2.3 Curves
26(16)
2.3.1 Straight Line
27(3)
2.3.2 Circle
30(3)
2.3.3 Ellipse
33(4)
2.3.4 Plethora of Curves
37(3)
2.3.5 Three-Dimensional Curves
40(2)
2.4 Surfaces
42(21)
2.4.1 Plane
43(5)
2.4.2 Polygons
48(1)
2.4.3 Bilinear Surfaces
49(2)
2.4.4 Quadrics
51(4)
2.4.5 Making Surfaces by Sweeping Curves
55(8)
2.5 Solid Objects
63(19)
2.5.1 Defining Solids by Parametric Functions
64(9)
2.5.2 Constructive Solid Geometry by Functions
73(9)
2.6 Summary
82(1)
References
83(2)
3 Transformations
85(38)
3.1 Mathematics of Transformations
85(2)
3.2 Matrix Representation of Affine Transformations
87(7)
3.2.1 Homogeneous Coordinates
87(1)
3.2.2 Identity Transformation
88(1)
3.2.3 Scaling and Reflection
89(2)
3.2.4 Shear
91(1)
3.2.5 Rotation
91(3)
3.2.6 Translation
94(1)
3.3 Composition of Transformations
94(13)
3.3.1 Rotation About a Point
95(1)
3.3.2 Scaling and Reflection About Points and Lines in 2D Space
95(2)
3.3.3 Deriving Matrix of an Arbitrary 2D Affine Transformation
97(1)
3.3.4 Rotation About an Axis
97(5)
3.3.5 Reflections About Any Point, Axis, or Plane in 3D Space
102(2)
3.3.6 Deriving Matrix of an Arbitrary 3D Affine Transformation
104(1)
3.3.7 Matrix Algebra Laws
105(1)
3.3.8 Definition of Sweeping by Transformation Matrices
106(1)
3.4 Projection Transformations
107(13)
3.4.1 Implementations of Projection Transformations
108(1)
3.4.2 Classifications of Projection Transformations
109(3)
3.4.3 Parallel Orthographic Projections
112(1)
3.4.4 Axonometric Parallel Projections
112(1)
3.4.5 Perspective Projections
112(4)
3.4.6 Axonometric Perspective Projections
116(1)
3.4.7 Projections on Any Plane
117(1)
3.4.8 Viewing Frustum
118(1)
3.4.9 Stereo Projection
118(2)
3.5 Summary
120(1)
References
121(2)
4 Motions
123(20)
4.1 Animating Geometry
123(8)
4.1.1 Motion of Points
123(4)
4.1.2 Animating Shape Definitions
127(1)
4.1.3 Time-Dependent Affine Transformations
128(2)
4.1.4 Shape Morphing
130(1)
4.2 Physically Based Motion Specifications
131(10)
4.2.1 Motion with Constant Acceleration
131(3)
4.2.2 Motion Under Gravity
134(4)
4.2.3 Rotation Motion
138(3)
4.3 Summary
141(1)
References
141(2)
5 Adding Visual Appearance to Geometry
143(18)
5.1 Illumination
143(1)
5.2 Lighting
144(6)
5.2.1 Ambient Reflection
146(1)
5.2.2 Diffuse Reflection
146(1)
5.2.3 Specular Reflection
147(1)
5.2.4 Phong Illumination
148(2)
5.3 Shading
150(3)
5.3.1 Flat Shading
150(1)
5.3.2 Gouraud Shading
151(1)
5.3.3 Phong Shading
152(1)
5.4 Shadows and Transparency
153(1)
5.5 Textures
154(3)
5.6 Colors by Functions
157(1)
5.7 Summary
158(2)
References
160(1)
6 Putting Everything Together
161(16)
6.1 Interactive and Real-Time Rendering
161(1)
6.2 Positioning the Observer
161(6)
6.2.1 Direction Cosines
162(2)
6.2.2 Fixed Angles
164(2)
6.2.3 Euler Angles
166(1)
6.3 Fast Rendering of Large Scenes
167(8)
6.3.1 Hierarchical Representation
167(1)
6.3.2 Current Transformation Matrix
168(1)
6.3.3 Logical and Spatial Organizations
169(2)
6.3.4 Bounding Boxes
171(1)
6.3.5 Level of Detail
172(3)
6.4 Summary
175(1)
References
176(1)
7 Let's Draw
177(68)
7.1 Programing Computer Graphics and Visualization
177(1)
7.2 Drawing with OpenGL
177(35)
7.2.1 Introduction to OpenGL
177(4)
7.2.2 Interaction with GLUT
181(1)
7.2.3 Drawing Parametric Shapes with OpenGL
182(11)
7.2.4 Animation and Surface Morphing with OpenGL and GLUT
193(3)
7.2.5 Interactive Solid Modeling with OpenGL and GLUT
196(16)
7.3 Drawing with POV-Ray
212(9)
7.3.1 The Persistence of Vision Ray Tracer
212(6)
7.3.2 Function-Based Shape Modeling with POV-Ray
218(3)
7.4 Drawing with VRML/X3D
221(19)
7.4.1 Introduction to VRML
221(5)
7.4.2 Introduction to X3D
226(1)
7.4.3 Function-Based Extension of VRML
226(6)
7.4.4 Function-Based Extension of X3D
232(8)
7.5 Drawing with Shape Explorer
240(3)
7.6 Summary
243(1)
References
243(2)
Index 245
Dr. Alexei Sourin got his MSc (1983) and PhD (1988) degrees in Russia in the prestigious National Research Nuclear University MEPHI (Moscow Engineering Physics Institute) where he also worked on challenging research tasks of visualization of complex atomic structures. Back in 1993, Dr. Sourin came to Singapore to become a faculty at the School of Computer Science and Engineering of the renowned Nanyang Technological University. Professor Sourin is working on research projects and teaching in the areas of computer graphics, virtual reality, user-computer interaction and sonification of geometry. Alexei Sourin is a Senior Member of IEEE. For many years, he was a Chair of the IFIP workgroup Computer Graphics and Virtual Reality. Dr. Sourin has many research awards, and he was invited to give talks at many scientific events. He is also a coordinator of the annual international conferences on cyberworldsimmersive virtual communities that immensely augment the way we interact, participatein business and receive information throughout the world.
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