An integrated introduction to computer graphics and geometric modeling:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Series: | A Chapman & Hall book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIX, 543 S. Ill., graph. Darst. |
| ISBN: | 9781439803349 |
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MARC
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| 100 | 1 | |a Goldman, Ron |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An integrated introduction to computer graphics and geometric modeling |c Ronald Goldman |
| 246 | 1 | 3 | |a Computer graphics and geometric modeling |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XXIX, 543 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A Chapman & Hall book | |
| 650 | 0 | |a Computer graphics | |
| 650 | 0 | |a Three-dimensional display systems | |
| 650 | 0 | |a Curves on surfaces / Mathematical models | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Computer graphics | |
| 650 | 4 | |a Curves on surfaces |x Mathematical models | |
| 650 | 4 | |a Three-dimensional display systems | |
| 650 | 0 | 7 | |a Computergrafik |0 (DE-588)4010450-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |D s |
| 689 | 0 | 1 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |D s |
| 689 | 0 | 2 | |a Computergrafik |0 (DE-588)4010450-3 |D s |
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| _version_ | 1822490889769975808 |
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Contents
Foreword
xv
Dedication
xvii
Preface
xix
Author
xxix
I Two-Dimensional Computer Graphics: From Common
Curves to Intricate Fractals
1
Turtle Graphics
.3
1.1
Turtle Graphics
.3
1.2
Turtle Commands
.4
1.3
Turtle Programs
.7
1.4
Summary
.9
Exercises
.9
2
Fractals from Recursive Turtle Programs
.13
2.1
Fractals
. 13
2.2
Looping Lemmas
. 13
2.3
Fractal Curves and Recursive Turtle Programs
. 17
2.3.1
Fractal Gaskets
. 17
2.3.2
Bump Fractals
. 19
2.4
Summary: Fractals
—
Recursion Made Visible
.20
Exercises
.21
Programming Projects
.23
3
Some Strange Properties of Fractal Curves
.29
3.1
Fractal Strangeness
.29
3.2
Dimension
.29
3.2.1
Fractal Dimension
.31
3.2.2
Computing Fractal Dimension from Recursive Turtle Programs
.32
3.3
Differentiability
.32
3.4
Attraction
.34
3.4.1
Base Cases for the Sierpinski Gasket
.34
3.4.2
Base Cases for the Koch Curve
.35
3.4.3
Attractors
.36
3.5
Summary
.36
Exercises
.37
vi
Contents
4
Affine
Transformations
.39
4.1
Transformations
.39
4.2
Conformai Transformations
.40
4.2.1
Translation
.40
4.2.2
Rotation
.41
4.2.3 Uniform
Scaling.
42
4.3
The Algebra of
Affine
Transformations
.43
4.4
The Geometry of
Affine
Transformations
.44
4.5 Affine
Coordinates and
Affine
Matrices
.45
4.6
Conformai
Transformations: Revisited
.46
4.7
General
Affine
Transformations
.46
4.7.1
Image of One Point and Two Lineary Independent Vectors
.47
4.7.2
Nonuniform
Scaling
.48
4.7.3
Image of Three Noncollinear Points
.50
4.8
Summary
.51
4.8.1
Affine
Transformations and
Affine
Coordinates
.51
4.8.2
Matrices for
Affine
Transformations in the Plane
.53
Exercises
.54
5
Affine
Geometry: A Connect-the-Dots Approach to Two-Dimensional
Computer Graphics
.61
5.1
Two Shortcomings of Turtle Graphics
.61
5.2
Affine
Graphics
.62
5.2.1
The
CODO
Language
.62
5.2.2
Sample
CODO
Programs
.63
5.3
Summary
.65
Exercises
.67
6
Fractals from Iterated Function Systems
.71
6.1
Generating Fractals by Iterating Transformations
.71
6.2
Fractals as Fixed Points of Iterated Function Systems
.73
6.3
Fractals as Attractors
.74
6.4
Fractals with Condensation Sets
.74
6.5
Summary
.76
Exercises
.77
Programming Project
.79
7
The Fixed-Point Theorem and Its Consequences
.81
7.1
Fixed Points and Iteration
.81
7.2
The Trivial Fixed Point Theorem
.82
7.3
Consequences of the Trivial Fixed-Point Theorem
.84
7.3.1
Root Finding Methods
.84
7.3.2
Relaxation Methods
.87
7.3.3
Fractals
.89
7.3.3.1
Compact Sets and the
Haussdorf
Metric
.90
7.3.3.2
Contractive Transformations and Iterated Function Systems
.91
7.3.3.3
Fractal Theorem, Fractal Algorithm, and Fractal Strategy
.92
7.4
Summary
.93
Exercises
.94
Programming Projects
.98
Contents
vii
8
Recursive Turtle Programs and
Conformai
Iterated
Function Systems
.101
8.1
Motivating Questions
. 101
8.2
The Effect of Changing the Turtle's Initial State
. 101
8.3
Equivalence Theorems
. 103
8.4
Conversion Algorithms
. 106
8.4.1
Ron's Algorithm
.106
8.4.2
Tao's Algorithm
. 107
8.5
Bump Fractals
. 109
8.6
Summary
.110
Exercises
.
Ill
Programming Projects
. 113
II Mathematical Methods for Three-Dimensional
Computer Graphics
9
Vector Geometry: A Coordinate-Free Approach
.117
9.1
Coordinate-Free Methods
. 117
9.2
Vectors and Vector Spaces
. 118
9.3
Points and
Affine
Spaces
. 119
9.4
Vector Products
. 120
9.4.1
Dot Product
. 121
9.4.2
Cross Product
. 122
9.4.3
Determinant
. 123
9.5
Summary
.123
Appendix A: The Nonassociativity of the Cross Product
. 124
Appendix B: The Algebra of Points and Vectors
. 126
Exercises
. 128
10
Coordinate Algebra
.131
10.1
Rectangular Coordinates
. 131
10.2
Addition, Subtraction, and Scalar Multiplication
.131
10.3
Vector Products
. 132
10.3.1
Dot Product
. 133
10.3.2
Cross Product
.133
10.3.3
Determinant
.134
10.4
Summary
. 134
Exercises
.135
11
Some Applications of Vector Geometry
.139
11.1
Introduction
. 139
11.2
Trigonometric Laws
. 139
11.2.1
Law of Cosines
. 139
11.2.2
Law of Sines
.140
11.3
Representations for Lines and Planes
. 141
11.3.1
Lines
.141
11.3.2
Planes
. 141
viii Contents
11.4
Metric
Formulas
.142
11.4.1
Distance
. 142
11.4.1.1
Distance
between Two
Points
.142
11.4.1.2
Distance
between
a Point
and a Line
. 143
11.4.1.3
Distance
between
a Point and a Plane
. 143
11.4.1.4
Distance
between Two
Lines
. 144
11.4.2
Area.
145
11.4.2.1
Triangles
and Parallelograms
. 145
11.4.2.2
Polygons:
Newelľs
Formula
. 146
11.4.3
Volume
.147
11.5
Intersection Formulas for Lines and Planes
. 148
11.5.1
Intersecting Two
Lines
. 148
11.5.2
Intersecting Three
Planes
.149
11.5.3
Intersecting Two Planes
. 150
11.6
Spherical Linear Interpolation
. 151
11.7
Inside-Outside Tests
. 153
11.7.1
Ray Casting
. 153
11.7.2
Winding Number
.154
11.8
Summary
. 156
11.8.1
Trigonometric Laws
. 156
11.8.2
Metric Formulas
. 157
11.8.2.1
Distance
.157
11.8.2.2
Area
.157
11.8.2.3
Volume
.158
11.8.3
Intersections
. 158
11.8.4
Interpolation
.158
11.8.5
Winding Number
. 158
Exercises
.159
12
Coordinate-Free Formulas for
Affine
and
Projective
Transformations
.163
12.1
Transformations for Three-Dimensional Computer Graphics
. 163
12.2
Affine
and
Projective
Transformations
. 163
12.3
Rigid Motions
. 164
12.3.1
Translation
.,. 165
12.3.2
Rotation
. 165
12.3.3
Mirror Image
. 167
12.4
Scaling
. 168
12.4.1
Uniform Scaling
. 169
12.4.2
Nonuniform
Scaling
.169
12.5
Projections
.170
12.5.1
Orthogonal Projection
. 171
12.5.2
Perspective
.171
12.6
Summary
.173
12.6.1
Affine
and
Projective
Transformations without Matrices
. 173
12.6.2
Formulas for
Affine
and
Projective
Transformations
. 174
Exercises
. 174
Contents ix
13 Matrix
Representations for
Affine
and Projective
Transformations
.179
13.1
Matrix Representations for
Affine
Transformations
.179
13.2
Linear Transformation Matrices and Translation Vectors
.181
13.2.1
Linear Transformation Matrices
.182
13.2.2
Translation Vectors
.183
13.3
Rigid Motions
. 183
13.3.1
Translation
. 183
13.3.2
Rotation
. 184
13.3.3
Mirror Image
. 185
13.4
Scaling
. 187
13.4.1
Uniform Scaling
.187
13.4.2
Nonuniform
Scaling
.187
13.5
Projections
.188
13.5.1
Orthogonal Projection
. 189
13.6
Perspective
. 189
13.6.1
Projective Transformations and Homogeneous Coordinates
. 190
13.6.2
Matrices for Perspective Projections
. 191
13.7
Summary
.193
13.7.1
Matrix Representations for
Affine
and Projective
Transformations
. 193
13.7.2
Matrices for
Affine
and Projective Transformations
.194
Exercises
. 195
Programming Projects
.199
14
Projective Space versus the Universal Space of Mass-Points
.205
14.1
Algebra and Geometry
.205
14.2
Projective Space: The Standard Model
.206
14.3
Mass-Points: The Universal Model
.210
14.4
Perspective and
Pseudoperspective
.213
14.4.1
Perspective and the Law of the Lever
.213
14.4.2
Pseudoperspective
and Pseudodepth
.214
14.5
Summary
.218
Exercises
.219
15
Quaternions: Multiplication in the Space of Mass-Points
.223
15.1
Vector Spaces and Division Algebras
.223
15.2
Complex Numbers
.224
15.3
Quaternions
.227
15.3.1
Quaternion Multiplication
.227
15.3.2
Quaternion Representations for
Conformai
Transformations
.230
15.3.3
Quaternions versus Matrices
.232
15.3.4
Avoiding Distortion
.233
15.3.5
Key Frame Animation
.234
15.3.6
Conversion Formulas
.235
15.4
Summary
.238
Exercises
.239
Programming Projects
.245
χ
Contents
III Three-Dimensional
Computer Graphics:
Realistic Rendering
16
Color and Intensity
.249
16.1
Motivation
.249
16.2
The RGB Color Model
.249
16.3
Ambient Light
.250
16.4
Diffuse Reflection
.251
16.5
Specular Reflection
.252
16.6
Total Intensity
.254
16.7
Summary
.255
Exercises
.256
17
Recursive Ray Tracing
.257
17.1
Raster Graphics
.257
17.2
Recursive Ray Tracing
.257
17.3
Shadows
.259
17.4
Reflection
.260
17.5
Refraction
.261
17.6
Summary
.264
Exercises
.265
18
Surfaces I: The General Theory
.267
18.1
Surface Representations
.267
18.1.1
Implicit Surfaces
.267
18.1.2
Parametric Surfaces
.267
18.1.3
Deformed Surfaces
.268
18.1.4
Procedural Surfaces
.268
18.2
Surface Normals
.269
18.2.1
Implicit Surfaces
.269
18.2.2
Parametric Surfaces
.269
18.2.3
Deformed Surfaces
.270
18.3
Ray-Surface Intersections
.272
18.3.1
Implicit Surfaces
.272
18.3.2
Parametric Surfaces
.272
18.3.3
Deformed Surfaces
.273
18.4
Mean and Gaussian Curvature
.274
18.4.1
Implicit Surfaces
.274
18.4.2
Parametric Surfaces
.275
18.4.3
Deformed Surfaces
.275
18.5
Summary
.275
18.5.1
Implicit Surfaces
.276
18.5.2
Parametric Surfaces
.276
18.5.3
Deformed Surfaces
.278
Exercises
.278
19
Surfaces II: Simple Surfaces
.281
19.1
Simple Surfaces
.281
19.2
Intersection Strategies
.281
19.3
Planes and Polygons
.282
Contents xi
19.4
Natural
Quadrics.284
19.4.1
Spheres
.284
19.4.1.1
Intersecting a Line and a Circle
.285
19.4.1.2
Inversion Formulas for the Line
.285
19.4.2
Cylinders
.287
19.4.2.1
Intersecting a Line and an Infinite Cylinder
.287
19.4.2.2
Intersecting a Line and a Bounded Cylinder
.289
19.4.3
Cones
.290
19.4.4
Ellipsoids, Elliptical Cylinders, and Elliptical Cones
.292
19.5
General Quadric Surfaces
.292
19.6
Tori
.295
19.6.1
Bounding the Torus
.298
19.7
Surfaces of Revolution
.299
19.8
Summary
.303
Exercises
.304
Programming Projects
.306
20
Solid Modeling
.309
20.1
Solids
.309
20.2
Constructive Solid Geometry
(CSG)
.309
20.3
Boundary Representations (B-Rep)
.313
20.4
Octrees
.317
20.5
Summary
.
3]9
Exercises
.319
Programming Projects
.322
21
Shading
.325
21.1
Polygonal Models
.325
21.1.1
Newell's Formula for the Normal to a Polygon
.326
21.2
Uniform Shading
.326
21.3
Gouraud Shading
.327
21.4
Phong Shading
.331
21.4.1
Naive Phong Shading
.331
21.4.2
Fast Phong Shading and Diffuse Reflection
.332
21.4.3
Fast Phong Shading and Specular Reflection
.334
21.4.4
Phong Shading and Spherical Linear Interpolation
.335
21.5
Summary
.337
Exercises
.339
Programming Project
.339
22
Hidden Surface Algorithms
.341
22.1
Hidden Surface Algorithms
.341
22.2
The Heedless Painter
.342
22.3
z-Buffer (Depth Buffer)
.342
22.4
Scan Line
.343
22.5
Ray Casting
.346
22.6
Depth Sort
.347
22.6.1
Polygon Splitting
.350
22.7
BSP-Tree
.351
xii Contents
22.8
Summary
.352
Exercises
.352
Programming Projects
.353
23
Radiosity
.355
23.1
Radiosity
.355
23.2
The Radiosity Equations
.355
23.2.1
The Rendering Equation
.356
23.2.2
The Radiosity Equation: Continuous Form
.356
23.2.3
The Radiosity Equation: Discrete Form
.359
23.3
Form Factors
.361
23.3.1
Hemi-Cubes
.363
23.4
The Radiosity Rendering Algorithm
.366
23.5
Solving the Radiosity Equations
.368
23.5.1
Gathering
.368
23.5.2
Shooting: Progressive Refinement
.370
23.6
Summary
.372
Exercises
.373
Programming Project
.375
IV Geometric Modeling: Freedom Curves and Surfaces
24 Bezier
Curves and Surfaces
.379
24.1
Interpolation and Approximation
.379
24.2
The
de Casteljau
Evaluation Algorithm
.380
24.3
The Bernstein Representation
.383
24.4
Geometric Properties of
Bezier
Curves
.384
24.4.1 Affine
Invariance.
385
24.4.2
Convex Hull Property
.386
24.4.3
Variation Diminishing Property
.386
24.4.4
Interpolation of the First and Last Control Points
.,.387
24.5
Differentiating the
de
Casteljau Algorithm
.388
24.5.1
Smoothly Joining Two
Bezier
Curves
.389
24.5.2
Uniqueness of the
Bezier
Control Points
.390
24.6
Tensor Product
Bezier
Patches
.:.391
24.7
Summary
.395
Exercises
.397
25 Bezier
Subdivision
.401
25.1
Divide and Conquer
.401
25.2
The
de
Casteljau Subdivision Algorithm
.401
25.3
Rendering and Intersection Algorithms
.405
25.3.1
Rendering and Intersecting
Bezier
Curves
.405
25.3.2
Rendering and Intersecting
Bezier
Surfaces
.407
25.4
The Variation Diminishing Property of
Bezier
Curves
.409
25.5
Joining
Bezier
Curves Smoothly
.410
25.6
Summary
.411
Exercises
.412
Programming Projects
.414
Contents xiii
26
Blossoming
.417
26.1 Motivation.417
26.2
The Blossom
.418
26.3
Blossoming and the
de Casteljau
Algorithm
.419
26.3.1 Bezier
Subdivision from Blossoming
.422
26.4
Differentiation and the Homogeneous Blossom
.423
26.4.1
Homogenization and the Homogeneous Blossom
.423
26.4.2
Differentiating the
de
Casteljau Algorithm
.427
26.4.3
Conversion Algorithms between Monomial and
Bezier Form.430
26.5
Summary
.431
Exercises
.434
27
B-Spline Curves and Surfaces
.437
27.1
Motivation
.437
27.2
Blossoming and the Local
de Boor
Algorithm
.438
27.3
B-Spline Curves and the Global
de Boor
Algorithm
.441
27.4
Smoothness
.443
27.5
Labeling and Locality in the Global
de Boor
Algorithm
.445
27.6
Every Spline is a B-Spline
.446
27.7
Geometric Properties of B-Spline Curves
.448
27.8
Tensor Product B-Spline Surfaces
.449
27.9
Non-Uniform Rational B-Splines (NURBS)
.451
27.10
Summary
.452
Exercises
.453
28
Knot Insertion Algorithms for B-Spline Curves and Surfaces
.457
28.1
Motivation
.457
28.2
Knot Insertion
.457
28.3
Local Knot Insertion Algorithms
.458
28.3.1
Boehm's Knot Insertion Algorithm
.458
28.3.2
The Oslo Algorithm
.460
28.3.3
Conversion from B-Spline to Piecewise
Bezier Form.461
28.3.4
The Variation Diminishing Property for B-Spline Curves
.461
28.3.5
Algorithms for Rendering and Intersecting B-Spline Curves
and Surfaces
.463
28.4
Global Knot Insertion Algorithms
.464
28.4.1
The Lane-Riesenfeld Algorithm
.464
28.4.2
Schaefer's Knot Insertion Algorithm
.467
28.4.3
Convergence of Knot Insertion Algorithms
.468
28.4.4
Algorithms for Rendering and Intersecting B-Spline Curves
and Surfaces Revisited
.470
28.5
Summary
.471
Exercises
.474
Programming Project
.475
29
Subdivision Matrices and Iterated Function Systems
.477
29.1
Subdivision Algorithms and Fractal Procedures
.477
29.2
Subdivision Matrices
.478
29.2.1
Subdivision Matrices for
Bezier
Curves
.479
29.2.2
Subdivision Matrices for Uniform B-Spline Curves
.481
xiv Contents
29.3
Iterated Function Systems Built from Subdivision Matrices
.485
29.3.1
Lifting the Control Points to Higher Dimensions
.485
29.3.2
Normal Curves
.489
29.4
Fractals with Control Points
.491
29.5
Summary
.493
29.5.1 Bezier
Curves
.494
29.5.2
Uniform B-Splines
.495
Exercises
.496
Programming Projects
.497
30
Subdivision Surfaces
.499
30.1
Motivation
.499
30.2
Box Splines
.500
30.2.1
Split and Average
.500
30.2.2
A Subdivision Procedure for Box Spline Surfaces
.500
30.3
Quadrilateral Meshes
.503
30.3.1
Centroid Averaging
.505
30.3.1.1
Uniform Bicubic B-Spline Surfaces
.505
30.3.1.2
Arbitrary Quadrilateral Meshes
.507
30.3.2
Stencils
.509
30.3.2.1
Stencils for Uniform B-Splines
.509
30.3.2.2
Stencils for Extraordinary Vertices
.511
30.4
Triangular Meshes
.512
30.4.1
Centroid Averaging for Triangular Meshes
.512
30.4.1.1
Three-Direction Quartic Box Splines
.512
30.4.1.2
Arbitrary Triangular Meshes
.514
30.4.2
Stencils for Triangular Meshes
.516
30.4.2.1
Stencils for Three-Direction Quartic Box Splines
.516
30.4.2.2
Stencils for Extraordinary Vertices
.517
30.5
Summary
.518
30.5.1
Bicubic Tensor Product B-Splines and Three-Direction
Quartic Box Splines
.518
30.5.1.1
Split and Average
.519
30.5.1.2
Centroid Averaging
.519
30.5.1.3
Stencils
.521
30.5.2
Centroid Averaging for Meshes of Arbitrary Topology
.521
30.5.3
Stencils for Extraordinary Vertices
.523
Exercises
.524
Programming Projects
.527
Further Readings
.529
Index
.533 |
| any_adam_object | 1 |
| author | Goldman, Ron |
| author_facet | Goldman, Ron |
| author_role | aut |
| author_sort | Goldman, Ron |
| author_variant | r g rg |
| building | Verbundindex |
| bvnumber | BV035483958 |
| callnumber-first | T - Technology |
| callnumber-label | T385 |
| callnumber-raw | T385 |
| callnumber-search | T385 |
| callnumber-sort | T 3385 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 380 ST 134 ST 320 |
| ctrlnum | (OCoLC)636300635 (DE-599)GBV588810444 |
| dewey-full | 006.6 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.6 |
| dewey-search | 006.6 |
| dewey-sort | 16.6 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV035483958 |
| illustrated | Illustrated |
| indexdate | 2025-01-28T11:12:33Z |
| institution | BVB |
| isbn | 9781439803349 |
| language | English |
| lccn | 2008054783 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017540457 |
| oclc_num | 636300635 |
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| owner_facet | DE-473 DE-BY-UBG DE-20 DE-11 DE-634 DE-29T DE-1050 |
| physical | XXIX, 543 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spelling | Goldman, Ron Verfasser aut An integrated introduction to computer graphics and geometric modeling Ronald Goldman Computer graphics and geometric modeling Boca Raton [u.a.] CRC Press 2009 XXIX, 543 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Computer graphics Three-dimensional display systems Curves on surfaces / Mathematical models Mathematisches Modell Curves on surfaces Mathematical models Computergrafik (DE-588)4010450-3 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s Algorithmische Geometrie (DE-588)4130267-9 s Computergrafik (DE-588)4010450-3 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017540457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldman, Ron An integrated introduction to computer graphics and geometric modeling Computer graphics Three-dimensional display systems Curves on surfaces / Mathematical models Mathematisches Modell Curves on surfaces Mathematical models Computergrafik (DE-588)4010450-3 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| subject_GND | (DE-588)4010450-3 (DE-588)4156717-1 (DE-588)4130267-9 |
| title | An integrated introduction to computer graphics and geometric modeling |
| title_alt | Computer graphics and geometric modeling |
| title_auth | An integrated introduction to computer graphics and geometric modeling |
| title_exact_search | An integrated introduction to computer graphics and geometric modeling |
| title_full | An integrated introduction to computer graphics and geometric modeling Ronald Goldman |
| title_fullStr | An integrated introduction to computer graphics and geometric modeling Ronald Goldman |
| title_full_unstemmed | An integrated introduction to computer graphics and geometric modeling Ronald Goldman |
| title_short | An integrated introduction to computer graphics and geometric modeling |
| title_sort | an integrated introduction to computer graphics and geometric modeling |
| topic | Computer graphics Three-dimensional display systems Curves on surfaces / Mathematical models Mathematisches Modell Curves on surfaces Mathematical models Computergrafik (DE-588)4010450-3 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| topic_facet | Computer graphics Three-dimensional display systems Curves on surfaces / Mathematical models Mathematisches Modell Curves on surfaces Mathematical models Computergrafik Geometrische Modellierung Algorithmische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017540457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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