Applied geometry for computer graphics and CAD:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2000
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 288 S. Ill., graph. Darst. |
| ISBN: | 1852330805 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1808860845327777792 |
|---|---|
| adam_text |
DUNCAN MARSH APPLIED GEOMETRY FOR COMPUTER GRAPHICS AND CAD WITH 95
FIGURES SPRINGER CONTENTS 1. TRANSFORMATIONS OF THE PLANE 1 1.1
INTRODUCTION 1 1.2 TRANSLATIONS 5 1.3 SCALING ABOUT THE ORIGIN 6 1.4
REFLECTIONS 8 1.5 ROTATION ABOUT THE ORIGIN 9 1.6 SHEARS 11 1.7
CONCATENATION OF TRANSFORMATIONS 13 1.8 APPLICATIONS 15 1.8.1 INSTANCING
15 1.8.2 ROBOTICS 17 2. HOMOGENEOUS COORDINATES AND TRANSFORMATIONS OF
THE PLANE 19 2.1 INTRODUCTION 19 2.1.1 HOMOGENEOUS COORDINATES 21 2.2
POINTS AT INFINITY 23 2.3 VISUALIZATION OF THE PROJECTIVE PLANE 24 2.3.1
LINE MODEL OF THE PROJECTIVE PLANE 24 2.3.2 SPHERICAL MODEL OF THE
PROJECTIVE PLANE 26 2.4 TRANSFORMATIONS IN HOMOGENEOUS COORDINATES 27
2.4.1 TRANSLATIONS 27 2.4.2 SCALING ABOUT THE ORIGIN 28 2.4.3 ROTATION
ABOUT THE ORIGIN 29 2.5 CONCATENATION OF TRANSFORMATIONS 30 2.5.1
INVERSE TRANSFORMATIONS 31 2.5.2 ROTATION ABOUT AN ARBITRARY POINT 33
APPLIED GEOMETRY FOR COMPUTER GRAPHICS AND CAD 2.5.3 REFLECTION IN AN
ARBITRARY LINE 34 2.6 APPLICATIONS 36 2.6.1 INSTANCING 36 2.6.2 DEVICE
COORDINATE TRANSFORMATION 37 2.7 POINT AND LINE GEOMETRY IN HOMOGENEOUS
COORDINATES 38 3. HOMOGENEOUS COORDINATES AND TRANSFORMATIONS OF SPACE
. 41 3.1 HOMOGENEOUS COORDINATES 41 3.2 TRANSFORMATIONS OF SPACE 42
3.2.1 TRANSLATIONS 42 3.2.2 SCALINGS AND REFLECTIONS 43 3.2.3 ROTATIONS
ABOUT THE COORDINATE AXES 43 3.2.4 ROTATION ABOUT AN ARBITRARY LINE 45
3.2.5 REFLECTION IN AN ARBITRARY PLANE 47 3.3 APPLICATIONS 49 3.3.1
COMPUTER-AIDED DESIGN 49 3.3.2 ORIENTATION OF A RIGID BODY 50 3.4
GEOMETRIC METHODS FOR LINES AND PLANES IN SPACE 51 4. PROJECTIONS AND
THE VIEWING PIPELINE 57 4. 1 INTRODUCTION 57 4.2 PROJECTIONS OF THE
PLANE 58 4.3 PROJECTIONS OF 3-DIMENSIONAL SPACE 62 4.4 THE VIEWPLANE
COORDINATE MAPPING 66 4.5 THE VIEWING PIPELINE 70 4.6 CLASSIFICATION OF
PROJECTIONS 74 4.6.1 CLASSIFICATION OF PARALLEL PROJECTIONS 75 4.6.2
CLASSIFICATION OF PERSPECTIVE PROJECTIONS 79 5. CURVES 85 5.1
INTRODUCTION 85 5.2 CURVE RENDERING 88 5.3 PARAMETRIC CURVES 89 5.4 ARC
LENGTH AND REPARAMETRIZATION 92 5.5 APPLICATION: NUMERICAL CONTROLLED
MACHINING AND OFFSETS 96 5.6 CONIES 98 5.6.1 CLASSIFICATION OF CONIES
101 5.6.2 CONIES IN STANDARD FORM 106 5.6.3 INTERSECTIONS OF A CONIC
WITH A LINE 110 5.6.4 PARAMETRIZATION OF AN IRREDUCIBLE CONIC 113 5.6.5
CONVERTING FROM PARAMETRIC FORM TO IMPLICIT FORM 115 5.7 CONIES IN SPACE
119 CONTENTS 5.8 APPLICATIONS OF CONIES 121 6. BEZIER CURVES I 125 6.1
INTRODUCTION 125 6.2 BEZIER CURVES OF LOW DEGREE 126 6.2.1 LINEAR BEZIER
CURVES 126 6.2.2 QUADRATIC BEZIER CURVES 126 6.2.3 CUBIC BEZIER CURVES
127 6.3 THE EFFECT OF ADJUSTING A CONTROL POINT 130 6.4 THE GENERAL
BEZIER CURVE 131 6.5 PROPERTIES OF THE BERNSTEIN POLYNOMIALS 134 6.6
CONVEX HULLS 136 6.7 PROPERTIES OF BEZIER CURVES 137 6.8 . THE DE
CASTELJAU ALGORITHM 141 6.9 SUBDIVISION OF A BEZIER CURVE 144 6.10
APPLICATIONS 146 6.10.1 RENDERING 146 6.10.2 INTERSECTION OF A PLANAR
BEZIER CURVE AND A LINE 148 6.10.3 INTERSECTION OF TWO BEZIER CURVES 149
7. BEZIER CURVES II 151 7.1 SPATIAL BEZIER CURVES 151 7.2 DERIVATIVES OF
BEZIER CURVES 152 7.3 CONVERSIONS BETWEEN REPRESENTATIONS 156 7.4
PIECEWISE BEZIER CURVES 158 7.5 RATIONAL BEZIER CURVES 164 7.5.1
PROPERTIES OF RATIONAL BEZIER CURVES 167 7.5.2 DE CASTELJAU ALGORITHM
FOR RATIONAL CURVES 170 7.5.3 PROJECTIONS OF RATIONAL BEZIER CURVES 171
7.5.4 DERIVATIVES OF RATIONAL BEZIER CURVES 174 8. B-SPLINES 177 8.1
INTEGRAL B-SPLINE CURVES 177 8.1.1 PROPERTIES OF THE B-SPLINE CURVE 184
8.1.2 B-SPLINE TYPES 185 8.1.3 APPLICATION: MORPHING OR SOFT OBJECT
ANIMATION 191 8.1.4 THE DE BOOR ALGORITHM 193 8.1.5 DERIVATIVES OF A
B-SPLINE 195 8.2 NON-UNIFORM RATIONAL B-SPLINES (NURBS) 200 8.2.1
PROJECTIONS OF NURBS CURVES 202 8.2.2 DERIVATIVES OF NURBS 204 8.2.3
RATIONAL DE BOOR ALGORITHM 206 APPLIED GEOMETRY FOR COMPUTER GRAPHICS
AND CAD 8.3 KNOT INSERTION 208 9. SURFACES 213 9.1 INTRODUCTION 213 9.2
QUADRIC SURFACES 216 9.3 BEZIER AND B-SPLINE SURFACES 220 9.3.1
PROPERTIES OF BEZIER AND B-SPLINE SURFACES 221 9.3.2 DERIVATIVES OF
BEZIER AND B-SPLINE SURFACES 223 9.4 SURFACE CONSTRUCTIONS 226 9.4.1
EXTRUDED SURFACES 226 9.4.2 RULED SURFACES 227 9.4.3 TRANSLATIONALLY
SWEPT SURFACES 229 9.4.4 SURFACES OF REVOLUTION 230 9.5 SURFACE
SUBDIVISION 233 10. CURVE AND SURFACE CURVATURES 237 10.1 CURVATURE OF A
PLANE CURVE 237 10.2 CURVATURE AND TORSION OF A SPACE CURVE 245 10.3
CURVATURE OF BEZIER CURVES 252 10.4 SURFACE CURVATURES 255 SOLUTIONS 267
REFERENCES 283 INDEX 285 |
| any_adam_object | 1 |
| author | Marsh, Duncan 1961- |
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| callnumber-first | T - Technology |
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| callnumber-raw | T385 |
| callnumber-search | T385 |
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| callnumber-subject | T - General Technology |
| classification_rvk | SK 240 SK 380 ST 300 |
| ctrlnum | (OCoLC)249338950 (DE-599)BVBBV013285903 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. print. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-31T00:28:49Z |
| institution | BVB |
| isbn | 1852330805 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009057908 |
| oclc_num | 249338950 |
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| physical | XII, 288 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Marsh, Duncan 1961- Verfasser (DE-588)120966018 aut Applied geometry for computer graphics and CAD Duncan Marsh 2. print. London [u.a.] Springer 2000 XII, 288 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Geometrie - CAD Geometrie - Computergraphik Computergrafik (DE-588)4010450-3 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf Computergrafik (DE-588)4010450-3 s Geometrie (DE-588)4020236-7 s DE-604 CAD (DE-588)4069794-0 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marsh, Duncan 1961- Applied geometry for computer graphics and CAD Geometrie - CAD Geometrie - Computergraphik Computergrafik (DE-588)4010450-3 gnd Geometrie (DE-588)4020236-7 gnd CAD (DE-588)4069794-0 gnd |
| subject_GND | (DE-588)4010450-3 (DE-588)4020236-7 (DE-588)4069794-0 |
| title | Applied geometry for computer graphics and CAD |
| title_auth | Applied geometry for computer graphics and CAD |
| title_exact_search | Applied geometry for computer graphics and CAD |
| title_full | Applied geometry for computer graphics and CAD Duncan Marsh |
| title_fullStr | Applied geometry for computer graphics and CAD Duncan Marsh |
| title_full_unstemmed | Applied geometry for computer graphics and CAD Duncan Marsh |
| title_short | Applied geometry for computer graphics and CAD |
| title_sort | applied geometry for computer graphics and cad |
| topic | Geometrie - CAD Geometrie - Computergraphik Computergrafik (DE-588)4010450-3 gnd Geometrie (DE-588)4020236-7 gnd CAD (DE-588)4069794-0 gnd |
| topic_facet | Geometrie - CAD Geometrie - Computergraphik Computergrafik Geometrie CAD |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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