Variational design of rational Bézier curves and surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
1993
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Kaiserslautern, Univ., Diss., 1993 |
| Physical Description: | II, 78 S. Ill., graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Bonneau, Georges-Pierre |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Variational design of rational Bézier curves and surfaces |c von Georges-Pierre Bonneau |
| 264 | 1 | |c 1993 | |
| 300 | |a II, 78 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Kaiserslautern, Univ., Diss., 1993 | ||
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Record in the Search Index
| _version_ | 1807594607041576960 |
|---|---|
| adam_text |
CONTENTS
I
CONTENTS
0
INTRODUCTION
.
1
1
FUNDAMENTALS
.
5
1.1
NOTATIONS
.
5
1.2
DIFFERENTIAL
ANALYSIS
.
6
1.3
DIFFERENTIAL
GEOMETRY
OF
CURVES
.
6
1.4
DIFFERENTIAL
GEOMETRY
OF
SURFACES
.
10
1.5
BEZIER
CURVES
AND
SURFACES
.
12
1.6
STRAIN
ENERGY
OF
A
SURFACE
.
18
2
VARIATIONAL
DESIGN
OF
RATIONAL
BEZIER
CURVES
BASED
UPON
LOCAL
MINIMIZATION
OF
THE
BENDING
ENERGY
.
22
2.1
RESTRICTION
OF
THE
PROBLEM
.
22
2.2
CALCULUS
OF
THE
LOCAL
BENDING
ENERGY
.
24
2.3
MINIMIZATION
OF
THE
CRITERION
FUNCTION
IN
THE
CUBIC
CASE
.
27
3
STIFFNESS
DEGREE
CONCEPT
.
32
3.1
A
LOCAL
CRITERION
.
32
3.1.1
DERIVATIVES
OF
A
RATIONAL
BEZIER
CURVE
.
32
3.1.2
THE
CRITERION
.
33
3.2
MINIMIZATION
IN
THE
ENDPOINTS
.
34
3.2.1
THE
RESOLVING
SYSTEM
OF
EQUATIONS
.
34
3.2.2
EXAMPLES
.
41
3.3
MINIMIZATION
IN
ANY
TWO
PARAMETER
VALUES
.
45
3.3.1
REDUCTION
OF
THE DEGREE
OF
THE
RESOLVING
SYSTEM
.
45
3.3.2
IMPLEMENTATION
.
49
3.3.3
EXAMPLES
.
50
4
RATIONAL
TENSOR
PRODUCT
BEZIER
PATCHES
WITH
TWIST
OF
MINIMUM
ENERGY
54
4.1
AN
OPTIMAL
NORMAL
COMPONENT
OF
THE
TWIST
VECTOR
.
54
4.2
MINIMUM
ENERGY
TWIST
WEIGHTS
.
55
4.2.1
THE
FIRST
AND
SECOND
FUNDAMENTAL
FORM
IN
THE
CORNERS
OF
A
RATIONAL
TENSOR
PRODUCT
BEZIER
PATCH
.
56
4.2.2
THE
WEIGHTS
FOR
THE
OPTIMAL
NORMAL
COMPONENT
OF
THE
TWIST
VECTORS
.
57
4.2.3
EXAMPLE
.
58
II
CONTENTS
5
RATIONAL
TENSOR
PRODUCT
BEZIER
PATCHES
WITH
LOCALLY
MINIMUM
NORM
OF
DERIVATIVES
.
60
5.1
STANDARD
REPARAMETRIZATION
FOR
RATIONAL
TENSOR
PRODUCT
BEZIER
SURFACES
.
61
5.2
THE
RESOLVING
SYSTEM
.
64
5.2.1
THE
DERIVATIVES
OF
A
RATIONAL
TENSOR
PRODUCT
BEZIER
PATCH
IN
THE
CORNERS
.
64
5.2.2
DEGREE
OF
THE
RESOLVING
SYSTEM
.
65
5.3
OTHER
CRITERIONS
.
66
6
STIFFNESS
DEGREE
FOR
RATIONAL
TRIANGULAR
BEZIER
PATCHES
.
69
6.1
STANDARD
REPARAMETRIZATION
FOR
RATIONAL
TRIANGULAR
BEZIER
PATCHES
.
69
6.2
THE
RESOLVING
SYSTEM
.
73
6.2.1
THE
DERIVATIVES
OF
A
RATIONAL
TRIANGULAR
BEZIER
PATCH
IN
THE
CORNERS
.
73
6.2.2
THE
DEGREE
OF
THE
RESOLVING
SYSTEM
.
75
7
REFERENCES
.
77 |
| any_adam_object | 1 |
| author | Bonneau, Georges-Pierre |
| author_facet | Bonneau, Georges-Pierre |
| author_role | aut |
| author_sort | Bonneau, Georges-Pierre |
| author_variant | g p b gpb |
| building | Verbundindex |
| bvnumber | BV008931581 |
| classification_tum | DAT 756d |
| ctrlnum | (OCoLC)257415167 (DE-599)BVBBV008931581 |
| discipline | Informatik |
| format | Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV008931581 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T01:02:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005890039 |
| oclc_num | 257415167 |
| open_access_boolean | |
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| owner_facet | DE-91 DE-BY-TUM DE-29T DE-355 DE-BY-UBR DE-739 DE-706 DE-83 |
| physical | II, 78 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| record_format | marc |
| spelling | Bonneau, Georges-Pierre Verfasser aut Variational design of rational Bézier curves and surfaces von Georges-Pierre Bonneau 1993 II, 78 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kaiserslautern, Univ., Diss., 1993 Bézier-Fläche (DE-588)4293190-3 gnd rswk-swf Rationale Funktion (DE-588)4225679-3 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Bézier-Kurve (DE-588)4308681-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bézier-Kurve (DE-588)4308681-0 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Bézier-Fläche (DE-588)4293190-3 s Rationale Funktion (DE-588)4225679-3 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005890039&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bonneau, Georges-Pierre Variational design of rational Bézier curves and surfaces Bézier-Fläche (DE-588)4293190-3 gnd Rationale Funktion (DE-588)4225679-3 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Bézier-Kurve (DE-588)4308681-0 gnd |
| subject_GND | (DE-588)4293190-3 (DE-588)4225679-3 (DE-588)4130267-9 (DE-588)4308681-0 (DE-588)4113937-9 |
| title | Variational design of rational Bézier curves and surfaces |
| title_auth | Variational design of rational Bézier curves and surfaces |
| title_exact_search | Variational design of rational Bézier curves and surfaces |
| title_full | Variational design of rational Bézier curves and surfaces von Georges-Pierre Bonneau |
| title_fullStr | Variational design of rational Bézier curves and surfaces von Georges-Pierre Bonneau |
| title_full_unstemmed | Variational design of rational Bézier curves and surfaces von Georges-Pierre Bonneau |
| title_short | Variational design of rational Bézier curves and surfaces |
| title_sort | variational design of rational bezier curves and surfaces |
| topic | Bézier-Fläche (DE-588)4293190-3 gnd Rationale Funktion (DE-588)4225679-3 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Bézier-Kurve (DE-588)4308681-0 gnd |
| topic_facet | Bézier-Fläche Rationale Funktion Algorithmische Geometrie Bézier-Kurve Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005890039&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bonneaugeorgespierre variationaldesignofrationalbeziercurvesandsurfaces |