Mathematical aspects of geometric modeling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1995
|
| Schriftenreihe: | CBMS-NSF regional conference series in applied mathematics
65 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index Preface -- A brief overview -- Chapter 1. Matrix subdivision -- Chapter 2. Stationary subdivision -- Chapter 3. Piecewise polynomial curves -- Chapter 4. Geometric methods for piecewise polynomial surfaces -- Chapter 5. Recursive algorithms for polynomial evaluation This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results |
| Beschreibung: | 1 online-Ressource (ix, 256 Seiten) |
| ISBN: | 0898713315 9780898713312 |
| DOI: | 10.1137/1.9781611970067 |
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| 245 | 1 | 0 | |a Mathematical aspects of geometric modeling |c Charles A. Micchelli |
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| 500 | |a Preface -- A brief overview -- Chapter 1. Matrix subdivision -- Chapter 2. Stationary subdivision -- Chapter 3. Piecewise polynomial curves -- Chapter 4. Geometric methods for piecewise polynomial surfaces -- Chapter 5. Recursive algorithms for polynomial evaluation | ||
| 500 | |a This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results | ||
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Datensatz im Suchindex
| _version_ | 1804148637560733696 |
|---|---|
| any_adam_object | |
| author | Micchelli, Charles A. 1924- |
| author_GND | (DE-588)1120439086 |
| author_facet | Micchelli, Charles A. 1924- |
| author_role | aut |
| author_sort | Micchelli, Charles A. 1924- |
| author_variant | c a m ca cam |
| building | Verbundindex |
| bvnumber | BV039747294 |
| classification_rvk | SK 905 SD 1990 SK 380 |
| collection | ZDB-72-SIA |
| ctrlnum | (OCoLC)775728858 (DE-599)BVBBV039747294 |
| discipline | Mathematik |
| doi_str_mv | 10.1137/1.9781611970067 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 0898713315 9780898713312 |
| language | English |
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| spelling | Micchelli, Charles A. 1924- Verfasser (DE-588)1120439086 aut Mathematical aspects of geometric modeling Charles A. Micchelli Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 1995 1 online-Ressource (ix, 256 Seiten) txt rdacontent c rdamedia cr rdacarrier CBMS-NSF regional conference series in applied mathematics 65 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index Preface -- A brief overview -- Chapter 1. Matrix subdivision -- Chapter 2. Stationary subdivision -- Chapter 3. Piecewise polynomial curves -- Chapter 4. Geometric methods for piecewise polynomial surfaces -- Chapter 5. Recursive algorithms for polynomial evaluation This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results Mathematisches Modell Curves on surfaces / Mathematical models / Congresses Surfaces / Mathematical models / Congresses Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Fläche (DE-588)4129864-0 s Geometrische Modellierung (DE-588)4156717-1 s DE-604 Kurve (DE-588)4033824-1 s Society for Industrial and Applied Mathematics Sonstige oth Erscheint auch als Druck-Ausgabe, Paperback 0898713315 Erscheint auch als Druck-Ausgabe, Paperback 9780898713312 CBMS-NSF regional conference series in applied mathematics 65 (DE-604)BV046682627 65 https://doi.org/10.1137/1.9781611970067 Verlag Volltext |
| spellingShingle | Micchelli, Charles A. 1924- Mathematical aspects of geometric modeling CBMS-NSF regional conference series in applied mathematics Mathematisches Modell Curves on surfaces / Mathematical models / Congresses Surfaces / Mathematical models / Congresses Geometrische Modellierung (DE-588)4156717-1 gnd Kurve (DE-588)4033824-1 gnd Fläche (DE-588)4129864-0 gnd |
| subject_GND | (DE-588)4156717-1 (DE-588)4033824-1 (DE-588)4129864-0 (DE-588)1071861417 |
| title | Mathematical aspects of geometric modeling |
| title_auth | Mathematical aspects of geometric modeling |
| title_exact_search | Mathematical aspects of geometric modeling |
| title_full | Mathematical aspects of geometric modeling Charles A. Micchelli |
| title_fullStr | Mathematical aspects of geometric modeling Charles A. Micchelli |
| title_full_unstemmed | Mathematical aspects of geometric modeling Charles A. Micchelli |
| title_short | Mathematical aspects of geometric modeling |
| title_sort | mathematical aspects of geometric modeling |
| topic | Mathematisches Modell Curves on surfaces / Mathematical models / Congresses Surfaces / Mathematical models / Congresses Geometrische Modellierung (DE-588)4156717-1 gnd Kurve (DE-588)4033824-1 gnd Fläche (DE-588)4129864-0 gnd |
| topic_facet | Mathematisches Modell Curves on surfaces / Mathematical models / Congresses Surfaces / Mathematical models / Congresses Geometrische Modellierung Kurve Fläche Konferenzschrift |
| url | https://doi.org/10.1137/1.9781611970067 |
| volume_link | (DE-604)BV046682627 |
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