Mathematical aspects of geometric modeling:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| 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 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1137/1.9781611970067 https://doi.org/10.1137/1.9781611970067 https://doi.org/10.1137/1.9781611970067 https://doi.org/10.1137/1.9781611970067 https://doi.org/10.1137/1.9781611970067 |
| 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 |
| Umfang: | 1 online-Ressource (ix, 256 Seiten) |
| ISBN: | 0898713315 9780898713312 |
| DOI: | 10.1137/1.9781611970067 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV039747294 | ||
| 003 | DE-604 | ||
| 005 | 20210223 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 111207s1995 sz o|||| 10||| eng d | ||
| 010 | |a 94010478 | ||
| 020 | |a 0898713315 |c pbk. |9 0898713315 | ||
| 020 | |a 9780898713312 |c pbk. |9 9780898713312 | ||
| 024 | 7 | |a 10.1137/1.9781611970067 |2 doi | |
| 035 | |a (OCoLC)775728858 | ||
| 035 | |a (DE-599)BVBBV039747294 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a sz |c XA-CH | ||
| 049 | |a DE-91 |a DE-29 |a DE-706 |a DE-83 |a DE-20 | ||
| 084 | |a SK 905 |0 (DE-625)143269: |2 rvk | ||
| 084 | |a SD 1990 |0 (DE-625)142724: |2 rvk | ||
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 100 | 1 | |a Micchelli, Charles A. |d 1924- |e Verfasser |0 (DE-588)1120439086 |4 aut | |
| 245 | 1 | 0 | |a Mathematical aspects of geometric modeling |c Charles A. Micchelli |
| 264 | 1 | |a Philadelphia, Pa. |b Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) |c 1995 | |
| 300 | |a 1 online-Ressource (ix, 256 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a CBMS-NSF regional conference series in applied mathematics |v 65 | |
| 500 | |a Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader | ||
| 500 | |a Includes bibliographical references and index | ||
| 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 | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Curves on surfaces / Mathematical models / Congresses | |
| 650 | 4 | |a Surfaces / Mathematical models / Congresses | |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kurve |0 (DE-588)4033824-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fläche |0 (DE-588)4129864-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Fläche |0 (DE-588)4129864-0 |D s |
| 689 | 0 | 1 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Kurve |0 (DE-588)4033824-1 |D s |
| 689 | 1 | 1 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |D s |
| 689 | 2 | |5 DE-604 | |
| 710 | 2 | |a Society for Industrial and Applied Mathematics |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 0898713315 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 9780898713312 |
| 830 | 0 | |a CBMS-NSF regional conference series in applied mathematics |v 65 |w (DE-604)BV046682627 |9 65 | |
| 856 | 4 | 0 | |u https://doi.org/10.1137/1.9781611970067 |x Verlag |3 Volltext |
| 912 | |a ZDB-72-SIA | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024594825 | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970067 |l DE-91 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970067 |l DE-20 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970067 |l DE-706 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970067 |l DE-29 |p ZDB-72-SIA |x Verlag |3 Volltext | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 1805809 |
|---|---|
| _version_ | 1821933051869921280 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04458nam a2200697zcb4500</leader><controlfield tag="001">BV039747294</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210223 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">111207s1995 sz o|||| 10||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">94010478</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0898713315</subfield><subfield code="c">pbk.</subfield><subfield code="9">0898713315</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780898713312</subfield><subfield code="c">pbk.</subfield><subfield code="9">9780898713312</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1137/1.9781611970067</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)775728858</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039747294</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">sz</subfield><subfield code="c">XA-CH</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 905</subfield><subfield code="0">(DE-625)143269:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SD 1990</subfield><subfield code="0">(DE-625)142724:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Micchelli, Charles A.</subfield><subfield code="d">1924-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1120439086</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical aspects of geometric modeling</subfield><subfield code="c">Charles A. Micchelli</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia, Pa.</subfield><subfield code="b">Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online-Ressource (ix, 256 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">CBMS-NSF regional conference series in applied mathematics</subfield><subfield code="v">65</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Curves on surfaces / Mathematical models / Congresses</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Surfaces / Mathematical models / Congresses</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Modellierung</subfield><subfield code="0">(DE-588)4156717-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kurve</subfield><subfield code="0">(DE-588)4033824-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geometrische Modellierung</subfield><subfield code="0">(DE-588)4156717-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Kurve</subfield><subfield code="0">(DE-588)4033824-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Geometrische Modellierung</subfield><subfield code="0">(DE-588)4156717-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Geometrische Modellierung</subfield><subfield code="0">(DE-588)4156717-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Society for Industrial and Applied Mathematics</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">0898713315</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">9780898713312</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">CBMS-NSF regional conference series in applied mathematics</subfield><subfield code="v">65</subfield><subfield code="w">(DE-604)BV046682627</subfield><subfield code="9">65</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1137/1.9781611970067</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-72-SIA</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-024594825</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970067</subfield><subfield code="l">DE-91</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970067</subfield><subfield code="l">DE-20</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970067</subfield><subfield code="l">DE-706</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970067</subfield><subfield code="l">DE-29</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV039747294 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:01:25Z |
| institution | BVB |
| isbn | 0898713315 9780898713312 |
| language | English |
| lccn | 94010478 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594825 |
| oclc_num | 775728858 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| owner_facet | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| physical | 1 online-Ressource (ix, 256 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) |
| record_format | marc |
| series | CBMS-NSF regional conference series in applied mathematics |
| series2 | CBMS-NSF regional conference series in applied mathematics |
| 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 |
| work_keys_str_mv | AT micchellicharlesa mathematicalaspectsofgeometricmodeling AT societyforindustrialandappliedmathematics mathematicalaspectsofgeometricmodeling |