An algebraic approach to offsetting and blending of solids:
Abstract: "We propose to broaden the framework of CSG to a representation of solids as Boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Passau
1998
|
| Schriftenreihe: | MIP / Universität Passau, Fakultät für Mathematik und Informatik
1998,04 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We propose to broaden the framework of CSG to a representation of solids as Boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending are reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. In a collection of computational examples we demonstrate the capabilities of the Redlog package for the discussed operations on solids within our framework." |
| Beschreibung: | 24, 5 S. Ill. |
Internformat
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| 245 | 1 | 0 | |a An algebraic approach to offsetting and blending of solids |c Th. Sturm and V. Weispfenning |
| 264 | 1 | |a Passau |c 1998 | |
| 300 | |a 24, 5 S. |b Ill. | ||
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| 490 | 1 | |a MIP / Universität Passau, Fakultät für Mathematik und Informatik |v 1998,04 | |
| 520 | 3 | |a Abstract: "We propose to broaden the framework of CSG to a representation of solids as Boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending are reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. In a collection of computational examples we demonstrate the capabilities of the Redlog package for the discussed operations on solids within our framework." | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Geometry |x Data processing | |
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| 810 | 2 | |a Universität Passau, Fakultät für Mathematik und Informatik |t MIP |v 1998,04 |w (DE-604)BV000905393 |9 1998,04 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008120927 | |
Datensatz im Suchindex
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| id | DE-604.BV012001479 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008120927 |
| oclc_num | 41138345 |
| open_access_boolean | |
| owner | DE-154 DE-739 DE-12 DE-634 DE-91G DE-BY-TUM |
| owner_facet | DE-154 DE-739 DE-12 DE-634 DE-91G DE-BY-TUM |
| physical | 24, 5 S. Ill. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| record_format | marc |
| series2 | MIP / Universität Passau, Fakultät für Mathematik und Informatik |
| spelling | Sturm, Thomas Verfasser aut An algebraic approach to offsetting and blending of solids Th. Sturm and V. Weispfenning Passau 1998 24, 5 S. Ill. txt rdacontent n rdamedia nc rdacarrier MIP / Universität Passau, Fakultät für Mathematik und Informatik 1998,04 Abstract: "We propose to broaden the framework of CSG to a representation of solids as Boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending are reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. In a collection of computational examples we demonstrate the capabilities of the Redlog package for the discussed operations on solids within our framework." Datenverarbeitung Geometry Data processing Polynomials Semialgebraic sets Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Weispfenning, Volker 1944- Verfasser (DE-588)108063550 aut Universität Passau, Fakultät für Mathematik und Informatik MIP 1998,04 (DE-604)BV000905393 1998,04 |
| spellingShingle | Sturm, Thomas Weispfenning, Volker 1944- An algebraic approach to offsetting and blending of solids Datenverarbeitung Geometry Data processing Polynomials Semialgebraic sets Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | An algebraic approach to offsetting and blending of solids |
| title_auth | An algebraic approach to offsetting and blending of solids |
| title_exact_search | An algebraic approach to offsetting and blending of solids |
| title_full | An algebraic approach to offsetting and blending of solids Th. Sturm and V. Weispfenning |
| title_fullStr | An algebraic approach to offsetting and blending of solids Th. Sturm and V. Weispfenning |
| title_full_unstemmed | An algebraic approach to offsetting and blending of solids Th. Sturm and V. Weispfenning |
| title_short | An algebraic approach to offsetting and blending of solids |
| title_sort | an algebraic approach to offsetting and blending of solids |
| topic | Datenverarbeitung Geometry Data processing Polynomials Semialgebraic sets Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Datenverarbeitung Geometry Data processing Polynomials Semialgebraic sets Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT sturmthomas analgebraicapproachtooffsettingandblendingofsolids AT weispfenningvolker analgebraicapproachtooffsettingandblendingofsolids |