The potential method for blending surfaces and corners:
We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general...
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Ithaca, New York
1985
|
Schriftenreihe: | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report
699 |
Schlagworte: | |
Zusammenfassung: | We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general position We give two paradigms by which to understand the method. The first paradigm views the blends as surfaces swept out by a family of space curves. The second, more general paradigm considers the surfaces as result of deformation of a parameter space effected by substitution. The method has a general formulation based on projective parameter spaces, but is also the image under projective transformation of the simpler, affine formulation The deformation by substitution paradigm is extended to blend blending surfaces at solid vertices without a degree penalty, under the assumption that the vertex valence has been reduced to three. It may also lead to a general solution for blending patches of algebraic surfaces that meet tangentially. A special case of this problem is solved and illustrated |
Beschreibung: | 22 S. Ill., graph. Darst. |
Internformat
MARC
LEADER | 00000nam a2200000 cb4500 | ||
---|---|---|---|
001 | BV010589928 | ||
003 | DE-604 | ||
005 | 00000000000000.0 | ||
007 | t | ||
008 | 960130s1985 ad|| |||| 00||| engod | ||
035 | |a (OCoLC)14556670 | ||
035 | |a (DE-599)BVBBV010589928 | ||
040 | |a DE-604 |b ger |e rakddb | ||
041 | 0 | |a eng | |
049 | |a DE-91G | ||
100 | 1 | |a Hoffmann, Christoph |e Verfasser |4 aut | |
245 | 1 | 0 | |a The potential method for blending surfaces and corners |c Christopn Hoffmann ; John Hopcroft |
264 | 1 | |a Ithaca, New York |c 1985 | |
300 | |a 22 S. |b Ill., graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |v 699 | |
520 | 3 | |a We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general position | |
520 | 3 | |a We give two paradigms by which to understand the method. The first paradigm views the blends as surfaces swept out by a family of space curves. The second, more general paradigm considers the surfaces as result of deformation of a parameter space effected by substitution. The method has a general formulation based on projective parameter spaces, but is also the image under projective transformation of the simpler, affine formulation | |
520 | 3 | |a The deformation by substitution paradigm is extended to blend blending surfaces at solid vertices without a degree penalty, under the assumption that the vertex valence has been reduced to three. It may also lead to a general solution for blending patches of algebraic surfaces that meet tangentially. A special case of this problem is solved and illustrated | |
650 | 4 | |a Geometry, Algebraic | |
650 | 4 | |a Surfaces | |
700 | 1 | |a Hopcroft, John E. |d 1939- |e Verfasser |0 (DE-588)112071481 |4 aut | |
810 | 2 | |a Department of Computer Science: Technical report |t Cornell University <Ithaca, NY> |v 699 |w (DE-604)BV006185504 |9 699 | |
999 | |a oai:aleph.bib-bvb.de:BVB01-007061768 |
Datensatz im Suchindex
_version_ | 1804125060782358528 |
---|---|
any_adam_object | |
author | Hoffmann, Christoph Hopcroft, John E. 1939- |
author_GND | (DE-588)112071481 |
author_facet | Hoffmann, Christoph Hopcroft, John E. 1939- |
author_role | aut aut |
author_sort | Hoffmann, Christoph |
author_variant | c h ch j e h je jeh |
building | Verbundindex |
bvnumber | BV010589928 |
ctrlnum | (OCoLC)14556670 (DE-599)BVBBV010589928 |
format | Book |
fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02227nam a2200337 cb4500</leader><controlfield tag="001">BV010589928</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960130s1985 ad|| |||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)14556670</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010589928</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hoffmann, Christoph</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The potential method for blending surfaces and corners</subfield><subfield code="c">Christopn Hoffmann ; John Hopcroft</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Ithaca, New York</subfield><subfield code="c">1985</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">22 S.</subfield><subfield code="b">Ill., graph. Darst.</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cornell University <Ithaca, NY> / Department of Computer Science: Technical report</subfield><subfield code="v">699</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general position</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">We give two paradigms by which to understand the method. The first paradigm views the blends as surfaces swept out by a family of space curves. The second, more general paradigm considers the surfaces as result of deformation of a parameter space effected by substitution. The method has a general formulation based on projective parameter spaces, but is also the image under projective transformation of the simpler, affine formulation</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">The deformation by substitution paradigm is extended to blend blending surfaces at solid vertices without a degree penalty, under the assumption that the vertex valence has been reduced to three. It may also lead to a general solution for blending patches of algebraic surfaces that meet tangentially. A special case of this problem is solved and illustrated</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Algebraic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Surfaces</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hopcroft, John E.</subfield><subfield code="d">1939-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)112071481</subfield><subfield code="4">aut</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Department of Computer Science: Technical report</subfield><subfield code="t">Cornell University <Ithaca, NY></subfield><subfield code="v">699</subfield><subfield code="w">(DE-604)BV006185504</subfield><subfield code="9">699</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007061768</subfield></datafield></record></collection> |
id | DE-604.BV010589928 |
illustrated | Illustrated |
indexdate | 2024-07-09T17:55:34Z |
institution | BVB |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007061768 |
oclc_num | 14556670 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM |
owner_facet | DE-91G DE-BY-TUM |
physical | 22 S. Ill., graph. Darst. |
publishDate | 1985 |
publishDateSearch | 1985 |
publishDateSort | 1985 |
record_format | marc |
series2 | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |
spelling | Hoffmann, Christoph Verfasser aut The potential method for blending surfaces and corners Christopn Hoffmann ; John Hopcroft Ithaca, New York 1985 22 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cornell University <Ithaca, NY> / Department of Computer Science: Technical report 699 We survey the potential method for blending implicit algebraic surfaces, summarizing and extending work previously reported. The method is capable of deriving blends for pairs of algebraic surfaces, and is guaranteed to produce blending surfaces of lowest possible degree for two quadrics in general position We give two paradigms by which to understand the method. The first paradigm views the blends as surfaces swept out by a family of space curves. The second, more general paradigm considers the surfaces as result of deformation of a parameter space effected by substitution. The method has a general formulation based on projective parameter spaces, but is also the image under projective transformation of the simpler, affine formulation The deformation by substitution paradigm is extended to blend blending surfaces at solid vertices without a degree penalty, under the assumption that the vertex valence has been reduced to three. It may also lead to a general solution for blending patches of algebraic surfaces that meet tangentially. A special case of this problem is solved and illustrated Geometry, Algebraic Surfaces Hopcroft, John E. 1939- Verfasser (DE-588)112071481 aut Department of Computer Science: Technical report Cornell University <Ithaca, NY> 699 (DE-604)BV006185504 699 |
spellingShingle | Hoffmann, Christoph Hopcroft, John E. 1939- The potential method for blending surfaces and corners Geometry, Algebraic Surfaces |
title | The potential method for blending surfaces and corners |
title_auth | The potential method for blending surfaces and corners |
title_exact_search | The potential method for blending surfaces and corners |
title_full | The potential method for blending surfaces and corners Christopn Hoffmann ; John Hopcroft |
title_fullStr | The potential method for blending surfaces and corners Christopn Hoffmann ; John Hopcroft |
title_full_unstemmed | The potential method for blending surfaces and corners Christopn Hoffmann ; John Hopcroft |
title_short | The potential method for blending surfaces and corners |
title_sort | the potential method for blending surfaces and corners |
topic | Geometry, Algebraic Surfaces |
topic_facet | Geometry, Algebraic Surfaces |
volume_link | (DE-604)BV006185504 |
work_keys_str_mv | AT hoffmannchristoph thepotentialmethodforblendingsurfacesandcorners AT hopcroftjohne thepotentialmethodforblendingsurfacesandcorners |