Skinning and blending with rational envelope surfaces

Michal Bizzarri; Miroslav Lávicka; Jiri Kosinka

doi:10.1016/j.cad.2017.02.002

Skinning and blending with rational envelope surfaces

Michal Bizzarri, Miroslav Lávicka, Jiri Kosinka

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Abstract

We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.

Original language	English
Pages (from-to)	41-51
Number of pages	11
Journal	Computer-Aided design
Volume	87
DOIs	https://doi.org/10.1016/j.cad.2017.02.002
Publication status	Published - Jun-2017

Keywords

CANAL SURFACES
RINGED SURFACES
CURVES
REPRESENTATIONS
3D

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title = "Skinning and blending with rational envelope surfaces",

abstract = "We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.",

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TY - JOUR

T1 - Skinning and blending with rational envelope surfaces

AU - Bizzarri, Michal

AU - Lávicka, Miroslav

AU - Kosinka, Jiri

PY - 2017/6

Y1 - 2017/6

N2 - We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.

AB - We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.

KW - CANAL SURFACES

KW - RINGED SURFACES

KW - CURVES

KW - REPRESENTATIONS

KW - 3D

U2 - 10.1016/j.cad.2017.02.002

DO - 10.1016/j.cad.2017.02.002

M3 - Article

SN - 0010-4485

VL - 87

SP - 41

EP - 51

JO - Computer-Aided design

JF - Computer-Aided design

ER -