The kernel of a freeform surface and its duality with the convex hull of its tangential surface

Gershon Elber; John K. Johnstone; Myung Soo Kim; Joon Kyung Seong

doi:10.1142/S021865430600086X

The kernel of a freeform surface and its duality with the convex hull of its tangential surface

Gershon Elber^*
, John K. Johnstone
, Myung Soo Kim
, Joon Kyung Seong

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We present algorithms for computing the kernel of a closed freeform rational surface. The kernel computation is reformulated as a problem of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the kernel. Using a plane-point duality, this paper also explores a duality relationship between the kernel of a closed surface and the convex hull of its tangential surface.

Original language	English
Pages (from-to)	129-142
Number of pages	14
Journal	International Journal of Shape Modeling
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S021865430600086X
Publication status	Published - 2006 Dec
Externally published	Yes

Keywords

B-spline
Convex hull
Freeform rational surface
Gamma-kernel
Kernel
Symbolic computation
Zero-set finding

ASJC Scopus subject areas

Software
Modelling and Simulation
Computer Vision and Pattern Recognition
Computer Science Applications
Geometry and Topology
Applied Mathematics

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10.1142/S021865430600086X

Cite this

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abstract = "We present algorithms for computing the kernel of a closed freeform rational surface. The kernel computation is reformulated as a problem of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the kernel. Using a plane-point duality, this paper also explores a duality relationship between the kernel of a closed surface and the convex hull of its tangential surface.",

keywords = "B-spline, Convex hull, Freeform rational surface, Gamma-kernel, Kernel, Symbolic computation, Zero-set finding",

author = "Gershon Elber and Johnstone, \{John K.\} and Kim, \{Myung Soo\} and Seong, \{Joon Kyung\}",

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AU - Elber, Gershon

AU - Johnstone, John K.

AU - Kim, Myung Soo

AU - Seong, Joon Kyung

PY - 2006/12

Y1 - 2006/12

N2 - We present algorithms for computing the kernel of a closed freeform rational surface. The kernel computation is reformulated as a problem of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the kernel. Using a plane-point duality, this paper also explores a duality relationship between the kernel of a closed surface and the convex hull of its tangential surface.

AB - We present algorithms for computing the kernel of a closed freeform rational surface. The kernel computation is reformulated as a problem of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the kernel. Using a plane-point duality, this paper also explores a duality relationship between the kernel of a closed surface and the convex hull of its tangential surface.

KW - B-spline

KW - Convex hull

KW - Freeform rational surface

KW - Gamma-kernel

KW - Kernel

KW - Symbolic computation

KW - Zero-set finding

UR - https://www.scopus.com/pages/publications/33845739403

U2 - 10.1142/S021865430600086X

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JF - International Journal of Shape Modeling

IS - 2

ER -

The kernel of a freeform surface and its duality with the convex hull of its tangential surface

Abstract

Keywords

ASJC Scopus subject areas

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