The bisector surface of rational space curves

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The bisector surface of rational space curves

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ACM Transactions on Graphics (TOG) archive
Volume 17 , Issue 1 (January 1998) table of contents

Pages: 32 - 49

Year of Publication: 1998

ISSN:0730-0301

Authors

Gershon Elber	Technion–Israel Institute of Technology, Haifa, Israel
Myung-So Kim	POSTECH, Pohang, South Korea

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 31, Citation Count: 6

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abstract references cited by index terms review collaborative colleagues

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ABSTRACT

Given a point and a rational curve in the plane, their bisector curve is rational [Farouki and Johnston 1994a]. However, in general, the bisector of two rational curves in the plane is not rational [Farouki and Johnstone 1994b]. Given a point and a rational space curve, this art icle shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the degenerate case in which the two curves are coplanar).

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	DUTTA, D. AND HOFFMAN, C. 1993. On the skeleton of simple CSG objects. ASME J. Mech. Des. 115, 87-94.
	2	Rida T. Farouki , John K. Johnstone, The bisector of a point and a plane parametric curve, Computer Aided Geometric Design, v.11 n.2, p.117-151, April 1994 [doi>10.1016/0167-8396(94)90029-9]
	3	Rida T. Farouki , John K. Johnstone, Computing Point/Curve and Curve/Curve Bisectors, Proceedings of the 5th IMA Conference on the Mathematics of Surfaces, p.327-354, September 14-16, 1992
	4	FAROUKI, R. AND RAMAMURTHY, R. 1997. Specified-precision computation of curve/curve bisectors, To appear in Int. J. Comput. Geom. Appl.
	5	C. M. Hoffmann, A dimensionality paradigm for surface interrogations, Computer Aided Geometric Design, v.7 n.6, p.517-532, Nov. 1990 [doi>10.1016/0167-8396(90)90013-H]
	6	HOFFMANN, C. AND VERMEER, P. 1991. Eliminating extraneous solutions in curve and surface operations. Int. J. Comput. Geom. Appl. 1, 1, 47-66.
	7	IRIT 6.0 User's Manual. Feb. 1996. Technion. http://www.cs.technion.ac.il/-irit.
	8	Damian J. Sheehy , Cecil G. Armstrong , Desmond J. Robinson, Shape Description By Medial Surface Construction, IEEE Transactions on Visualization and Computer Graphics, v.2 n.1, p.62-72, March 1996 [doi>10.1109/2945.489387]
	9	Evan C. Sherbrooke , Nicholas M. Patrikalakis , Erik Brisson, An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids, IEEE Transactions on Visualization and Computer Graphics, v.2 n.1, p.44-61, March 1996 [doi>10.1109/2945.489386]

CITED BY 6

	Gershon Elber , Myung-Soo Kim, Geometric constraint solver using multivariate rational spline functions, Proceedings of the sixth ACM symposium on Solid modeling and applications, p.1-10, May 2001, Ann Arbor, Michigan, United States
	Gershon Elber , Myung-Soo Kim, Rational bisectors of CSG primitives, Proceedings of the fifth ACM symposium on Solid modeling and applications, p.159-166, June 08-11, 1999, Ann Arbor, Michigan, United States
	Gershon Elber , Myung-Soo Kim, Computing Rational Bisectors, IEEE Computer Graphics and Applications, v.19 n.6, p.76-81, November 1999
	Iddo Hanniel , Ramanathan Muthuganapathy , Gershon Elber , Myung-Soo Kim, Precise Voronoi cell extraction of free-form rational planar closed curves, Proceedings of the 2005 ACM symposium on Solid and physical modeling, p.51-59, June 13-15, 2005, Cambridge, Massachusetts
	Vladlen Koltun , Micha Sharir, Three dimensional euclidean Voronoi diagrams of lines with a fixed number of orientations, Proceedings of the eighteenth annual symposium on Computational geometry, p.217-226, June 05-07, 2002, Barcelona, Spain
	M. Ramanathan , B. Gurumoorthy, Constructing medial axis transform of extruded and revolved 3D objects with free-form boundaries, Computer-Aided Design, v.37 n.13, p.1370-1387, November, 2005

INDEX TERMS

Primary Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS

General Terms:
Algorithms, Design, Theory

Keywords:
Voronoi surface, bisector, medical surface, skeleton

REVIEW

"Paolo E. Sabella : Reviewer"

A technique is presented for obtaining the parametric representation of a surface, called the bisector surface, defined as the set of points equidistant from two rational space curves. Previous work has shown that, except in special cases, the more...

Collaborative Colleagues:

Gershon Elber: colleagues

Myung-So Kim: colleagues

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