Projection of curves on B-spline surfaces using quadratic reparameterization

Authors:
Yi-Jun Yang;Wei Zeng;Hui Zhang;Jun-Hai Yong;Jean-Claude Paul
Affiliations:
GMSV center, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia and INRIA, Villers Les Nancy 54600, France and School of Software, Tsinghua University, Beijing 100 ...;Computer Science Department, Stony Brook University, Stony Brook, NY 11790, USA;School of Software, Tsinghua University, Beijing 100084, PR China;School of Software, Tsinghua University, Beijing 100084, PR China;INRIA, Villers Les Nancy 54600, France and School of Software, Tsinghua University, Beijing 100084, PR China
Venue:
Graphical Models
Year:
2010

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Abstract

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bezier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is @e"T-G^1 continuous, where @e"T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm.