Reducing control points in lofted B-spline surface interpolation using common knot vector determination

  • Authors:

  • Wen-Ke Wang;Hui Zhang;Hyungjun Park;Jun-Hai Yong;Jean-Claude Paul;Jia-Guang Sun

  • Affiliations:

  • School of Software, Tsinghua University, Beijing 100084, PR China and Department of Computer Science and Tech., Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information Sys ...;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China;Department of Industrial Engineering, Chosun University, Gwangju 501-759, South Korea;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and INRIA, France;School of Software, Tsinghua University, Beijing 100084, PR China and Department of Computer Science and Tech., Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information Sys ...

  • Venue:
  • Computer-Aided Design
  • Year:
  • 2008

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Abstract

A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method.