Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
권호 표지

Computing Planar Curve Offset Based on Surface/Surface Intersection

교차곡선 연산을 이용한 평면 곡선의 오프셋 계산

  • 최정주 (한국전자통신연구원 컴퓨터소프트웨어기술연구소)
  • Published : 1998.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

Keywords

References

  1. Computer Aided Geometric Design v.7 Algebraic Properties of Plane Offset Curves Farouki, R.;Neff, C.
  2. Computer Aided Geometric Design v.7 Analytic Properties of Plane Offset Curves Farouki, R.;Neff, C.
  3. Computer Aided Geometric Design v.5 Spline Approximation of Offset Curves Hoschek, J.
  4. Computer-Aided Design v.20 no.8 Optimal Approximation Conversion of Spline Curves and Spline Approximation of Offset Curves Hoschek, J.;Wissel, N.
  5. Computer-Aided Design v.28 no.8 Planar Curve Offset Based on Circle Approximation Lee, I. K.;Kim, M. S.;Elber, G.
  6. IBM Journal of Research Development v.34 Pythagorean Hodograph Farouki, R.;Sakkalis, T.
  7. Computer Aided Geometric Design v.12 Rational Curves and Surfaces with Rational Offsets Pottmann, H.
  8. Computer Aided Geometric Design v.15 A Laguerre Geometric Approach to Rational Offsets Peternell, M.;Pottmann, H.
  9. IEEE Computer Graphics and Applications v.17 no.3 Comparing Offset Curve Approximation Methods Elber, G.;Lee, I. K.;Kim, M. S.
  10. Lecture Notes in Computer Science v.500 On the Computational Geometry of Pocket Machining Held, M.
  11. Computational Geometry in C O'Rouke, J.
  12. Computer Aided Geometric Design v.15 Applications of Laguerre Geometry in CAGD Pottmann, H.;Peternell, M.
  13. Fundamentals of Computer Aided Geometric Design Hoschek, J.;Lasser, D.
  14. The Mathematics of Surfaces Surface/surface Intersection Problems Pratt, M.;Geisow, A.;J. A. Gregory(ed.)
  15. Ph.D. Thesis, Dept. of Computer Science, POSTECH Local Canonical Cubic Curve Tracing along Surface/Surface Intersections Choi, J. J.
  16. Computer Aided Geometric Design v.14 A New Approach to the Surface Intersections Problem Grandine, T.;Klein, F.
  17. Differential Geometry of Curves and Surfaces do Carmo, m.
  18. In workshop proceedings of Differential/Topological Techniques in Geometric Modeling and Processing '98 Ruled/ruled Surface Intersection Heo, H. S.;Kim, M. S.;Elber, G.
  19. IRIT 7.0α User's Manual Elber, G.