Surface Intersections for Geometric Modeling

[+] Author and Article Information
N. M. Patrikalakis

Department of Ocean Engineering, Design Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139

P. V. Prakash

Prime Computer Inc., Bedford, MA 01730

J. Mech. Des 112(1), 100-107 (Mar 01, 1990) (8 pages) doi:10.1115/1.2912565 History: Received May 01, 1989; Online June 02, 2008


Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution procedure. Using turning and singular points, the intersection problem can be partitioned into subdomains that can be processed independently and which involve intersection segments that can be traced with faceting methods. This partitioning and the tracing of individual segments is carried out using an adaptive subdivision algorithm for Bezier/B-spline surfaces followed by Newton correction of the approximation. The method has been successfully tested in tracing complex algebraic curves and in solving actual intersection problems with diverse features.

Copyright © 1990 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In