Robust techniques for curve and surface intersections

Dinesh Manocha

doi:10.1117/12.131733

1 November 1992 Robust techniques for curve and surface intersections

Dinesh Manocha

Proceedings Volume 1830, Curves and Surfaces in Computer Vision and Graphics III; (1992) https://doi.org/10.1117/12.131733
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

The problems of computing the intersection of curves and surfaces are fundamental to computer graphics and geometric and solid modeling. Earlier algorithms were based either on subdivision methods or algebraic techniques. They are generally restricted to simple intersections. It has been generally regarded that algebraic approach is impractical due to numerical problems on higher degree curves and surfaces (beyond cubics). In our earlier work we have applied Elimination theory and reduced the problem of intersections of curves and surfaces to matrix computations. These include Gauss elimination, matrix inversion, singular value decomposition, eigenvalues and eigenvectors etc. In this paper, we present robust algorithms based on techniques from linear algebra and numerical analysis for computing the zero dimensional intersections of curves and surface. These include intersection of parametric and algebraic curves and curve-surface intersections. In particular, we present a robust algorithm for computer higher order intersections.

Citation Download Citation

Dinesh Manocha "Robust techniques for curve and surface intersections", Proc. SPIE 1830, Curves and Surfaces in Computer Vision and Graphics III, (1 November 1992); https://doi.org/10.1117/12.131733

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available