论文信息 - A Two-Dimensional Ellipse–Rectangle Intersection Test

A Two-Dimensional Ellipse–Rectangle Intersection Test

We present an efficient algorithm for testing whether or not a filled rectangle and a filled ellipse intersect. The algorithm requires at most two evaluations of the quadratic polynomial that defines the ellipse and the execution of a few simple arithmetic expressions. The convexity and monotonicity properties of this polynomial are the main tools for the design of the algorithm.

Jon G. Rokne | Helmut Ratschek | J. Rokne | H. Ratschek

[1] David F. Rogers,et al. Mathematical elements for computer graphics , 1976 .

[2] Jon G. Rokne,et al. Exact computation of the sign of a finite sum , 1999, Appl. Math. Comput..

[3] V. Leitáo,et al. Computer Graphics: Principles and Practice , 1995 .

[4] Subhash Suri,et al. Analysis of a bounding box heuristic for object intersection , 1999, SODA '99.

[5] Ibrahim Zeid,et al. CAD/CAM theory and practice , 1991 .

[6] Karel Drábek. Plane Curves and Constructions , 1994 .

[7] M. Carter. Computer graphics: Principles and practice , 1997 .

[8] Kenneth J. Hill. Matrix-based Ellipse Geometry , 1995 .

[9] I. Faux,et al. Computational Geometry for Design and Manufacture , 1979 .

[10] Joshua Levin,et al. A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces , 1976, CACM.

[11] G. Forsythe. Pitfalls in computation, or why a math book isn''t enough , 1970 .

[12] Jon G. Rokne,et al. Computer Methods for the Range of Functions , 1984 .

[13] William H. Press,et al. Numerical recipes in C , 2002 .