TY - GEN

T1 - Complete subdivision algorithms, I

T2 - 22nd Annual Symposium on Computational Geometry 2006, SCG'06

AU - Yap, Chee K.

PY - 2006

Y1 - 2006

N2 - We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

AB - We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

KW - Bezier curves

KW - Computational geometry

KW - Curve intersection

KW - Exact geometric computation

KW - Robust numerical algorithms

KW - Subdivision method

UR - http://www.scopus.com/inward/record.url?scp=33748060965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748060965&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33748060965

SN - 1595933409

SN - 9781595933409

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 217

EP - 226

BT - Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06

Y2 - 5 June 2006 through 7 June 2006

ER -