On the minors of the implicitization Bézout matrix for a rational plane curve

2001 ◽  
Vol 18 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Eng-Wee Chionh ◽  
Thomas W. Sederberg
Keyword(s):  
Plane Curve ◽  
Rational Plane ◽  
Bezout Matrix ◽  
Rational Plane Curve

Iterative computation of the convex hull of a rational plane curve

2015 ◽  
Vol 49 (2) ◽  
pp. 52-52
Author(s):  
Juan G. Alcázar ◽  
Carlos Hermoso ◽  
Jorge Caravantes ◽  
Gema M. Díaz-Toca
Keyword(s):  
Convex Hull ◽  
Plane Curve ◽  
Iterative Computation ◽  
Rational Plane ◽  
Rational Plane Curve

scholarly journals The Newton Polygon of a Rational Plane Curve

2010 ◽  
Vol 4 (1) ◽  
pp. 3-24 ◽  
Author(s):  
Carlos D’Andrea ◽  
Martín Sombra
Keyword(s):  
Plane Curve ◽  
Newton Polygon ◽  
Rational Plane ◽  
Rational Plane Curve

On the Nodes of a Rational Plane Curve

1947 ◽  
Vol 31 (295) ◽  
pp. 161
Author(s):  
Harold Simpson
Keyword(s):  
Plane Curve ◽  
Rational Plane ◽  
Rational Plane Curve

Specified–Precision Computation of Curve/Curve Bisectors

1998 ◽  
Vol 08 (05n06) ◽  
pp. 599-617 ◽  
Author(s):  
Rida T. Farouki ◽  
Rajesh Ramamurthy
Keyword(s):  
Plane Curve ◽  
Plane Curves ◽  
Rational Form ◽  
Error Measure ◽  
Distance Error ◽  
Adaptive Schemes ◽  
Sample Data ◽  
Rational Plane ◽  
Rational Parameterization ◽  
Piecewise Parabolic

The bisector of two plane curve segments (other than lines and circles) has, in general, no simple — i.e., rational — parameterization, and must therefore be approximated by the interpolation of discrete data. A procedure for computing ordered sequences of point/tangent/curvature data along the bisectors of polynomial or rational plane curves is described, with special emphasis on (i) the identification of singularities (tangent–discontinuities) of the bisector; (ii) capturing the exact rational form of those portions of the bisector with a terminal footpoint on one curve; and (iii) geometrical criteria the characterize extrema of the distance error for interpolants to the discretely–sample data. G1 piecewise– parabolic and G2 piecewise–cubic approximations (with O(h4) and O(h6) convergence) are described which, used in adaptive schemes governed by the exact error measure, can be made to satisfy any prescribed geometrical tolerance.

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