bezier_angle: Intersection of two Bezier curves

Description

Description of the intersection of two Bezier curves including position and angle of the point of intersection.

Usage

bezier_angle(P1, P2)
bezier_intersect(P1,P2, type='pos', ...)

Arguments

P1,P2: Control points for two Bezier curves as per bezier()
type: In function bezier_intersect(), string argument governing what exactly is to be returned; see details.
...: In function bezier_intersect(), further arguments passed to constOptim()

Author

Robin K. S. Hankin

Details

Function bezier_intersect() uses constOptim() to find the point of closest approach.

Function bezier_angle() returns the square of the cosine of the intersection angle (so strands crossing at right angles return zero). If the strands do not intersect, then return 1. This is needed because sometimes, strands which intersect are perturbed by the optimization routine so that they are disjoint.

Examples

Run this code




P1 <- matrix(c(1, 3, 6, 4, 7, 3, 2, 2),ncol=2)
P2 <- matrix(c(4, 5, 5, 3, 7, 2, 5, 1),ncol=2)

x1 <- bezier(P1,n=100)
x2 <- bezier(P2,n=100)

plot(x1,asp=1,xlim=c(0,8),ylim=c(0,8))
points(x2)

myseg(P1)
myseg(P2)

jj <- bezier_intersect(P1,P2)
points(x=jj[1],y=jj[2],pch=16,cex=3,col='blue')

# looks close to orthogonal, actually 82 degrees:
acos(sqrt(bezier_angle(P1,P2)))*180/pi