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.

In function bezier_intersect(), argument type may take the following values:

pos: Position of intersection point
cons: Boolean, indicating whether the strands abut; the ‘intersection’ point is the end of one curve and the beginning of the other
bool: Boolean, indicating whether or not the strands actually intersect
para: Bezier parameter \(t\) for the intersection point; actually return two parameters, one for each curve
opt: Details of the optimization output
all: Everything

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