bezier_angle: Intersection of two Bezier curves
In knotR: Knot Diagrams using Bezier Curves

Description Usage Arguments Details Note Author(s) See Also Examples

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

1 2	bezier_angle(P1, P2) bezier_intersect(P1,P2, type='pos', ...)

`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()`

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.

If the curves intersect in more than one point, the behaviour of these routines is not defined.

Robin K. S. Hankin

bezier

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