bezier_angle: Intersection of two Bezier curves

In knotR: Knot Diagrams using Bezier Curves

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()

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

Note

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

Author(s)

Robin K. S. Hankin

See Also

bezier

Examples

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 

knotR documentation built on June 22, 2024, 6:56 p.m.