knotR (version 1.0-2)

bezier_integrals: Arcwise integrals over Bezier curves

Description

Various integrals over Bezier curves such as total arc length and bending energy

Usage

bezier_arclength(P, t1=0,t2=1,give=FALSE,...)
bezier_bending_energy(P, t1=0,t2=1, give=FALSE, power=2, ...)

Arguments

P

Control points in the form of a 4 by 2 matrix with rows corresponding to \(P_0\) to \(P_3\)

give

Boolean, with TRUE meaning to return more information and default FALSE meaning to return just the value of the integration as estimated by the numerical routine

power

Function bezier_bending_energy() returns bending energy is \(\int_S\frac{ds}{R^\mathrm{power}}\), where \(R=R(s)\) is the radius of curvature. If \(\mathrm{power}=2\) this corresponds to the Eulerian bending energy of a flexible beam

t1,t2

In function bezier_arclength(), the values of t to start and end the integration at

...

Further arguments passed to integrate()

Author

Robin K. S. Hankin

Details

These functions use numerical integration, specifically integrate(), between two specified points on a Bezier curve.

1. Function bezier_bending_energy() gives the and bending energy (\(\int R^{-1}ds\)).

2. Function bezier_arclength() gives the arc length.

See Also

bezier_angle

Examples

P <- matrix(c(0, 1, 2, 2, 2, 0, 3, 2),4,2)

bezier_arclength(P)