# bezier_integral: Arcwise integrals over Bezier curves In RobinHankin/knotR: Knot Diagrams using Bezier Curves

## Description

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

## Usage

 1 2 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 ds/R^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()

## 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 (S ds/R).

2. Function bezier_arclength() gives the arc length.

## Author(s)

Robin K. S. Hankin

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