Curvature Comb / Jacob Rus

geodetic computer

Published

Edited

Jan 9, 2019

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curvature_transformation = (k) => 400*Math.atan(50*k)/Math.PI

curvature_comb = function(bezier) {

const curve_cheb = bez3_to_cheb(bezier);

const [x, y] = curve_cheb;

const Dx = diff(x), Dy = diff(y);

const DDx = diff(Dx), DDy = diff(Dy);

return function curvature_comb(p) {

const xp = chebeval(x, p), yp = chebeval(y, p);

const Dxp = chebeval(Dx, p), Dyp = chebeval(Dy, p);

const DDxp = chebeval(DDx, p), DDyp = chebeval(DDy, p);

const Ds_inv = 1 / Math.sqrt(Dxp*Dxp + Dyp*Dyp);

const curvature = (Dxp*DDyp - Dyp*DDxp) * (Ds_inv*Ds_inv*Ds_inv);

const squished_curvature = Ds_inv * curvature_transformation(curvature);

// const squished_curvature = Ds_inv * curvature * 2000;

// return Dx * squished_curvature

return [xp + squished_curvature * Dyp, yp - squished_curvature * Dxp];

}

viewof bez = new View([[489,287],[739,68],[197,222],[534,350]])

import {bez3_to_cheb} from '@jrus/bezier-segment-arclength'

import {evaluate as chebeval, diff, cumsum, sum, coeffs2vals, vals2coeffs, chebpts} from "@jrus/cheb"

import {bezeval, bezpts_to_svgpath} from "@jrus/bezplot"

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