@davepagurek/flo-mat/src/mat/simplify-mat-map-only.ts

Medial / Scale Axis Transform (MAT/SAT) Library.

import { closestPointOnBezier, hausdorffDistance, toCubic } from 'flo-bezier3';
import { CpNode, isTerminating } from '../cp-node/cp-node.js';
import { getBranches } from './get-branches.js';
import { getCurveToNext } from '../cp-node/get-curve-to-next.js';
import { getCurveBetween } from '../get-curve/get-curve-between.js';


/**
 * Simplifies the given MAT by replacing the piecewise quad beziers composing 
 * the MAT with fewer ones to within a given tolerance. Returns the map of
 * to be deleted nodes only - does not actually delete them. Use simplifyMat
 * instead if you want to delete the nodes.
 * @param cpNode A representation of the MAT
 * @param anlgeTolerance Tolerance given as the degrees difference of the unit 
 * direction vectors at the interface between curves. A tolerance of zero means
 * perfect smoothness is required - defaults to 15.
 * @param hausdorffTolerance The approximate maximum Hausdorff Distance tolerance -
 * defaults to 0.1
 * @param hausdorffSpacing The spacing on the curves used to calculate the Hausdorff
 * Distance - defaults to 1
 */
function simplifyMatMapOnly(
        cpNode: CpNode,
        anlgeTolerance = 15,
        hausdorffTolerance = 1e-1,
        hausdorffSpacing = 1e0) {

    const simpleMap: Map<CpNode, { ps: number[][], ts: number[] }> = new Map();

    // Start from a leaf
    while (!isTerminating(cpNode)) {
        cpNode = cpNode.next;
    }

    const branches = getBranches(cpNode, anlgeTolerance);

    const canDeletes: CpNode[] = [];
    for (let k=0; k<branches.length; k++) {
        const branch = branches[k];

        // Try to remove some
        let j = 0;
        while (j < branch.length) {
            const i = j;
            while (true) {
                j++;

                if (j === branch.length) { break; }

                const hd = getTotalHausdorffDistance(i, j, branch, hausdorffSpacing);

                if (hd > hausdorffTolerance) {
                    break;
                } else {
                    canDeletes.push(branch[j]);
                }
            }

            if (i + 1 === j) { 
                // no simplification occured
            } else {
                const branStart = branch[i];
                const branEnd = branch[j-1];

                const medial = toCubic(getCurveBetween(branStart, branEnd.next));
                const rev = medial.slice().reverse();
                let curCpNode = branStart;
                let prevT = 0;
                while (curCpNode !== branEnd) {
                    const t = closestPointOnBezier(medial, curCpNode.next.cp.circle.center).t;
                    simpleMap.set(curCpNode, { ps: medial, ts: [prevT, t] });
                    const oppositeCpNode = curCpNode.nextOnCircle.prev;
                    simpleMap.set(oppositeCpNode, { ps: rev, ts: [1-t, 1-prevT] });

                    prevT = t;
                    curCpNode = curCpNode.next;
                }
                simpleMap.set(curCpNode, { ps: medial, ts: [prevT, 1] });

                const oppositeCpNode = curCpNode.nextOnCircle.prev;
                simpleMap.set(oppositeCpNode, { ps: rev, ts: [0, 1-prevT] });
            }
        }
    }

    return { simpleMap, cpNode };
}


function getTotalHausdorffDistance(
        i: number, 
        j: number, 
        branch: CpNode[],
        hausdorffSpacing: number) {

    const hds: number[] = [];
    const longCurve = getCurveBetween(branch[i], branch[j].next);
    for (let m=i; m<j+1; m++) {
        hds.push(hausdorffDistance(
            getCurveToNext(branch[m]), 
            longCurve,
            hausdorffSpacing
        ));
    }

    return Math.max(...hds);
}


export { simplifyMatMapOnly }