@davepagurek/flo-mat/src/find-2-prong/reduce-radius.ts

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

import { evalDeCasteljau } from "flo-bezier3";
import { dot, lineLineIntersection, squaredDistanceBetween } from "flo-vector2d";
import { BezierPiece } from '../mat/bezier-piece.js';


/**
 * @internal
 * 
 * Reduces the circle radius initially as an optimization step.
 */
function reduceRadius(
        extreme: number,
        bezierPieces: BezierPiece[], 
        p: number[],
        x: number[]) {

    const TOLERANCE = 1 + 2**-10;

    let prevP: number[] | undefined = undefined;
    let minRadius = Number.POSITIVE_INFINITY;
    for (let i=0; i<bezierPieces.length; i++) {
        const bezierPiece = bezierPieces[i];

        const ps = bezierPiece.curve.ps;

        let r1 = Number.POSITIVE_INFINITY;
        const p1 = evalDeCasteljau(ps, bezierPiece.ts[0]);

        // Prevent evaluating the same points twice
        if (!prevP || prevP[0] !== p1[0] || prevP[1] !== p1[1]) {
            const cc1 = getCircleCenterFrom2PointsAndNormal(extreme, p, x, p1);
            if (cc1) { r1 = squaredDistanceBetween(p, cc1);	}
        }
        
        let r2 = Number.POSITIVE_INFINITY;
        const p2 = evalDeCasteljau(ps, bezierPiece.ts[1]);

        const cc2 = getCircleCenterFrom2PointsAndNormal(extreme, p, x, p2);
        if (cc2) { r2 = squaredDistanceBetween(p, cc2);	}
        
        prevP = p2;
        
        const d = Math.min(r1, r2); 
        
        if (d < minRadius) {
            minRadius = d;  
        }
    }

    // The extra bit is to account for floating point precision.
    return TOLERANCE*minRadius;
}


/**
 * @internal
 * @param p A point on the circle with normal pointing to x towards the center
 * of the circle.
 * @param x
 * @param p1 Another point on the circle.
 */
function getCircleCenterFrom2PointsAndNormal(
        extreme: number, 
        p: number[], 
        x: number[],
        p1: number[]) {

    const TOLERANCE = (2**-14*extreme)**2;

    // Ignore if p and p1 are too close together
    if (squaredDistanceBetween(p,p1) < TOLERANCE) {
        return undefined;
    }

    /** The perpindicular bisector between the two given points on the circle */
    const pb = [
        (p[0] + p1[0]) / 2,
        (p[1] + p1[1]) / 2,
    ];
    const tan = [p1[0] - p[0], p1[1] - p[1]];
    const norm  = [-tan[1], tan[0]]; // Rotate by 90 degrees
    const pb2 = [pb[0] + norm[0], pb[1] + norm[1]];

    const res = lineLineIntersection([p,x], [pb, pb2]);

    if (!res) { return undefined; }

    const resO = [res[0] - p[0], res[1] - p[1]];
    const xO = [x[0] - p[0], x[1] - p[1]];
    if (dot(resO, xO) < 0) {
        return undefined;
    }

    return res;
}


export { reduceRadius }