@davepagurek/flo-mat/src/mat/get-branches.ts

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

import { tangent } from 'flo-bezier3';
import { cross, toUnitVector } from 'flo-vector2d';
import { CpNode, getChildren, isFullyTerminating, isTerminating } from '../cp-node/cp-node.js';
import { getCurveToNext } from '../cp-node/get-curve-to-next.js';


/** @internal */
const defaultTolerance = 1; // 1 degree


/**
 * Traverses all edges (depth first) of the given MAT tree starting at the given 
 * vertex (represented by a [[CpNode]]). Returns the result as an array of
 * smooth branches, where smoothness is total or within a given tolerance.
 * @param cpNode Any [[CpNode]] representing the start vertex.
 * @param tolerance 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.
 */
function getBranches(
		cpNode: CpNode, 
		tolerance: number = defaultTolerance): CpNode[][] {

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

	const branches: CpNode[][] = [];

	// Since the tree is unrooted we must iterate in all directions from the
	// given vertex.
	const cps = [cpNode.prevOnCircle];

	let branchCpNodes: CpNode[] = [];
	while (cps.length) {
		const cp = cps.pop()!;
		branchCpNodes.push(cp);

		let children = getChildren(cp);

		if (isFullyTerminating(cp)) {
			if (branchCpNodes.length > 1) {
				branches.push(branchCpNodes);
			}
			branchCpNodes = [];
			continue; 
		}

		if (children.length === 1) {
			cps.push(children[0]);
			continue;
		}

		children = children.filter(cpNode => !isTerminating(cpNode));

		if (children.length === 0) {
			branches.push(branchCpNodes);
			branchCpNodes = [];
			continue;
		}

		if (children.length > 1) {
			// More than one branch comes together
			branches.push(branchCpNodes);
			branchCpNodes = [];
			cps.push(...children);
			continue;
		}

		const backPointingTan = toUnitVector(tangent(
			getCurveToNext(cp.next.prevOnCircle), 
			0
		));
		const forwardPointingTan = toUnitVector(tangent(
			getCurveToNext(children[0]), 
			0
		));

		const cross_ = cross(backPointingTan, forwardPointingTan);
		const angle = Math.abs(Math.asin( cross_ ) * (180/Math.PI));

		if (angle > tolerance) {
			branches.push(branchCpNodes);
			branchCpNodes = [];
		}

		cps.push(children[0]);
	}

	if (branchCpNodes.length) { branches.push(branchCpNodes); }

	return branches;
}


export { getBranches }