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

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

import { cross, dot, toUnitVector } from "flo-vector2d";
import { Corner } from "./corner";
import { getInterfaceCcw } from './get-interface-ccw.js';


/** 
 * @internal
 * Angle in degrees to radians.
 */
const DEGREES = {
	//'0'    : 0.0000,
	0.25 : 0.0050,
	1    : 0.0167,
	4    : 0.0698,
	16   : 0.2756,
};


/** @internal */
//const DEGREE_LIMIT = DEGREES[1];
const DEGREE_LIMIT = DEGREES[4]; 
//const DEGREE_LIMIT = DEGREES[16]; 


/**
 * @internal
 * Returns a new corner with properties.
 * 
 * PRECONDITION: The beziers has control points with max bit-length of 26 and
 * aligned to a 'grid' to have the same exponent. This is so the vectors between
 * control points can be calculated exactly without resorting to adaptive 
 * infinite precision floating point operations.
 * 
 * @param psI The incoming bezier that ends in the corner
 * @param psO The outgoing bezier that starts at the corner
 */
function getCorner(
		psI: number[][],
		psO: number[][]): Corner {

	// getInterfaceCcw must return a number !== 0 if psI and psO are not the
	// same as seen as a curve extension with t ∈ [-∞,+∞]
	const ccw = getInterfaceCcw(psI, psO);
	const isSharp = ccw < 0;
	const isDull  = ccw > 0;

	// Find (non-normalized) tangent of curve.ps at t === 1
	const p0E = psI[psI.length-2];
	const p1E = psI[psI.length-1];
	const xE = p1E[0] - p0E[0];
	const yE = p1E[1] - p0E[1];
	const tangentAtEnd = [xE,yE];

	// Find (non-normalized) tangent of curve.next.ps at t === 0
	const p0S = psO[0];
	const p1S = psO[1];
	const xS = p1S[0] - p0S[0];
	const yS = p1S[1] - p0S[1];
	const tangentAtStart = [xS,yS];

	// These use square root and are thus not exact
	const tangents_ = [
		toUnitVector(tangentAtEnd), 
		toUnitVector(tangentAtStart), 
	];

	// The cross calculated below should be exact due to beziers having been
	// normalized!
	const crossTangents = cross(tangents_[0], tangents_[1]);

	let isQuiteSharp: boolean; 
	let isQuiteDull: boolean; 
	const dotTangents = dot(tangentAtEnd, tangentAtStart);
	if (dotTangents > 0) {
		// Curves go in same direction
		isQuiteSharp = crossTangents < -DEGREE_LIMIT;
		isQuiteDull = crossTangents > +DEGREE_LIMIT;
	} else {
		isQuiteSharp = isSharp;
		isQuiteDull  = isDull;
	}

	return {
		tangents: tangents_, 
		crossTangents, 
		isSharp,
		isDull, 
		isQuiteSharp,
		isQuiteDull
	};
}


export { getCorner }