1

2026-09-24 16:25:22 +08:00
commit 7428184f01
1198 changed files with 314515 additions and 0 deletions
@@ -0,0 +1,78 @@
+type callbackFunType = (x:number)=>number
+let kSplineTableSize = 11;
+let kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);
+
+function A(aA1:number, aA2:number):number { return 1.0 - 3.0 * aA2 + 3.0 * aA1 }
+function B(aA1:number, aA2:number):number { return 3.0 * aA2 - 6.0 * aA1 }
+function C(aA1:number):number { return 3.0 * aA1 }
+
+function calcBezier(aT:number, aA1:number, aA2:number):number { return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT }
+function getSlope(aT:number, aA1:number, aA2:number):number { return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1) }
+
+function binarySubdivide(aX:number, aA:number, aB:number, mX1:number, mX2:number):number {
+	let currentX = 0;
+	let currentT = 0;
+	let i = 0;
+	do {
+		currentT = aA + (aB - aA) / 2.0;
+		currentX = calcBezier(currentT, mX1, mX2) - aX;
+		if (currentX > 0.0) { aB = currentT; } else { aA = currentT; }
+	} while (Math.abs(currentX) > 0.0000001 && ++i < 10);
+	return currentT;
+}
+
+function newtonRaphsonIterate(aX:number, aGuessT:number, mX1:number, mX2:number):number {
+	let pat = aGuessT;
+	for (let i = 0; i < 4; ++i) {
+		let currentSlope = getSlope(aGuessT, mX1, mX2);
+		if (currentSlope == 0.0) { return aGuessT; }
+		let currentX = calcBezier(aGuessT, mX1, mX2) - aX;
+		pat -= currentX / currentSlope;
+	}
+	return pat;
+}
+
+function bezier(mX1:number, mY1:number, mX2:number, mY2:number):callbackFunType|null {
+
+	if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) { return null; }
+	let sampleValues:number[] = [];
+
+	if (mX1 != mY1 || mX2 != mY2) {
+		for (let i = 0; i < kSplineTableSize; ++i) {
+			sampleValues.push(calcBezier(i * kSampleStepSize, mX1, mX2))
+		}
+	}
+
+	function getTForX(aX:number):number {
+
+		let intervalStart = 0;
+		let currentSample = 1;
+		let lastSample = kSplineTableSize - 1;
+
+		for (; currentSample != lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
+			intervalStart += kSampleStepSize;
+		}
+
+		--currentSample;
+
+		let dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
+		let guessForT:number = intervalStart + dist * kSampleStepSize;
+		let initialSlope = getSlope(guessForT, mX1, mX2);
+
+		if (initialSlope >= 0.001) {
+			return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
+		} else if (initialSlope == 0.0) {
+			return guessForT;
+		}
+		return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
+	}
+
+	return function (x:number):number {
+		if (mX1 == mY1 && mX2 == mY2) { return x; }
+		if (x == 0 || x == 1) { return x; }
+		return calcBezier(getTForX(x), mY1, mY2);
+	}
+
+}
+
+export default bezier