Initial work of ESM transformation

font-src/support/geometry/transform.mjs

@@ -0,0 +1,81 @@
+export class Transform {
+	constructor(xx, yx, xy, yy, x, y) {
+		this.xx = xx;
+		this.yx = yx;
+		this.xy = xy;
+		this.yy = yy;
+		this.x = x;
+		this.y = y;
+	}
+	static Id() {
+		return new Transform(1, 0, 0, 1, 0, 0);
+	}
+	static Translate(x, y) {
+		return new Transform(1, 0, 0, 1, x, y);
+	}
+	apply(pt) {
+		return this.applyXY(pt.x, pt.y);
+	}
+	applyXY(x, y) {
+		return {
+			x: x * this.xx + y * this.yx + this.x,
+			y: x * this.xy + y * this.yy + this.y
+		};
+	}
+	applyOffset(delta) {
+		return this.applyOffsetXY(delta.x, delta.y);
+	}
+	applyOffsetXY(deltaX, deltaY) {
+		return {
+			x: deltaX * this.xx + deltaY * this.yx,
+			y: deltaX * this.xy + deltaY * this.yy
+		};
+	}
+	unapply(pt) {
+		const xx = pt.x - this.x;
+		const yy = pt.y - this.y;
+		const denom = this.xx * this.yy - this.xy * this.yx;
+		return {
+			x: (xx * this.yy - yy * this.yx) / denom,
+			y: (yy * this.xx - xx * this.xy) / denom
+		};
+	}
+	inverse() {
+		const denom = this.xx * this.yy - this.xy * this.yx;
+		return new Transform(
+			this.yy / denom,
+			-this.yx / denom,
+			-this.xy / denom,
+			this.xx / denom,
+			-(this.x * this.yy - this.y * this.yx) / denom,
+			-(-this.x * this.xy + this.y * this.xx) / denom
+		);
+	}
+	toString() {
+		return `[[${this.xx} ${this.xy}] [${this.yx} ${this.yy}]] + [[${this.x}] [${this.y}]]`;
+	}
+	static isTranslate(tfm) {
+		return tfm.xx === 1 && tfm.yy === 1 && tfm.xy === 0 && tfm.yx === 0;
+	}
+	static isIdentity(tfm) {
+		return this.isTranslate(tfm) && tfm.x === 0 && tfm.y === 0;
+	}
+	static Combine(...tfms) {
+		let z00 = { x: 0, y: 0 };
+		let z10 = { x: 1, y: 0 };
+		let z01 = { x: 0, y: 1 };
+		for (const tfm of tfms) {
+			z00 = tfm.apply(z00);
+			z10 = tfm.apply(z10);
+			z01 = tfm.apply(z01);
+		}
+		return new Transform(
+			z10.x - z00.x,
+			z01.x - z00.x,
+			z10.y - z00.y,
+			z01.y - z00.y,
+			z00.x,
+			z00.y
+		);
+	}
+}