4 files changed, 203 insertions, 0 deletions
diff --git a/src/renderer/runtime/math/circle.ts b/src/renderer/runtime/math/circle.ts
new file mode 100644
index 0000000..f4e855a
--- /dev/null
+++ b/src/renderer/runtime/math/circle.ts
@@ -0,0 +1,15 @@
+import { Collidable } from './collision';
+import { Movement } from './line';
+import { Point } from './point';
+
+import { vec2 } from 'gl-matrix';
+
+export class Circle implements Collidable, Point {
+	private pointCollide = Point.prototype.collide;
+
+	constructor(public readonly p: vec2, public readonly r: number) {}
+
+	public collide(out: vec2, move: Movement, r: number): boolean {
+		return this.pointCollide(out, move, r + this.r);
+	}
+}
diff --git a/src/renderer/runtime/math/collision.ts b/src/renderer/runtime/math/collision.ts
new file mode 100644
index 0000000..3df811a
--- /dev/null
+++ b/src/renderer/runtime/math/collision.ts
@@ -0,0 +1,7 @@
+import { Movement } from './line';
+
+import { vec2 } from 'gl-matrix';
+
+export interface Collidable {
+	collide(out: vec2, move: Movement, r: number): boolean;
+}
diff --git a/src/renderer/runtime/math/line.ts b/src/renderer/runtime/math/line.ts
new file mode 100644
index 0000000..db99035
--- /dev/null
+++ b/src/renderer/runtime/math/line.ts
@@ -0,0 +1,141 @@
+import { mat2, vec2 } from 'gl-matrix';
+import { Collidable } from './collision';
+
+const rot90 = mat2.fromValues(
+	0, 1,
+	-1, 0,
+);
+
+export function normal(out: vec2, a: vec2): vec2 {
+	return vec2.transformMat2(out, a, rot90);
+}
+
+export function crossz(a: vec2, b: vec2): number {
+	return a[0] * b[1] - a[1] * b[0];
+}
+
+export class Line {
+	constructor(
+		public readonly p: vec2,
+		public readonly v: vec2,
+	) {}
+
+	public getNormal(out: vec2): vec2 {
+		return normal(out, this.v);
+	}
+
+	public projectPointDistance(p2: vec2): number {
+		const v2 = vec2.sub(vec2.create(), p2, this.p);
+		return vec2.dot(this.v, v2);
+	}
+
+	public projectPoint(out: vec2, p2: vec2): vec2 {
+		const d = this.projectPointDistance(p2);
+		return vec2.scaleAndAdd(out, this.p, this.v, d);
+	}
+
+	public distancePoint(p2: vec2): number {
+		const v2 = vec2.sub(vec2.create(), p2, this.p);
+		return crossz(this.v, v2);
+	}
+
+	public intersectLine(out: vec2, l2: Line): vec2 {
+		const vp = vec2.sub(vec2.create(), l2.p, this.p);
+		const d = crossz(vp, this.v);
+		const d2 = d / crossz(this.v, l2.v);
+		return vec2.scaleAndAdd(out, l2.p, l2.v, d2);
+	}
+}
+
+export class Movement {
+	public readonly v: vec2;
+
+	constructor(
+		public readonly src: vec2,
+		public readonly dest: vec2,
+	) {
+		this.v = vec2.sub(vec2.create(), dest, src);
+	}
+
+	public intersectLine(out: vec2, l: Line): vec2 {
+		const vp = vec2.sub(vec2.create(), l.p, this.src);
+		const d = crossz(vp, this.v);
+		const d2 = d / crossz(this.v, l.v);
+		return vec2.scaleAndAdd(out, l.p, l.v, d2);
+	}
+
+	public passes(p: vec2): boolean {
+		const vp = vec2.sub(vec2.create(), p, this.src);
+		const d = vec2.dot(this.v, vp);
+		return d >= 0 && d <= vec2.sqrLen(this.v);
+	}
+
+	public toLineSegment(): LineSegment {
+		return LineSegment.fromPoints(this.src, this.dest);
+	}
+
+	public translate(t: vec2): Movement {
+		const src = vec2.add(vec2.create(), this.src, t);
+		const dest = vec2.add(vec2.create(), this.dest, t);
+		return new Movement(src, dest);
+	}
+}
+
+export class LineSegment extends Line implements Collidable {
+	public static fromPoints(p1: vec2, p2: vec2): LineSegment {
+		const d = vec2.dist(p1, p2);
+		const v = vec2.sub(vec2.create(), p2, p1);
+		vec2.scale(v, v, 1 / d);
+
+		return new LineSegment(p1, v, d);
+	}
+
+	constructor(
+		p: vec2,
+		v: vec2,
+		public readonly l: number,
+	) {
+		super(p, v);
+	}
+
+	public getP2(out: vec2): vec2 {
+		return vec2.scaleAndAdd(out, this.p, this.v, this.l);
+	}
+
+	public containsPoint(p2: vec2): boolean {
+		const d = this.projectPointDistance(p2);
+		return (d >= 0 && d <= this.l);
+	}
+
+	public collide(out: vec2, move: Movement, r: number): boolean {
+		if (this.distancePoint(move.src) < 0)
+			return false;
+
+		if (crossz(move.v, this.v) < 0)
+			return false;
+
+		const t = this.getNormal(vec2.create());
+		vec2.scale(t, t, -r);
+
+		const refMove = move.translate(t);
+
+		if (!this.collideRef(out, refMove))
+			return false;
+
+		vec2.sub(out, out, t);
+		return true;
+	}
+
+	private collideRef(out: vec2, move: Movement): boolean {
+		if (this.distancePoint(move.dest) >= 0)
+			return false;
+
+		const x = move.intersectLine(vec2.create(), this);
+		if (!this.containsPoint(x))
+			return false;
+
+		this.projectPoint(out, move.dest);
+
+		return true;
+	}
+}
diff --git a/src/renderer/runtime/math/point.ts b/src/renderer/runtime/math/point.ts
new file mode 100644
index 0000000..0865b8f
--- /dev/null
+++ b/src/renderer/runtime/math/point.ts
@@ -0,0 +1,40 @@
+import { Collidable } from './collision';
+import { Line, Movement, normal } from './line';
+
+import { vec2 } from 'gl-matrix';
+
+export class Point implements Collidable {
+	constructor(public readonly p: vec2) {}
+
+	public collide(out: vec2, move: Movement, r: number): boolean {
+		const moveLine = move.toLineSegment();
+
+		if (moveLine.projectPointDistance(this.p) < 0)
+			return false;
+
+		const d = moveLine.distancePoint(this.p) / r;
+		if (Math.abs(d) >= 1)
+			return false;
+
+		const e = Math.sqrt(1 - d * d);
+
+		const t = moveLine.getNormal(vec2.create());
+		vec2.scale(t, t, d);
+		vec2.scaleAndAdd(t, t, moveLine.v, e);
+
+		const tr = vec2.scale(vec2.create(), t, r);
+
+		const refMove = move.translate(tr);
+
+		if (vec2.sqrDist(this.p, move.src) > r * r && !refMove.passes(this.p))
+			return false;
+
+		normal(t, t);
+
+		const tang = new Line(this.p, t);
+		tang.projectPoint(out, refMove.dest);
+		vec2.sub(out, out, tr);
+
+		return true;
+	}
+}