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Diffstat (limited to 'src/client/northstar/utils/MathUtil.ts')
| -rw-r--r-- | src/client/northstar/utils/MathUtil.ts | 236 |
1 files changed, 236 insertions, 0 deletions
diff --git a/src/client/northstar/utils/MathUtil.ts b/src/client/northstar/utils/MathUtil.ts new file mode 100644 index 000000000..3ed8628ee --- /dev/null +++ b/src/client/northstar/utils/MathUtil.ts @@ -0,0 +1,236 @@ + + +export class PIXIPoint { + public x: number; + public y: number; + constructor(x: number, y: number) { + this.x = x; + this.y = y; + } +} +export class PIXIRectangle { + public x: number; + public y: number; + public width: number; + public height: number + public get left() { return this.x } + public get right() { return this.x + this.width; } + public get top() { return this.y } + public get bottom() { return this.top + this.height } + constructor(x: number, y: number, width: number, height: number) { + this.x = x; + this.y = y; + this.width = width; + this.height = height; + } +} + +export class MathUtil { + + public static EPSILON: number = 0.001; + + public static Sign(value: number): number { + return value >= 0 ? 1 : -1; + } + + public static AddPoint(p1: PIXIPoint, p2: PIXIPoint, inline: boolean = false): PIXIPoint { + if (inline) { + p1.x += p2.x; + p1.y += p2.y; + return p1; + } + else { + return new PIXIPoint(p1.x + p2.x, p1.y + p2.y); + } + } + + public static Perp(p1: PIXIPoint): PIXIPoint { + return new PIXIPoint(-p1.y, p1.x); + } + + public static DividePoint(p1: PIXIPoint, by: number, inline: boolean = false): PIXIPoint { + if (inline) { + p1.x /= by; + p1.y /= by; + return p1; + } + else { + return new PIXIPoint(p1.x / by, p1.y / by); + } + } + + public static MultiplyConstant(p1: PIXIPoint, by: number, inline: boolean = false) { + if (inline) { + p1.x *= by; + p1.y *= by; + return p1; + } + else { + return new PIXIPoint(p1.x * by, p1.y * by); + } + } + + public static SubtractPoint(p1: PIXIPoint, p2: PIXIPoint, inline: boolean = false): PIXIPoint { + if (inline) { + p1.x -= p2.x; + p1.y -= p2.y; + return p1; + } + else { + return new PIXIPoint(p1.x - p2.x, p1.y - p2.y); + } + } + + public static Area(rect: PIXIRectangle): number { + return rect.width * rect.height; + } + + public static DistToLineSegment(v: PIXIPoint, w: PIXIPoint, p: PIXIPoint) { + // Return minimum distance between line segment vw and point p + var l2 = MathUtil.DistSquared(v, w); // i.e. |w-v|^2 - avoid a sqrt + if (l2 == 0.0) return MathUtil.Dist(p, v); // v == w case + // Consider the line extending the segment, parameterized as v + t (w - v). + // We find projection of point p onto the line. + // It falls where t = [(p-v) . (w-v)] / |w-v|^2 + // We clamp t from [0,1] to handle points outside the segment vw. + var dot = MathUtil.Dot( + MathUtil.SubtractPoint(p, v), + MathUtil.SubtractPoint(w, v)) / l2; + var t = Math.max(0, Math.min(1, dot)); + // Projection falls on the segment + var projection = MathUtil.AddPoint(v, + MathUtil.MultiplyConstant( + MathUtil.SubtractPoint(w, v), t)); + return MathUtil.Dist(p, projection); + } + + public static LineSegmentIntersection(ps1: PIXIPoint, pe1: PIXIPoint, ps2: PIXIPoint, pe2: PIXIPoint): PIXIPoint | undefined { + var a1 = pe1.y - ps1.y; + var b1 = ps1.x - pe1.x; + + var a2 = pe2.y - ps2.y; + var b2 = ps2.x - pe2.x; + + var delta = a1 * b2 - a2 * b1; + if (delta == 0) { + return undefined; + } + var c2 = a2 * ps2.x + b2 * ps2.y; + var c1 = a1 * ps1.x + b1 * ps1.y; + var invdelta = 1 / delta; + return new PIXIPoint((b2 * c1 - b1 * c2) * invdelta, (a1 * c2 - a2 * c1) * invdelta); + } + + public static PointInPIXIRectangle(p: PIXIPoint, rect: PIXIRectangle): boolean { + if (p.x < rect.left - this.EPSILON) + return false; + if (p.x > rect.right + this.EPSILON) + return false; + if (p.y < rect.top - this.EPSILON) + return false; + if (p.y > rect.bottom + this.EPSILON) + return false; + + return true; + } + + public static LinePIXIRectangleIntersection(lineFrom: PIXIPoint, lineTo: PIXIPoint, rect: PIXIRectangle): Array<PIXIPoint> { + var r1 = new PIXIPoint(rect.left, rect.top); + var r2 = new PIXIPoint(rect.right, rect.top); + var r3 = new PIXIPoint(rect.right, rect.bottom); + var r4 = new PIXIPoint(rect.left, rect.bottom); + var ret = new Array<PIXIPoint>(); + var dist = this.Dist(lineFrom, lineTo) + var inter = this.LineSegmentIntersection(lineFrom, lineTo, r1, r2); + if (inter != null && this.PointInPIXIRectangle(inter, rect) && + this.Dist(inter, lineFrom) < dist && this.Dist(inter, lineTo) < dist) + ret.push(inter); + inter = this.LineSegmentIntersection(lineFrom, lineTo, r2, r3); + if (inter != null && this.PointInPIXIRectangle(inter, rect) && + this.Dist(inter, lineFrom) < dist && this.Dist(inter, lineTo) < dist) + ret.push(inter); + inter = this.LineSegmentIntersection(lineFrom, lineTo, r3, r4); + if (inter != null && this.PointInPIXIRectangle(inter, rect) && + this.Dist(inter, lineFrom) < dist && this.Dist(inter, lineTo) < dist) + ret.push(inter); + inter = this.LineSegmentIntersection(lineFrom, lineTo, r4, r1); + if (inter != null && this.PointInPIXIRectangle(inter, rect) && + this.Dist(inter, lineFrom) < dist && this.Dist(inter, lineTo) < dist) + ret.push(inter); + return ret; + } + + public static Intersection(rect1: PIXIRectangle, rect2: PIXIRectangle): PIXIRectangle { + const left = Math.max(rect1.x, rect2.x); + const right = Math.min(rect1.x + rect1.width, rect2.x + rect2.width); + const top = Math.max(rect1.y, rect2.y); + const bottom = Math.min(rect1.y + rect1.height, rect2.y + rect2.height); + return new PIXIRectangle(left, top, right - left, bottom - top); + } + + public static Dist(p1: PIXIPoint, p2: PIXIPoint): number { + return Math.sqrt(MathUtil.DistSquared(p1, p2)); + } + + public static Dot(p1: PIXIPoint, p2: PIXIPoint): number { + return p1.x * p2.x + p1.y * p2.y + } + + public static Normalize(p1: PIXIPoint) { + var d = this.Length(p1); + return new PIXIPoint(p1.x / d, p1.y / d); + } + + public static Length(p1: PIXIPoint): number { + return Math.sqrt(p1.x * p1.x + p1.y * p1.y); + } + + public static DistSquared(p1: PIXIPoint, p2: PIXIPoint): number { + const a = p1.x - p2.x; + const b = p1.y - p2.y; + return (a * a + b * b) + } + + public static RectIntersectsRect(r1: PIXIRectangle, r2: PIXIRectangle): boolean { + return !(r2.x > r1.x + r1.width || + r2.x + r2.width < r1.x || + r2.y > r1.y + r1.height || + r2.y + r2.height < r1.y); + } + + public static ArgMin(temp: number[]): number { + let index = 0; + let value = temp[0]; + for (let i = 1; i < temp.length; i++) { + if (temp[i] < value) { + value = temp[i]; + index = i; + } + } + return index; + } + + public static ArgMax(temp: number[]): number { + let index = 0; + let value = temp[0]; + for (let i = 1; i < temp.length; i++) { + if (temp[i] > value) { + value = temp[i]; + index = i; + } + } + return index; + } + + public static Combinations<T>(chars: T[]) { + let result = new Array<T>(); + let f = (prefix: any, chars: any) => { + for (let i = 0; i < chars.length; i++) { + result.push(prefix.concat(chars[i])); + f(prefix.concat(chars[i]), chars.slice(i + 1)); + } + }; + f([], chars); + return result; + } +}
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