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+``` + +## Authors + +- Karsten Schmidt + +## License + +© 2018 Karsten Schmidt // Apache Software License 2.0 diff --git a/packages/geom-isec/package.json b/packages/geom-isec/package.json new file mode 100644 index 0000000000..a8a2d46c4f --- /dev/null +++ b/packages/geom-isec/package.json @@ -0,0 +1,57 @@ +{ + "name": "@thi.ng/geom-isec", + "version": "0.0.1", + "description": "2D/3D shape intersection checks", + "module": "./index.js", + "main": "./lib/index.js", + "umd:main": "./lib/index.umd.js", + "typings": "./index.d.ts", + "repository": { + "type": "git", + "url": "https://github.com/thi-ng/umbrella.git" + }, + "homepage": "https://github.com/thi-ng/umbrella/tree/master/packages/geom-isec", + "author": "Karsten Schmidt ", + "license": "Apache-2.0", + "scripts": { + "build": "yarn clean && yarn build:es6 && yarn build:bundle", + "build:es6": "tsc --declaration", + "build:bundle": "../../scripts/bundle-module geomIsec geom-closest-point math vectors", + "test": "rimraf build && tsc -p test/tsconfig.json && nyc mocha build/test/*.js", + "clean": "rimraf *.js *.d.ts .nyc_output build coverage doc lib", + "cover": "yarn test && nyc report --reporter=lcov", + "doc": "node_modules/.bin/typedoc --mode modules --out doc src", + "pub": "yarn build && yarn publish --access public" + }, + "devDependencies": { + "@types/mocha": "^5.2.5", + "@types/node": "^10.12.15", + "mocha": "^5.2.0", + "nyc": "^13.1.0", + "typedoc": "^0.14.0", + "typescript": "^3.2.2" + }, + "dependencies": { + "@thi.ng/geom-closest-point": "^0.0.1", + "@thi.ng/math": "^1.0.1", + "@thi.ng/vectors": "^2.1.0" + }, + "keywords": [ + "2D", + "3D", + "AABB", + "circle", + "ES6", + "geometry", + "intersection", + "line", + "ray", + "rect", + "sphere", + "typescript" + ], + "publishConfig": { + "access": "public" + }, + "sideEffects": false +} \ No newline at end of file diff --git a/packages/geom-isec/src/api.ts b/packages/geom-isec/src/api.ts new file mode 100644 index 0000000000..0413d57d56 --- /dev/null +++ b/packages/geom-isec/src/api.ts @@ -0,0 +1,21 @@ +import { Vec } from "@thi.ng/vectors"; + +export const enum IntersectionType { + NONE, + PARALLEL, + COINCIDENT, + COINCIDENT_NO_INTERSECT, + INTERSECT, + INTERSECT_OUTSIDE, +} + +export interface IntersectionResult { + type: IntersectionType; +} + +export interface LineIntersection extends IntersectionResult { + isec?: Vec; + det?: number; + alpha?: number; + beta?: number; +} diff --git a/packages/geom-isec/src/circle-circle.ts b/packages/geom-isec/src/circle-circle.ts new file mode 100644 index 0000000000..9830f25b26 --- /dev/null +++ b/packages/geom-isec/src/circle-circle.ts @@ -0,0 +1,37 @@ +import { eqDeltaFixed } from "@thi.ng/math"; +import { + add, + distSq, + maddN, + mag, + mulN, + perpendicularLeft2, + ReadonlyVec, + sub +} from "@thi.ng/vectors"; +import { IntersectionType } from "./api"; + +export const intersectCircleCircle = + (a: ReadonlyVec, b: ReadonlyVec, ar: number, br: number) => { + const delta = sub([], b, a); + const d = mag(delta); + if (eqDeltaFixed(d, 0)) { + return { type: IntersectionType.COINCIDENT }; + } + if (d <= ar + br && d >= Math.abs(ar - br)) { + ar *= ar; + const alpha = (ar - br * br + d * d) / (2 * d); + const h = Math.sqrt(ar - alpha * alpha); + const p = maddN([], a, delta, alpha / d); + const t = mulN(null, perpendicularLeft2(null, delta), h / d); + return { + type: IntersectionType.INTERSECT, + isec: [add([], p, t), sub([], p, t)] + }; + } + return { type: IntersectionType.NONE }; + }; + +export const testCircleCircle = + (a: ReadonlyVec, b: ReadonlyVec, ar: number, br: number) => + distSq(a, b) <= Math.pow(ar + br, 2); diff --git a/packages/geom-isec/src/index.ts b/packages/geom-isec/src/index.ts new file mode 100644 index 0000000000..1bace0c0df --- /dev/null +++ b/packages/geom-isec/src/index.ts @@ -0,0 +1,8 @@ +export * from "./api"; +export * from "./circle-circle"; +export * from "./line-line"; +export * from "./ray-circle"; +export * from "./ray-line"; +export * from "./ray-poly"; +export * from "./rect-circle"; +export * from "./rect-rect"; diff --git a/packages/geom-isec/src/line-line.ts b/packages/geom-isec/src/line-line.ts new file mode 100644 index 0000000000..608b5c0e75 --- /dev/null +++ b/packages/geom-isec/src/line-line.ts @@ -0,0 +1,57 @@ +import { closestPointSegment } from "@thi.ng/geom-closest-point"; +import { EPS, eqDeltaFixed } from "@thi.ng/math"; +import { mixN2, ReadonlyVec } from "@thi.ng/vectors"; +import { IntersectionType, LineIntersection } from "./api"; + +export const intersectLineLine = + (a: ReadonlyVec, b: ReadonlyVec, c: ReadonlyVec, d: ReadonlyVec, eps = EPS): LineIntersection => { + + const bax = b[0] - a[0]; + const bay = b[1] - a[1]; + const dcx = d[0] - c[0]; + const dcy = d[1] - c[1]; + const acx = a[0] - c[0]; + const acy = a[1] - c[1]; + const det = dcy * bax - dcx * bay; + let alpha = dcx * acy - dcy * acx; + let beta = bax * acy - bay * acx; + if (eqDeltaFixed(det, 0, eps)) { + if (eqDeltaFixed(alpha, 0, eps) && eqDeltaFixed(beta, 0, eps)) { + let isec = + closestPointSegment(c, a, b, undefined, true) || + closestPointSegment(d, a, b, undefined, true); + return { + type: isec ? + IntersectionType.COINCIDENT : + IntersectionType.COINCIDENT_NO_INTERSECT, + isec, + }; + } + return { type: IntersectionType.PARALLEL }; + } + alpha /= det; + beta /= det; + const ieps = 1 - eps; + return { + type: (eps < alpha && alpha < ieps) && (eps < beta && beta < ieps) ? + IntersectionType.INTERSECT : + IntersectionType.INTERSECT_OUTSIDE, + isec: mixN2([], a, b, alpha), + alpha, + beta, + det, + }; + }; + +/** + * 2D only. Returns true if line `a`,`b` is parallel (or coincident) to + * line `c`,`d`. + * + * @param a + * @param b + * @param c + * @param d + */ +export const isParallelLine = + (a: ReadonlyVec, b: ReadonlyVec, c: ReadonlyVec, d: ReadonlyVec) => + eqDeltaFixed((d[1] - c[1]) * (b[0] - a[0]) - (d[0] - c[0]) * (b[1] - a[1]), 0); diff --git a/packages/geom-isec/src/ray-circle.ts b/packages/geom-isec/src/ray-circle.ts new file mode 100644 index 0000000000..24e000e468 --- /dev/null +++ b/packages/geom-isec/src/ray-circle.ts @@ -0,0 +1,28 @@ +import { + dot, + maddN, + magSq, + ReadonlyVec, + sub +} from "@thi.ng/vectors"; + +export const intersectRayCircle = + (rpos: ReadonlyVec, dir: ReadonlyVec, spos: ReadonlyVec, r: number) => { + const delta = sub([], spos, rpos); + const w = dot(delta, dir); + let d = r * r + w * w - magSq(delta); + if (d >= 0) { + d = Math.sqrt(d); + const a = w + d; + const b = w - d; + return a >= 0 ? + b >= 0 ? + a > b ? + [maddN(delta, rpos, dir, b), maddN([], rpos, dir, a)] : + [maddN(delta, rpos, dir, a), maddN([], rpos, dir, b)] : + [maddN(delta, rpos, dir, a)] : + b >= 0 ? + [maddN(delta, rpos, dir, b)] : + undefined; + } + }; diff --git a/packages/geom-isec/src/ray-line.ts b/packages/geom-isec/src/ray-line.ts new file mode 100644 index 0000000000..e5ff243470 --- /dev/null +++ b/packages/geom-isec/src/ray-line.ts @@ -0,0 +1,17 @@ +import { eqDeltaFixed } from "@thi.ng/math"; +import { ReadonlyVec } from "@thi.ng/vectors"; + +export const intersectRayLine = + (rpos: ReadonlyVec, dir: ReadonlyVec, a: ReadonlyVec, b: ReadonlyVec) => { + const bax = b[0] - a[0]; + const bay = b[1] - a[1]; + const d = dir[0] * bay - dir[1] * bax; + if (eqDeltaFixed(d, 0)) return; + const arx = a[0] - rpos[0]; + const ary = a[1] - rpos[1]; + const t = (bay * arx - bax * ary) / d; + const s = (dir[1] * arx - dir[0] * ary) / d; + return t >= 0 && s >= 0 && s <= 1 ? + t : + undefined; + }; diff --git a/packages/geom-isec/src/ray-poly.ts b/packages/geom-isec/src/ray-poly.ts new file mode 100644 index 0000000000..df7e0080ec --- /dev/null +++ b/packages/geom-isec/src/ray-poly.ts @@ -0,0 +1,56 @@ +import { maddN2, ReadonlyVec } from "@thi.ng/vectors"; +import { IntersectionType } from "./api"; +import { intersectRayLine } from "./ray-line"; + +export const intersectRayPolyline = + (rpos: ReadonlyVec, dir: ReadonlyVec, pts: ReadonlyVec[], closed = false) => { + const n = pts.length - 1; + let minD = Infinity; + let cross = 0; + let i, j; + if (closed) { + i = pts[n]; + j = pts[0]; + } else { + i = pts[0]; + j = pts[1]; + } + for (let k = 0; k <= n; i = j, j = pts[++k]) { + const d = intersectRayLine(rpos, dir, i, j); + if (d !== undefined) { + cross++; + if (d < minD) minD = d; + } + } + return cross > 0 ? + { + type: IntersectionType.INTERSECT, + isec: maddN2([], rpos, dir, minD), + dist: minD, + inside: !(cross & 1) + } : + { + type: IntersectionType.NONE + }; + }; + +export const intersectRayPolylineAll = + (rpos: ReadonlyVec, dir: ReadonlyVec, pts: ReadonlyVec[], closed = false) => { + const n = pts.length - 1; + let i, j; + if (closed) { + i = pts[n]; + j = pts[0]; + } else { + i = pts[0]; + j = pts[1]; + } + const res = []; + for (let k = 0; k <= n; i = j, j = pts[++k]) { + const d = intersectRayLine(rpos, dir, i, j); + if (d !== undefined) { + res.push([d, maddN2([], rpos, dir, d)]); + } + } + return res.sort((a, b) => a[0] - b[0]); + }; diff --git a/packages/geom-isec/src/rect-circle.ts b/packages/geom-isec/src/rect-circle.ts new file mode 100644 index 0000000000..40708bcf38 --- /dev/null +++ b/packages/geom-isec/src/rect-circle.ts @@ -0,0 +1,31 @@ +import { ReadonlyVec } from "@thi.ng/vectors"; + +export const testRectCircle = ( + [rx, ry]: ReadonlyVec, + [w, h]: ReadonlyVec, + [cx, cy]: ReadonlyVec, + r: number +) => ( + axis(cx, rx, w) + + axis(cy, ry, h) +) <= r * r; + +export const testAABBSphere = ( + [rx, ry, rz]: ReadonlyVec, + [w, h, d]: ReadonlyVec, + [cx, cy, cz]: ReadonlyVec, + r: number +) => ( + axis(cx, rx, w) + + axis(cy, ry, h) + + axis(cz, rz, d) +) <= r * r; + +const axis = (a: number, b: number, c: number) => + Math.pow( + a < b ? + a - b : + a > b + c ? + a - b - c : + 0, + 2); diff --git a/packages/geom-isec/src/rect-rect.ts b/packages/geom-isec/src/rect-rect.ts new file mode 100644 index 0000000000..07e87b503b --- /dev/null +++ b/packages/geom-isec/src/rect-rect.ts @@ -0,0 +1,29 @@ +import { ReadonlyVec } from "@thi.ng/vectors"; + +export const testRectRect = ( + [ax, ay]: ReadonlyVec, + [aw, ah]: ReadonlyVec, + [bx, by]: ReadonlyVec, + [bw, bh]: ReadonlyVec +) => + !( + (ax > bx + bw) || + (bx > ax + aw) || + (ay > by + bh) || + (by > ay + ah) + ); + +export const testAabbAabb = ( + [ax, ay, az]: ReadonlyVec, + [aw, ah, ad]: ReadonlyVec, + [bx, by, bz]: ReadonlyVec, + [bw, bh, bd]: ReadonlyVec +) => + !( + (ax > bx + bw) || + (bx > ax + aw) || + (ay > by + bh) || + (by > ay + ah) || + (az > bz + bd) || + (bz > az + ad) + ); diff --git a/packages/geom-isec/test/index.ts b/packages/geom-isec/test/index.ts new file mode 100644 index 0000000000..4b38f19781 --- /dev/null +++ b/packages/geom-isec/test/index.ts @@ -0,0 +1,6 @@ +// import * as assert from "assert"; +// import * as gi from "../src/index"; + +describe("geom-isec", () => { + it("tests pending"); +}); diff --git a/packages/geom-isec/test/tsconfig.json b/packages/geom-isec/test/tsconfig.json new file mode 100644 index 0000000000..f6e63560dd --- /dev/null +++ b/packages/geom-isec/test/tsconfig.json @@ -0,0 +1,11 @@ +{ + "extends": "../../../tsconfig.json", + "compilerOptions": { + "outDir": "../build", + "module": "commonjs" + }, + "include": [ + "./**/*.ts", + "../src/**/*.ts" + ] +} diff --git a/packages/geom-isec/tsconfig.json b/packages/geom-isec/tsconfig.json new file mode 100644 index 0000000000..893b9979c5 --- /dev/null +++ b/packages/geom-isec/tsconfig.json @@ -0,0 +1,11 @@ +{ + "extends": "../../tsconfig.json", + "compilerOptions": { + "outDir": ".", + "module": "es6", + "target": "es6" + }, + "include": [ + "./src/**/*.ts" + ] +}