feat(geom): add closestPoint() impls for splines, line, polygons, pol…

…yline

packages/geom3/src/internal/closest-point.ts

@@ -1,16 +1,20 @@
+import { Fn } from "@thi.ng/api";
+import { partial } from "@thi.ng/compose";
 import {
     distSq,
     dot,
     empty,
     magSq,
+    mixCubic,
     mixN,
+    mixQuadratic,
     ReadonlyVec,
     set,
     sub,
     Vec
 } from "@thi.ng/vectors3";
 
-export const closestPointRaw =
+export const closestPointArray =
     (p: ReadonlyVec, pts: Vec[]) => {
 
         let minD = Infinity;
@@ -53,17 +57,16 @@ export const closestPointSegment =
         const t = closestCoeff(p, a, b);
         if (t !== undefined && (!insideOnly || t >= 0 && t <= 1)) {
             out = out || empty(p);
-            return t <= 0.0 ?
+            return t <= 0 ?
                 set(out, a) :
-                t >= 1.0 ?
+                t >= 1 ?
                     set(out, b) :
                     mixN(out, a, b, t);
         }
     };
 
 export const closestPointPolyline =
     (p: ReadonlyVec, pts: ReadonlyArray<Vec>, closed = false) => {
-
         const closest = empty(pts[0]);
         const tmp = empty(closest);
         const n = pts.length - 1;
@@ -100,7 +103,7 @@ export const closestPointPolyline =
  * @param to
  */
 export const farthestPointSegment =
-    (a: Vec, b: Vec, points: Vec[], from = 0, to = points.length) => {
+    (a: ReadonlyVec, b: ReadonlyVec, points: ReadonlyVec[], from = 0, to = points.length) => {
         let maxD = -1;
         let maxIdx;
         const tmp = empty(a);
@@ -114,3 +117,95 @@ export const farthestPointSegment =
         }
         return [maxIdx, Math.sqrt(maxD)];
     };
+
+/**
+ * Performs recursive search for closest point to `p` on cubic curve
+ * defined by control points `a`,`b`,`c`,`d`. The `res` and `recur`
+ * params are used to control the recursion behavior. See `closestT`.
+ *
+ * @param p
+ * @param a
+ * @param b
+ * @param c
+ * @param d
+ * @param res
+ * @param iter
+ */
+export const closestPointCubic = (
+    p: ReadonlyVec,
+    a: ReadonlyVec,
+    b: ReadonlyVec,
+    c: ReadonlyVec,
+    d: ReadonlyVec,
+    res = 8,
+    iter = 4
+) => {
+    const fn = partial(mixCubic, [], a, b, c, d);
+    return fn(closestT(fn, p, res, iter, 0, 1));
+};
+
+/**
+ * Performs recursive search for closest point to `p` on quadratic curve
+ * defined by control points `a`,`b`,`c`. The `res` and `recur` params
+ * are used to control the recursion behavior. See `closestT`.
+ *
+ * @param p
+ * @param a
+ * @param b
+ * @param c
+ * @param res
+ * @param iter
+ */
+export const closestPointQuadratic = (
+    p: ReadonlyVec,
+    a: ReadonlyVec,
+    b: ReadonlyVec,
+    c: ReadonlyVec,
+    res = 8,
+    iter = 4
+) => {
+    const fn = partial(mixQuadratic, [], a, b, c);
+    return fn(closestT(fn, p, res, iter, 0, 1));
+};
+
+/**
+ * Recursively evaluates function `fn` for `res` uniformly spaced values
+ * `t` in the closed interval `[start,end]` to compute points on a curve
+ * and returns the `t` producing the minimum distance to query point
+ * `p`. At each level of recursion the search interval is increasingly
+ * centered around the currently best `t`.
+ *
+ * @param fn
+ * @param p
+ * @param res
+ * @param iter
+ * @param start
+ * @param end
+ */
+const closestT = (
+    fn: Fn<number, Vec>,
+    p: ReadonlyVec,
+    res: number,
+    iter: number,
+    start: number,
+    end: number
+) => {
+    if (iter <= 0) return (start + end) / 2;
+    const delta = (end - start) / res;
+    let minT = start;
+    let minD = Infinity;
+    for (let i = 0; i <= res; i++) {
+        const t = start + i * delta;
+        const q = fn(t);
+        const d = distSq(p, q);
+        if (d < minD) {
+            minD = d;
+            minT = t;
+        }
+    }
+    return closestT(
+        fn, p, res, iter - 1,
+        Math.max(minT - delta, 0),
+        Math.min(minT + delta, 1)
+    );
+};

packages/geom3/src/ops/closest-point.ts

@@ -1,21 +1,68 @@
 import { defmulti } from "@thi.ng/defmulti";
 import {
-    add2,
+    add,
     normalize,
     ReadonlyVec,
-    sub2,
+    sub,
     Vec
 } from "@thi.ng/vectors3";
-import { Circle, IShape, Type } from "../api";
+import {
+    Circle,
+    Cubic,
+    IShape,
+    Line,
+    PCLike,
+    Quadratic,
+    Type
+} from "../api";
+import {
+    closestPointArray,
+    closestPointCubic,
+    closestPointPolyline,
+    closestPointQuadratic,
+    closestPointSegment
+} from "../internal/closest-point";
 import { dispatch } from "../internal/dispatch";
+import { vertices } from "./vertices";
 
 export const closestPoint = defmulti<IShape, ReadonlyVec, Vec>(dispatch);
 
 closestPoint.addAll({
 
     [Type.CIRCLE]:
         ($: Circle, p) =>
-            add2(null, normalize(null, sub2([], p, $.pos), $.r), $.pos),
+            add(null, normalize(null, sub([], p, $.pos), $.r), $.pos),
+
+    [Type.CUBIC]:
+        ({ points }: Cubic, p) =>
+            closestPointCubic(p, points[0], points[1], points[2], points[3]),
+
+    [Type.LINE]:
+        ({ points }: Line, p) =>
+            closestPointSegment(p, points[0], points[1]),
+
+    [Type.POLYGON]:
+        ($: PCLike, p) =>
+            closestPointArray(p, $.points),
+
+    [Type.POLYGON]:
+        ($: PCLike, p) =>
+            closestPointPolyline(p, $.points, true),
+
+    [Type.POLYLINE]:
+        ($: PCLike, p) =>
+            closestPointPolyline(p, $.points),
+
+    [Type.QUADRATIC]:
+        ({ points }: Quadratic, p) =>
+            closestPointQuadratic(p, points[0], points[1], points[2]),
+
+    [Type.RECT]:
+        ($, p) =>
+            closestPointPolyline(p, vertices($), true),
 
 });
 
+closestPoint.isa(Type.QUAD, Type.POLYGON);
+closestPoint.isa(Type.SPHERE, Type.CIRCLE);
+closestPoint.isa(Type.TRIANGLE, Type.POLYGON);