fix(geom): update arcFrom2Points()

thi-ng · Jan 19, 2019 · 62ec49f · 62ec49f
1 parent 910529d
commit 62ec49f
Showing 1 changed file with 63 additions and 36 deletions.
diff --git a/packages/geom3/src/ctors/arc.ts b/packages/geom3/src/ctors/arc.ts
@@ -1,10 +1,15 @@
 import { isNumber } from "@thi.ng/checks";
-import { TAU } from "@thi.ng/math";
+import { EPS, TAU } from "@thi.ng/math";
 import {
     abs2,
     angleBetween2,
+    div2,
+    eqDelta2,
     mulN2,
+    neg,
+    powN2,
     ReadonlyVec,
+    sub2,
     submN2,
     Vec,
     X2
@@ -21,49 +26,71 @@ export const arc = (
     clockwise = false
 ) => new Arc(pos, isNumber(r) ? [r, r] : r, axis, start, end, xl, clockwise);
 
+/**
+ * https://svgwg.org/svg2-draft/implnote.html#ArcConversionEndpointToCenter
+ *
+ * Returns undefined if `a` & `b` are equal or any `radii` component is
+ * zero.
+ *
+ * @param a start point
+ * @param b end point
+ * @param radii ellipse radii
+ * @param axisTheta in radians
+ * @param xl large arc flag
+ * @param cw clockwise flag
+ */
 export const arcFrom2Points = (
     a: ReadonlyVec,
     b: ReadonlyVec,
     radii: ReadonlyVec,
     axisTheta = 0,
-    large = false,
-    clockwise = false
+    xl = false,
+    cw = false
 ) => {
 
     const r = abs2([], radii);
-    const co = Math.cos(axisTheta);
-    const si = Math.sin(axisTheta);
-    const m = submN2([], a, b, 0.5);
-    // const m = mulN2(null, sub2([], a, b), 0.5);
-    const px = co * m[0] + si * m[1];
-    const py = -si * m[0] + co * m[1];
-    const px2 = px * px;
-    const py2 = py * py;
-
-    const l = px2 / (r[0] * r[0]) + py2 / (r[1] * r[1]);
-    l > 1 && mulN2(null, r, Math.sqrt(l));
-
-    const rx2 = r[0] * r[0];
-    const ry2 = r[1] * r[1];
-    const rxpy = rx2 * py2;
-    const rypx = ry2 * px2;
-    const rad = ((large === clockwise) ? -1 : 1) *
-        Math.sqrt(Math.max(0, rx2 * ry2 - rxpy - rypx) / (rxpy + rypx));
-
-    const tx = rad * r[0] / r[1] * py;
-    const ty = -rad * r[1] / r[0] * px;
-    const c = [co * tx - si * ty + (a[0] + b[0]) / 2, si * tx + co * ty + (a[1] + b[1]) / 2];
-    const d1 = [(px - tx) / r[0], (py - ty) / r[1]];
-    const d2 = [(-px - tx) / r[0], (-py - ty) / r[1]];
-
-    const theta = angleBetween2(X2, d1);
-    let delta = angleBetween2(d1, d2);
-
-    if (clockwise && delta < 0) {
-        delta += TAU;
-    } else if (!clockwise && delta > 0) {
-        delta -= TAU;
+    if (eqDelta2(a, b) || r[0] < EPS || r[1] < EPS) {
+        return;
+    }
+    axisTheta %= TAU;
+    const d = submN2([], a, b, 0.5);
+    const c = Math.cos(axisTheta);
+    const s = Math.sin(axisTheta);
+    // transformed point
+    const tp = [
+        c * d[0] + s * d[1],
+        -s * d[0] + c * d[1]
+    ];
+    const [tx2, ty2] = powN2([], tp, 2);
+    // ensure radii
+    const rc = tx2 / (r[0] * r[0]) + ty2 / (r[1] * r[1]);
+    rc > 1 && mulN2(r, r, Math.sqrt(rc));
+    const [rx, ry] = r;
+    const rx2 = rx * rx;
+    const ry2 = ry * ry;
+    // transformed center
+    const radicant = Math.max(0, (rx2 * ry2 - rx2 * ty2 - ry2 * tx2) / (rx2 * ty2 + ry2 * tx2));
+    const coeff = (xl !== cw ? 1 : -1) * Math.sqrt(radicant);
+    const tc = [
+        coeff * ((rx * tp[1]) / ry),
+        coeff * (-(ry * tp[0]) / rx)
+    ];
+    // actual center
+    const center = [
+        c * tc[0] - s * tc[1] + (a[0] + b[0]) / 2,
+        s * tc[0] + c * tc[1] + (a[1] + b[1]) / 2
+    ];
+    // transformed end points & angles
+    const ta = div2(null, sub2([], tp, tc), r);
+    const tb = div2(null, sub2(null, neg([], tp), tc), r);
+    const start = angleBetween2(X2, ta);
+    let sweep = angleBetween2(ta, tb);
+    if (!cw && sweep > 0) {
+        sweep -= TAU;
+    } else if (cw && sweep < 0) {
+        sweep += TAU;
     }
+    sweep %= TAU;
 
-    return new Arc(c, r, axisTheta, theta, theta + delta, large, clockwise);
+    return new Arc(center, r, axisTheta, start, start + sweep, xl, cw);
 };