feat(geom-splines): add cubicTangentAt / quadraticTangentAt()

packages/geom-splines/src/cubic-tangent.ts

@@ -0,0 +1,26 @@
+import {
+    addW4,
+    normalize,
+    ReadonlyVec,
+    Vec
+} from "@thi.ng/vectors";
+
+export const cubicTangentAt = (
+    out: Vec,
+    a: ReadonlyVec,
+    b: ReadonlyVec,
+    c: ReadonlyVec,
+    d: ReadonlyVec,
+    t: number,
+    len = 1
+) => {
+    const s = 1 - t;
+    const ss = s * s;
+    const tt = t * t;
+    const ts2 = 2 * t * s;
+    return normalize(
+        out,
+        addW4(out, a, b, c, d, -3 * ss, 3 * (ss - ts2), 3 * (ts2 - tt), 3 * tt),
+        len
+    );
+};

packages/geom-splines/src/index.ts

@@ -7,11 +7,13 @@ export * from "./cubic-line";
 export * from "./cubic-quadratic";
 export * from "./cubic-sample";
 export * from "./cubic-split";
+export * from "./cubic-tangent";
 
 export * from "./quadratic-bounds";
 export * from "./quadratic-closest-point";
 export * from "./quadratic-line";
 export * from "./quadratic-sample";
 export * from "./quadratic-split";
+export * from "./quadratic-tangent";
 
 export * from "./point-at";

packages/geom-splines/src/quadratic-tangent.ts

@@ -0,0 +1,21 @@
+import {
+    addW2,
+    normalize,
+    ReadonlyVec,
+    sub,
+    Vec
+} from "@thi.ng/vectors";
+
+export const quadraticTangentAt = (
+    out: Vec,
+    a: ReadonlyVec,
+    b: ReadonlyVec,
+    c: ReadonlyVec,
+    t: number,
+    len = 1
+) =>
+    normalize(
+        out,
+        addW2(out, sub(out, b, a), sub([], c, b), 2 * (1 - t), 2 * t),
+        len
+    );