Precise highlights

packages/math/src/curve.ts

@@ -2,6 +2,7 @@ import type { Bounds } from "@excalidraw/element/bounds";
 
 import { isPoint, pointDistance, pointFrom } from "./point";
 import { rectangle, rectangleIntersectLineSegment } from "./rectangle";
+import { vector } from "./vector";
 
 import type { Curve, GlobalPoint, LineSegment, LocalPoint } from "./types";
 
@@ -82,7 +83,7 @@ function solve(
   return [t0, s0];
 }
 
-const bezierEquation = <Point extends GlobalPoint | LocalPoint>(
+export const bezierEquation = <Point extends GlobalPoint | LocalPoint>(
   c: Curve<Point>,
   t: number,
 ) =>
@@ -274,6 +275,26 @@ export function isCurve<P extends GlobalPoint | LocalPoint>(
   );
 }
 
+export function curveTangent<Point extends GlobalPoint | LocalPoint>(
+  [p0, p1, p2, p3]: Curve<Point>,
+  t: number,
+) {
+  return vector(
+    -3 * (1 - t) * (1 - t) * p0[0] +
+      3 * (1 - t) * (1 - t) * p1[0] -
+      6 * t * (1 - t) * p1[0] -
+      3 * t * t * p2[0] +
+      6 * t * (1 - t) * p2[0] +
+      3 * t * t * p3[0],
+    -3 * (1 - t) * (1 - t) * p0[1] +
+      3 * (1 - t) * (1 - t) * p1[1] -
+      6 * t * (1 - t) * p1[1] -
+      3 * t * t * p2[1] +
+      6 * t * (1 - t) * p2[1] +
+      3 * t * t * p3[1],
+  );
+}
+
 function curveBounds<Point extends GlobalPoint | LocalPoint>(
   c: Curve<Point>,
 ): Bounds {

packages/math/src/vector.ts

@@ -143,3 +143,8 @@ export const vectorNormalize = (v: Vector): Vector => {
 
   return vector(v[0] / m, v[1] / m);
 };
+
+/**
+ * Calculate the right-hand normal of the vector.
+ */
+export const vectorNormal = (v: Vector): Vector => vector(v[1], -v[0]);