fix: Remove absolute position effect from optimal bezier interpolatio…

…n for consistent result

CHANGELOG.md

@@ -6,6 +6,10 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 ## [Unreleased]
 
+## [3.1.1] - 2023-11-18
+### Fixed
+- Remove absolute position effect from optimal bezier interpolation for consistent result
+
 ## [3.1.0] - 2023-11-17
 ### Added
 - Optimal bezier interpolation

package.json

@@ -1,6 +1,6 @@
 {
   "name": "okageo",
-  "version": "3.1.0",
+  "version": "3.1.1",
   "description": "parse SVG to polygons",
   "main": "./dist/okageo.js",
   "module": "./dist/okageo.mjs",

src/geo.ts

@@ -1631,17 +1631,25 @@ export function getBezierInterpolation(
   const len = points.length
   if (len < 3) return []
 
-  const A = solveBezierInterpolationEquations(points)
+  // This algorithm appears dependent on the absolute position of the line.
+  // => Remove the absolute position effect for consistency.
+  const origin = points[0]
+  const adjustedPoints = points.map((p) => sub(p, origin))
+
+  const A = solveBezierInterpolationEquations(adjustedPoints)
   const B: IVec2[] = []
-  for (let i = 0; i < points.length - 2; i++) {
-    B[i] = sub(multi(points[i + 1], 2), A[i + 1])
+  for (let i = 0; i < adjustedPoints.length - 2; i++) {
+    B[i] = sub(multi(adjustedPoints[i + 1], 2), A[i + 1])
   }
-  B[points.length - 2] = multi(
-    add(A[points.length - 2], points[points.length - 1]),
+  B[adjustedPoints.length - 2] = multi(
+    add(
+      A[adjustedPoints.length - 2],
+      adjustedPoints[adjustedPoints.length - 1]
+    ),
     1 / 2
   )
 
-  return A.map((a, i) => [a, B[i]])
+  return A.map((a, i) => [add(a, origin), add(B[i], origin)])
 }
 
 /**

test/geo.test.ts

@@ -1983,4 +1983,16 @@ describe('getBezierInterpolation', () => {
     expect(ret0[1][1].x).toBeCloseTo(10.385, 3)
     expect(ret0[1][1].y).toBeCloseTo(5.769, 3)
   })
+
+  it('should return bezier control points: non-zero origin', () => {
+    const ret0 = geo.getBezierInterpolation([
+      { x: 1, y: 1 },
+      { x: 11, y: 1 },
+      { x: 11, y: 11 },
+    ])
+    expect(ret0[0][0].x).toBeCloseTo(5.615, 3)
+    expect(ret0[0][0].y).toBeCloseTo(1 - 0.769, 3)
+    expect(ret0[1][1].x).toBeCloseTo(11.385, 3)
+    expect(ret0[1][1].y).toBeCloseTo(6.769, 3)
+  })
 })