the constraint solver for non auto-intersections now iterates untils the min-error distance is low enough, for now max error is of 1%

frontend/lib/math/math.js

@@ -50,6 +50,22 @@ export const Vec2 = {
         const norm = Vec2.norm2([x, y])
         return [x / norm, y / norm]
     },
+
+    findNearest(curve, pt) {
+        let index = -1
+        let minDist = +Infinity
+
+        for (let i = 0; i < curve.length; i++) {
+            const d = Vec2.distance2(curve[i], pt)
+
+            if (d < minDist) {
+                index = i
+                minDist = d
+            }
+        }
+
+        return [index, minDist]
+    },
 }
 
 export const Vec3 = {
@@ -99,9 +115,9 @@ export const Vec3 = {
         const norm = Vec3.norm2([x, y, z])
         return [x / norm, y / norm, z / norm]
     },
-    findNearest3d(curve, pt) {
-        let index = 0
-        let minDist = Infinity
+    findNearest(curve, pt) {
+        let index = -1
+        let minDist = +Infinity
 
         for (let i = 0; i < curve.length; i++) {
             const d = Vec3.distance2(curve[i], pt)

frontend/src/components/KnotLayer.jsx

@@ -61,7 +61,10 @@ class KnotSimulation {
             this.ghostPath = []
         }
         if (buttons === 2) {
-            const [i] = Vec3.findNearest3d(this.particleSimulation.positions, [...this.mousePosition, 0])
+            const [i] = Vec2.findNearest(
+                this.particleSimulation.positions.map(([x, y]) => [x, y]),
+                this.mousePosition
+            )
             this.draggingIndex = i
         }
         if (buttons === 4) {
@@ -147,35 +150,62 @@ class KnotSimulation {
             const next = positions.at((i + 1) % N)
 
             const baseForce = Vec3.scale(Vec3.add(Vec3.sub(prev, curr), Vec3.sub(next, curr)), 0.5)
-            const jointFactor = 0.5
+            const jointFactor = 0.1
 
             Vec3.Mutate.add(positions.at((i - 1) % N), Vec3.scale(baseForce, -jointFactor / 2))
             Vec3.Mutate.add(positions[i], Vec3.scale(baseForce, jointFactor))
             Vec3.Mutate.add(positions.at((i + 1) % N), Vec3.scale(baseForce, -jointFactor / 2))
         }
 
-        // repulsione per ogni coppia
-        for (let i = 0; i < N; i++) {
-            for (let j = 0; j < N; j++) {
-                if (
-                    i < j &&
-                    Math.abs(i - j) > PASSTHROUGH_MIN_INDICES &&
-                    Math.abs(i - j + N) > PASSTHROUGH_MIN_INDICES &&
-                    Math.abs(i - j - N) > PASSTHROUGH_MIN_INDICES
-                ) {
-                    const p1 = positions[i]
-                    const p2 = positions[j]
-
-                    const dist = Vec3.distance2(p1, p2)
-                    if (dist <= NODE_BALL_RADIUS) {
-                        const [newPt1, newPt2] = enforceDistance(p1, p2, NODE_BALL_RADIUS)
-                        positions[i] = newPt1
-                        positions[j] = newPt2
+        // the error of the next constraint will be at most of 90%
+        let globalNodeMinDistance = 0
+        let iter = 0
+        while (globalNodeMinDistance < NODE_BALL_RADIUS * 0.99 && iter++ < 100) {
+            // repulsione per ogni coppia
+            for (let i = 0; i < N; i++) {
+                for (let j = i + 1; j < N; j++) {
+                    if (
+                        Math.abs(i - j) > PASSTHROUGH_MIN_INDICES &&
+                        Math.abs(i - j + N) > PASSTHROUGH_MIN_INDICES &&
+                        Math.abs(i - j - N) > PASSTHROUGH_MIN_INDICES
+                    ) {
+                        const p1 = positions[i]
+                        const p2 = positions[j]
+
+                        const dist = Vec3.distance2(p1, p2)
+                        if (dist <= NODE_BALL_RADIUS) {
+                            const [newPt1, newPt2] = enforceDistance(p1, p2, NODE_BALL_RADIUS)
+                            positions[i] = newPt1
+                            positions[j] = newPt2
+                        }
+                    }
+                }
+            }
+
+            // estimating global previous constraint error
+            globalNodeMinDistance = +Infinity
+            for (let i = 0; i < N; i++) {
+                for (let j = i + 1; j < N; j++) {
+                    if (
+                        Math.abs(i - j) > PASSTHROUGH_MIN_INDICES &&
+                        Math.abs(i - j + N) > PASSTHROUGH_MIN_INDICES &&
+                        Math.abs(i - j - N) > PASSTHROUGH_MIN_INDICES
+                    ) {
+                        const p1 = positions[i]
+                        const p2 = positions[j]
+
+                        const dist = Vec3.distance2(p1, p2)
+
+                        if (dist < globalNodeMinDistance) {
+                            globalNodeMinDistance = dist
+                        }
                     }
                 }
             }
         }
 
+        console.log(`Reached solution in ${iter} iterations with global min distance ${globalNodeMinDistance}`)
+
         this.particleSimulation.update(newAccelerations)
 
         // attrito viscoso