verlet gravity first cut

config.js

@@ -14,12 +14,12 @@ export const VELOCITY_VECTOR_COLOR = 'rgb(150, 150, 150)'; // optionally set to
 export const VELOCITY_VECTOR_WIDTH = 1.5;
 export const VELOCITY_VECTOR_ARROWHEAD = true;
 
-export const ACCELERATION_VECTOR_SCALE = 1E-4;
+export const ACCELERATION_VECTOR_SCALE = 1E-1;
 export const ACCELERATION_VECTOR_COLOR = 'rgb(0, 255, 0)'; // optionally set to 'object color'
 export const ACCELERATION_VECTOR_WIDTH = 1.5;
 export const ACCELERATION_VECTOR_ARROWHEAD = true;
 
-export const MOTION_TIME_SCALE = 5E-4;
+export const MOTION_TIME_SCALE = 5E-5;
 export const PAN_VELOCITY_SCALE_FACTOR = 1E-3;
 
 export const ARROWHEAD_LENGTH = 7;
@@ -31,7 +31,7 @@ export const ZOOM_IN_FACTOR = 1;
 export const ZOOM_OUT_FACTOR = -1;
 export const SCALE_POWER_MAX = 8;
 export const SCALE_POWER_MIN = -8; 
-export const GRAVITATIONAL_CONSTANT = 1E6;
+export const GRAVITATIONAL_CONSTANT = 1E5;
 
 export const DRAGGABLE_ELEMENT_CLASSNAME = 'lhg-draggable-element';
 

object.js

@@ -7,6 +7,7 @@ export class MassObject {
   color = {r: undefined, g: undefined, b: undefined};
   created = undefined;
   forces = []; // [{x, y}]
+  active = false;
 
   constructor(x, y, index) {
     this.index = index;

objects.js

@@ -24,7 +24,11 @@ export class Objects {
   }
 
   doneCreatingObject() {
-    this.creatingObject = undefined;
+    if (this.creatingObject !== undefined) {
+      const obj = this.objects[this.creatingObject];
+      obj.active = true;
+      this.creatingObject = undefined;
+    }
   }
 
   object(i) {
@@ -119,6 +123,7 @@ export class Objects {
       const A = this.objects[i];
       for (let j = i + 1; j < this.objects.length; j++) {
         const B = this.objects[j];
+        if (!A.active || !B.active) continue;
         const dx = (B.position.x - A.position.x);
         const dy = (B.position.y - A.position.y);
         const dSquared = dx ** 2 + dy ** 2;
@@ -145,20 +150,38 @@ export class Objects {
       // Calculate forces due to gravity. 
       this.computeForces(elapsedTime);
       
-      // Update velocities. Simple euler method for now.
+      // Generate predicted positions (Velocity verlet method)
       for (let i = 0; i < this.objects.length; i++) {
         const obj = this.objects[i];
-        const acceleration = obj.acceleration;
-        obj.velocity.x += acceleration.x * MOTION_TIME_SCALE * elapsedTime;
-        obj.velocity.y += acceleration.y * MOTION_TIME_SCALE * elapsedTime;
+        obj.currentAcceleration = {...obj.acceleration};
+        obj.projectedPosition = {
+          x: obj.position.x + MOTION_TIME_SCALE * elapsedTime *
+            (obj.velocity.x + 1/2 * obj.currentAcceleration.x * elapsedTime),
+          y: obj.position.y + MOTION_TIME_SCALE * elapsedTime *
+            (obj.velocity.y + 1/2 * obj.currentAcceleration.y * elapsedTime),
+        };
+        obj.currentPosition = {...obj.position};
+        obj.position = obj.projectedPosition;
+      }
+      
+      // Recompute forces
+      this.computeForces();
+
+      // Average first and second predicted accelerations
+      for (let i = 0; i < this.objects.length; i++) {
+        const obj = this.objects[i];
+        const acceleration = {...obj.acceleration};
+        const meanAcceleration = {
+          x: (obj.currentAcceleration.x + acceleration.x) / 2,
+          y: (obj.currentAcceleration.y + acceleration.y) / 2,
+        };
+        obj.velocity.x += meanAcceleration.x * MOTION_TIME_SCALE * elapsedTime;
+        obj.velocity.y += meanAcceleration.y * MOTION_TIME_SCALE * elapsedTime;
+
+        obj.position.x = obj.currentPosition.x + obj.velocity.x * MOTION_TIME_SCALE * elapsedTime;
+        obj.position.y = obj.currentPosition.y + obj.velocity.y * MOTION_TIME_SCALE * elapsedTime;
       }
 
-      // Update positions. Simple Euler method for now.
-      for (let i = 0; i < this.objects.length; i++) {
-        const obj = this.objects[i];
-        obj.position.x += obj.velocity.x * MOTION_TIME_SCALE * elapsedTime;
-        obj.position.y += obj.velocity.y * MOTION_TIME_SCALE * elapsedTime;
-      }
     }
 
     // Display objects info