first implementation

.gitignore

@@ -70,3 +70,4 @@ crashlytics-build.properties
 # Temporary auto-generated Android Assets
 /[Aa]ssets/[Ss]treamingAssets/aa.meta
 /[Aa]ssets/[Ss]treamingAssets/aa/*
+/Assets/TextMesh Pro

Assets/CableJointsAlgorithm.cs

@@ -0,0 +1,92 @@
+using System;
+using System.Collections.Generic;
+using UnityEngine;
+using static System.Math;
+
+public static class CableJointsAlgorithm {
+    public static void TimeStep(List<Cable> cables) {
+        //handle each cable individually
+        foreach (var cable in cables) {
+            //calculate new attachment points for all joints
+            for(var go = cable.firstRoller; go != null; go = go.GetComponent<RollerProperties>().linkTo) {
+                if (go.GetComponent<RollerProperties>().linkTo != null) {
+                    var dist = go.GetComponent<DistanceJoint2D>();
+                    var rp = go.GetComponent<RollerProperties>();
+                    var (left, right) = TangentCircleCircle(go, rp.linkTo);
+
+                    //TODO: assumes circles are flat for sufficiently small timesteps
+                    var leftSurfaceDist =
+                        (go.transform.TransformPoint(dist.anchor) - go.transform.TransformPoint(left)).magnitude;
+                    var rightSurfaceDist = (dist.attachedRigidbody.transform.TransformPoint(dist.connectedAnchor) -
+                                            dist.attachedRigidbody.transform.TransformPoint(right)).magnitude;
+                    
+                    Debug.Log(go.name+": left dist: "+leftSurfaceDist+" right Dist: "+rightSurfaceDist);
+
+                    dist.anchor = left;
+                    dist.connectedAnchor = right;
+                }
+            }
+        }
+    }
+
+
+    public static (Vector2, Vector2) TangentCircleCircle(GameObject g1, GameObject g2) {
+        var roller1 = g1.GetComponent<RollerProperties>();
+        var roller2 = g2.GetComponent<RollerProperties>();
+        var t1 = g1.transform;
+        var t2 = g2.transform;
+
+        //assume round rollers only
+        var r1 = t1.lossyScale.x/2;
+        var r2 = t2.lossyScale.x/2;
+
+        Vector2 d = t2.Position2d() - t1.Position2d();
+        float r = r1 + r2;
+        if (roller1.clockwise == roller2.clockwise) {
+            r = r2 - r1;
+        }
+
+        var dLen = d.magnitude;
+        if (dLen > r) {
+            float alpha;
+            if (d.x >= 0) {
+                alpha = (float)Asin(d.y / dLen);
+            }
+            else {
+                alpha = (float)(PI - Asin(d.y / dLen));
+            }
+
+            float phi = (float)Asin(r / dLen); //TODO verify, paper says "|c|"
+
+            float alpha1, alpha2;
+            if (roller1.clockwise == roller2.clockwise) {
+                if (roller1.clockwise) {
+                    alpha1 = (float)(alpha - PI / 2 - phi);
+                    alpha2 = (float)(alpha - PI / 2 + phi);
+                }
+                else {
+                    alpha1 = (float)(alpha + PI / 2 + phi);
+                    alpha2 = (float)(alpha + PI / 2 + phi);
+                }
+            }
+            else {
+                if (roller1.clockwise) {
+                    alpha1 = (float)(alpha - PI / 2 + phi);
+                    alpha2 = (float)(alpha + PI / 2 + phi);
+                }
+                else {
+                    alpha1 = (float)(alpha + PI / 2 - phi);
+                    alpha2 = (float)(alpha - PI / 2 - phi);
+                }
+            }
+
+            var p1 = t1.Position2d() + r1 * new Vector2((float)Cos(alpha1), (float)Sin(alpha1));
+            var p2 = t2.Position2d() + r2 * new Vector2((float)Cos(alpha2), (float)Sin(alpha2));
+
+            return (t1.InverseTransformPoint(p1), t2.InverseTransformPoint(p2));
+
+        }
+
+        throw new Exception("Overlapping Rollers Error");
+    }
+}

Assets/CableJointsAlgorithm.cs.meta

@@ -0,0 +1,3 @@
+fileFormatVersion: 2
+guid: 091ab8204ddb43eabfb870958861ae96
+timeCreated: 1700149837

Assets/Controller.cs

@@ -1,27 +1,116 @@
 using System.Collections;
 using System.Collections.Generic;
+using NUnit.Framework;
+using TMPro;
+using Unity.Collections;
+using Unity.VisualScripting;
 using UnityEditor;
 using UnityEngine;
-using UnityEngine.SceneManagement;
+using FontWeight = TMPro.FontWeight;
 
-public class Controller : MonoBehaviour
-{
-    // Start is called before the first frame update
-    void Start() {
-        
+public class Controller : MonoBehaviour {
+    private List<Cable> cables = new();
+
+    //Initialize
+    void OnEnable() {
+
+        var rotatableSprite = Resources.Load<Sprite>("Rotatable");
+        var fixedSprite = Resources.Load<Sprite>("Fixed");
+        var poweredSprite = Resources.Load<Sprite>("Powered");
+        var freeSprite = Resources.Load<Sprite>("Free");
+
+        //prepare rollers
         var gameObjects = FindObjectsByType<GameObject>(FindObjectsInactive.Exclude, FindObjectsSortMode.None);
         foreach (GameObject go in gameObjects) {
-            if (go.GetComponent<SpriteRenderer>() != null) {
-                Debug.Log("Object: "+go.name);
+            RollerProperties rp = go.GetComponent<RollerProperties>();
+            if (rp != null) {
+                Rigidbody2D settings = go.GetOrAddComponent<Rigidbody2D>();
                 
-                go.AddComponent<RollerProperties>();
+                switch (rp.movement) {
+                    case RollerProperties.RotationType.Rotatable:
+                        go.GetComponent<SpriteRenderer>().sprite = rotatableSprite;
+                        break;
+                    case RollerProperties.RotationType.Fixed:
+                        go.GetComponent<SpriteRenderer>().sprite = fixedSprite;
+                        break;
+                    case RollerProperties.RotationType.Free:
+                        go.GetComponent<SpriteRenderer>().sprite = freeSprite;
+                        break;
+                    case RollerProperties.RotationType.Powered:
+                        go.GetComponent<SpriteRenderer>().sprite = poweredSprite;
+                        break;
+                }
+                
+                if (rp.movement == RollerProperties.RotationType.Fixed) {
+                    settings.bodyType = RigidbodyType2D.Static;
+                }
+
+                if (rp.start) {
+                    cables.Add(new Cable { firstRoller = go });
+                }
+
+                Debug.Log("Initialized roller: " + go.name);
             }
         }
+
+        //create canvas to display information
+        var canvas = FindAnyObjectByType<Canvas>();
+
+        //prepare joints
+        foreach (var go in gameObjects) {
+            RollerProperties rp = go.GetComponent<RollerProperties>();
+            if (rp != null) {
+                if (rp.linkTo != null) {
+                    var dist = go.AddComponent<DistanceJoint2D>();
+                    dist.enableCollision = true;
+                    dist.connectedBody = rp.linkTo.GetComponent<Rigidbody2D>();
+                    dist.maxDistanceOnly = true;
+                    var (left, right) = CableJointsAlgorithm.TangentCircleCircle(go, rp.linkTo);
+                    dist.anchor = left;
+                    dist.connectedAnchor = right;
+                    rp.currentDistance = dist.distance = dist.DistanceInWorld(left, right);
+                }
+
+                if (rp.movement == RollerProperties.RotationType.Rotatable ||
+                    rp.movement == RollerProperties.RotationType.Powered) {
+                    var wheel = go.AddComponent<HingeJoint2D>();
+                    wheel.anchor = Vector2.zero;
+                    if (rp.movement == RollerProperties.RotationType.Powered) {
+                        wheel.useMotor = true;
+                        wheel.motor = new JointMotor2D() { maxMotorTorque = 10000, motorSpeed = 10 };
+                    }
+                }
+
+                //create names on objects
+                GameObject text = new GameObject(go.name + "_text");
+                text.transform.parent = canvas.transform;
+                
+                var textMeshPro = text.AddComponent<TextMeshPro>();
+                textMeshPro.text = go.name + "\n" + (rp.clockwise ? "cw" : "ccw") + " - " + rp.movement;
+                textMeshPro.fontSize = .3f;
+                textMeshPro.color = Color.red;
+                textMeshPro.fontWeight = FontWeight.Bold;
+                textMeshPro.outlineColor = Color.white;
+                textMeshPro.outlineWidth = 1;
+                textMeshPro.horizontalAlignment = HorizontalAlignmentOptions.Center;
+                textMeshPro.verticalAlignment = VerticalAlignmentOptions.Middle;
+                textMeshPro.transform.localScale = new Vector3(100, 100, 1);
+                textMeshPro.fontSize = .03f;
+                textMeshPro.autoSizeTextContainer = true;
+                textMeshPro.fontSizeMin = 0;
+                rp.text = text;
+            }
+        }
+
     }
 
+
     // Update is called once per frame
-    void Update()
-    {
-        
+    void Update() {
+        CableJointsAlgorithm.TimeStep(cables);
     }
 }
+
+public class Cable {
+    public GameObject firstRoller;
+}

Assets/Extensions.cs

@@ -0,0 +1,23 @@
+using System.Collections;
+using System.Collections.Generic;
+using UnityEngine;
+
+public static class Extensions
+{
+    public static ComponentA GetOrAddComponent<ComponentA>(this GameObject gameObject)
+        where ComponentA : Component {
+
+        ComponentA result = gameObject.GetComponent<ComponentA>();
+        return result == null ? gameObject.AddComponent<ComponentA>() : result;
+    }
+
+    public static Vector2 Position2d(this Transform t) {
+        Vector3 pos = t.position;
+        return new Vector2(pos.x, pos.y);
+    }
+
+    public static float DistanceInWorld(this DistanceJoint2D dist, Vector2 pointInSelf, Vector2 pointInConnected) {
+        return (dist.transform.TransformPoint(dist.anchor) -
+                dist.connectedBody.transform.TransformPoint(pointInConnected)).magnitude;
+    }
+}

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Assets/Resources/Textures.kra.meta

@@ -1,5 +1,5 @@
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+guid: af13a4aad11a6794a89698ce12bb39be
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Assets/RollerProperties.cs

@@ -1,19 +1,51 @@
+using System;
 using System.Collections;
 using System.Collections.Generic;
+using NUnit.Framework.Internal;
+using TMPro;
+using UnityEditor;
 using UnityEngine;
+using UnityEngine.Serialization;
 
+[System.Serializable]
 public class RollerProperties : MonoBehaviour {
-    public bool Direction { get; set; } = false;
-    
-    // Start is called before the first frame update
-    void Start()
-    {
-        
+    [SerializeField] public bool start = false;
+
+    [SerializeField] public bool clockwise = false;
+
+    [SerializeField] public GameObject linkTo = null;
+
+    [SerializeField] public RotationType movement = RotationType.Fixed;
+
+    protected internal float currentDistance;
+
+    protected internal GameObject text;
+
+    private void Update() {
+        if (text != null) {
+            text.transform.position = transform.position;
+            text.transform.rotation = transform.rotation;
+        }
     }
 
     // Update is called once per frame
-    void Update()
-    {
-        
+    void OnDrawGizmos() {
+        foreach (var distanceJoint in gameObject.GetComponents<DistanceJoint2D>()) {
+            Gizmos.color = new Color(1, .3f, 0);
+            var cableStart = transform.TransformPoint(distanceJoint.anchor);
+            var cableEnd = distanceJoint.connectedBody.transform.TransformPoint(distanceJoint.connectedAnchor);
+            Gizmos.DrawLine(cableStart, cableEnd);
+            Gizmos.color = Color.yellow;
+            Gizmos.DrawCube(cableStart, new Vector3(0.1f, 0.1f, 0.1f));
+            Gizmos.color = Color.red;
+            Gizmos.DrawCube(cableEnd, new Vector3(0.1f, 0.1f, 0.1f));
+        }
     }
-}
+
+    public enum RotationType {
+        Fixed,
+        Rotatable,
+        Powered,
+        Free
+    }
+}

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