How to make individual anchor points of bezier continuous or non-continuous

Question

I am creating bezier curves with the following code. The curves can be extended to join several bezier curves by shift clicking in the scene view. My code has functionality for making the whole curve continuous or non-continuous. I realised that I need to make individual points (specifically anchor points) have this functionality.

I believe the most ideal way to go about this is creating a new class for the points with this functionality (making points continuous or non-continuous) since this can be used to add other properties that might be specific to the points. How can do this?

Path

[System.Serializable]
public class Path {

[SerializeField, HideInInspector]
List<Vector2> points;

[SerializeField, HideInInspector]
public bool isContinuous;

public Path(Vector2 centre)
{
    points = new List<Vector2>
    {
        centre+Vector2.left,
        centre+(Vector2.left+Vector2.up)*.5f,
        centre + (Vector2.right+Vector2.down)*.5f,
        centre + Vector2.right
    };
}

public Vector2 this[int i]
{
    get
    {
        return points[i];
    }
}

public int NumPoints
{
    get
    {
        return points.Count;
    }
}

public int NumSegments
{
    get
    {
        return (points.Count - 4) / 3 + 1;
    }
}

public void AddSegment(Vector2 anchorPos)
{
    points.Add(points[points.Count - 1] * 2 - points[points.Count - 2]);
    points.Add((points[points.Count - 1] + anchorPos) * .5f);
    points.Add(anchorPos);
}

public Vector2[] GetPointsInSegment(int i)
{
    return new Vector2[] { points[i * 3], points[i * 3 + 1], points[i * 3 + 2], points[i * 3 + 3] };
}

public void MovePoint(int i, Vector2 pos)
{

    if (isContinuous)
    { 

        Vector2 deltaMove = pos - points[i];
        points[i] = pos;

        if (i % 3 == 0)
        {
            if (i + 1 < points.Count)
            {
                points[i + 1] += deltaMove;
            }
            if (i - 1 >= 0)
            {
                points[i - 1] += deltaMove;
            }
        }
        else
        {
            bool nextPointIsAnchor = (i + 1) % 3 == 0;
            int correspondingControlIndex = (nextPointIsAnchor) ? i + 2 : i - 2;
            int anchorIndex = (nextPointIsAnchor) ? i + 1 : i - 1;

            if (correspondingControlIndex >= 0 && correspondingControlIndex < points.Count)
            {
                float dst = (points[anchorIndex] - points[correspondingControlIndex]).magnitude;
                Vector2 dir = (points[anchorIndex] - pos).normalized;
            points[correspondingControlIndex] = points[anchorIndex] + dir * dst;
                }
            }
        }
    }

    else {
         points[i] = pos;
    }
}

PathCreator

public class PathCreator : MonoBehaviour {

[HideInInspector]
public Path path;


public void CreatePath()
{
    path = new Path(transform.position);
}
}   

PathEditor

[CustomEditor(typeof(PathCreator))]
public class PathEditor : Editor {

PathCreator creator;
Path path;

public override void OnInspectorGUI()
{
    base.OnInspectorGUI();
    EditorGUI.BeginChangeCheck();

    bool continuousControlPoints = GUILayout.Toggle(path.isContinuous, "Set Continuous Control Points");
    if (continuousControlPoints != path.isContinuous)
    {
        Undo.RecordObject(creator, "Toggle set continuous controls");
        path.isContinuous = continuousControlPoints;
    }

    if (EditorGUI.EndChangeCheck())
    {
        SceneView.RepaintAll();
    }
}

void OnSceneGUI()
{
    Input();
    Draw();
}

void Input()
 {
    Event guiEvent = Event.current;
    Vector2 mousePos = HandleUtility.GUIPointToWorldRay(guiEvent.mousePosition).origin;

    if (guiEvent.type == EventType.MouseDown && guiEvent.button == 0 && guiEvent.shift)
    {
        Undo.RecordObject(creator, "Add segment");
        path.AddSegment(mousePos);
    }
}

void Draw()
{

    for (int i = 0; i < path.NumSegments; i++)
    {
        Vector2[] points = path.GetPointsInSegment(i);
        Handles.color = Color.black;
        Handles.DrawLine(points[1], points[0]);
        Handles.DrawLine(points[2], points[3]);
        Handles.DrawBezier(points[0], points[3], points[1], points[2], Color.green, null, 2);
    }

    Handles.color = Color.red;
    for (int i = 0; i < path.NumPoints; i++)
    {
        Vector2 newPos = Handles.FreeMoveHandle(path[i], Quaternion.identity, .1f, Vector2.zero, Handles.CylinderHandleCap);
        if (path[i] != newPos)
        {
            Undo.RecordObject(creator, "Move point");
            path.MovePoint(i, newPos);
        }
    }
}

void OnEnable()
{
    creator = (PathCreator)target;
    if (creator.path == null)
    {
        creator.CreatePath();
    }
    path = creator.path;
}
}

Answer 1

I think your idea is fine: you can write two classes, named ControlPoint and HandlePoint (make them serializable).

ControlPoint may represent p0 and p3 of each curve - the points the path indeed pass through. For continuity, you must assert that p3 of one segment equals to p0 of the next segment.

HandlePoint may represent p1 and p2 of each curve - the points that are tangents of the curve and provide direction and inclination. For smoothness, you must assert that (p3 - p2).normalized of one segment equals to (p1 - p0).normalized of the next segment. (if you want symetric smoothness, p3 - p2 of one must equals p1 - p0 of the other.)

Tip #1: Always consider matrix transformations when assigning or comparing points of each segment. I suggest you to convert any point to global space before performing the operations.

Tip #2: consider applying a constraint between points inside a segment, so when you move arround p0 or p3 of a curve, p1 or p2 move accordingly by the same amount, respectively (just like any graphics editor software do on bezier curves).

---

Edit -> Code provided

I did a sample implementation of the idea. Actually, after start coding I realized that just one class ControlPoint (instead of two) will do the job. A ControlPoint have 2 tangents. The desired behaviour is controled by the field smooth, that can be set for each point.

ControlPoint.cs

using System;
using UnityEngine;

[Serializable]
public class ControlPoint
{
  [SerializeField] Vector2 _position;
  [SerializeField] bool _smooth;
  [SerializeField] Vector2 _tangentBack;
  [SerializeField] Vector2 _tangentFront;

  public Vector2 position
  {
    get { return _position; }
    set { _position = value; }
  }

  public bool smooth
  {
    get { return _smooth; }
    set { if (_smooth = value) _tangentBack = -_tangentFront; }
  }

  public Vector2 tangentBack
  {
    get { return _tangentBack; }
    set
    {
      _tangentBack = value;
      if (_smooth) _tangentFront = _tangentFront.magnitude * -value.normalized;
    }
  }

  public Vector2 tangentFront
  {
    get { return _tangentFront; }
    set
    {
      _tangentFront = value;
      if (_smooth) _tangentBack = _tangentBack.magnitude * -value.normalized;
    }
  }

  public ControlPoint(Vector2 position, bool smooth = true)
  {
    this._position = position;
    this._smooth = smooth;
    this._tangentBack = -Vector2.one;
    this._tangentFront = Vector2.one;
  }
}

I also coded a custom PropertyDrawer for the ControlPoint class, so it can be shown better on the inspector. It is just a naive implementation. You could improve it very much.

ControlPointDrawer.cs

using UnityEngine;
using UnityEditor;

[CustomPropertyDrawer(typeof(ControlPoint))]
public class ControlPointDrawer : PropertyDrawer
{
  public override void OnGUI(Rect position, SerializedProperty property, GUIContent label)
  {

    EditorGUI.BeginProperty(position, label, property);
    int indent = EditorGUI.indentLevel;
    EditorGUI.indentLevel = 0; //-= 1;
    var propPos = new Rect(position.x, position.y, position.x + 18, position.height);
    var prop = property.FindPropertyRelative("_smooth");
    EditorGUI.PropertyField(propPos, prop, GUIContent.none);
    propPos = new Rect(position.x + 20, position.y, position.width - 20, position.height);
    prop = property.FindPropertyRelative("_position");
    EditorGUI.PropertyField(propPos, prop, GUIContent.none);
    EditorGUI.indentLevel = indent;
    EditorGUI.EndProperty();
  }

  public override float GetPropertyHeight(SerializedProperty property, GUIContent label)
  {
    return EditorGUIUtility.singleLineHeight;
  }
}

I followed the same architecture of your solution, but with the needed adjustments to fit the ControlPoint class, and other fixes/changes. For example, I stored all the point values in local coordinates, so the transformations on the component or parents reflect in the curve.

Path.cs

using System;
using UnityEngine;
using System.Collections.Generic;

[Serializable]
public class Path
{
  [SerializeField] List<ControlPoint> _points;

  [SerializeField] bool _loop = false;

  public Path(Vector2 position)
  {
    _points = new List<ControlPoint>
    {
      new ControlPoint(position),
      new ControlPoint(position + Vector2.right)
    };
  }

  public bool loop { get { return _loop; } set { _loop = value; } }

  public ControlPoint this[int i] { get { return _points[(_loop && i == _points.Count) ? 0 : i]; } }

  public int NumPoints { get { return _points.Count; } }

  public int NumSegments { get { return _points.Count - (_loop ? 0 : 1); } }

  public ControlPoint InsertPoint(int i, Vector2 position, bool smooth)
  {
    _points.Insert(i, new ControlPoint(position, smooth));
    return this[i];
  }
  public ControlPoint RemovePoint(int i)
  {
    var item = this[i];
    _points.RemoveAt(i);
    return item;
  }
  public Vector2[] GetBezierPointsInSegment(int i)
  {
    var pointBack = this[i];
    var pointFront = this[i + 1];
    return new Vector2[4]
    {
      pointBack.position,
      pointBack.position + pointBack.tangentFront,
      pointFront.position + pointFront.tangentBack,
      pointFront.position
    };
  }

  public ControlPoint MovePoint(int i, Vector2 position)
  {
    this[i].position = position;
    return this[i];
  }

  public ControlPoint MoveTangentBack(int i, Vector2 position)
  {
    this[i].tangentBack = position;
    return this[i];
  }

  public ControlPoint MoveTangentFront(int i, Vector2 position)
  {
    this[i].tangentFront = position;
    return this[i];
  }
}

PathEditor is pretty much the same thing.

PathCreator.cs

using UnityEngine;

public class PathCreator : MonoBehaviour
{

  public Path path;

  public Path CreatePath()
  {
    return path = new Path(Vector2.zero);
  }

  void Reset()
  {
    CreatePath();
  }
}

Finally, all the magic happens in the PathCreatorEditor. Two comments here:

1) I moved the drawing of the lines to a custom DrawGizmo static function, so you can have the lines even when the object is not Active (i.e. shown in the Inspector) You could even make it pickable if you want to. I don't know if you want this behaviour, but you could easily revert;

2) Notice the Handles.matrix = creator.transform.localToWorldMatrix lines over the class. It automatically transforms the scale and rotation of the points to the world coordinates. There is a detail with PivotRotation over there too.

PathCreatorEditor.cs

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(PathCreator))]
public class PathCreatorEditor : Editor
{
  PathCreator creator;
  Path path;
  SerializedProperty property;

  public override void OnInspectorGUI()
  {
    serializedObject.Update();
    EditorGUI.BeginChangeCheck();
    EditorGUILayout.PropertyField(property, true);
    if (EditorGUI.EndChangeCheck()) serializedObject.ApplyModifiedProperties();
  }

  void OnSceneGUI()
  {
    Input();
    Draw();
  }

  void Input()
  {
    Event guiEvent = Event.current;
    Vector2 mousePos = HandleUtility.GUIPointToWorldRay(guiEvent.mousePosition).origin;
    mousePos = creator.transform.InverseTransformPoint(mousePos);
    if (guiEvent.type == EventType.MouseDown && guiEvent.button == 0 && guiEvent.shift)
    {
      Undo.RecordObject(creator, "Insert point");
      path.InsertPoint(path.NumPoints, mousePos, false);
    }
    else if (guiEvent.type == EventType.MouseDown && guiEvent.button == 0 && guiEvent.control)
    {
      for (int i = 0; i < path.NumPoints; i++)
      {
        if (Vector2.Distance(mousePos, path[i].position) <= .25f)
        {
          Undo.RecordObject(creator, "Remove point");
          path.RemovePoint(i);
          break;
        }
      }
    }
  }

  void Draw()
  {
    Handles.matrix = creator.transform.localToWorldMatrix;
    var rot = Tools.pivotRotation == PivotRotation.Local ? creator.transform.rotation : Quaternion.identity;
    var snap = Vector2.zero;
    Handles.CapFunction cap = Handles.CylinderHandleCap;
    for (int i = 0; i < path.NumPoints; i++)
    {
      var pos = path[i].position;
      var size = .1f;
      Handles.color = Color.red;
      Vector2 newPos = Handles.FreeMoveHandle(pos, rot, size, snap, cap);
      if (pos != newPos)
      {
        Undo.RecordObject(creator, "Move point position");
        path.MovePoint(i, newPos);
      }
      pos = newPos;
      if (path.loop || i != 0)
      {
        var tanBack = pos + path[i].tangentBack;
        Handles.color = Color.black;
        Handles.DrawLine(pos, tanBack);
        Handles.color = Color.red;
        Vector2 newTanBack = Handles.FreeMoveHandle(tanBack, rot, size, snap, cap);
        if (tanBack != newTanBack)
        {
          Undo.RecordObject(creator, "Move point tangent");
          path.MoveTangentBack(i, newTanBack - pos);
        }
      }
      if (path.loop || i != path.NumPoints - 1)
      {
        var tanFront = pos + path[i].tangentFront;
        Handles.color = Color.black;
        Handles.DrawLine(pos, tanFront);
        Handles.color = Color.red;
        Vector2 newTanFront = Handles.FreeMoveHandle(tanFront, rot, size, snap, cap);
        if (tanFront != newTanFront)
        {
          Undo.RecordObject(creator, "Move point tangent");
          path.MoveTangentFront(i, newTanFront - pos);
        }
      }
    }
  }

  [DrawGizmo(GizmoType.Selected | GizmoType.NonSelected)]
  static void DrawGizmo(PathCreator creator, GizmoType gizmoType)
  {
    Handles.matrix = creator.transform.localToWorldMatrix;
    var path = creator.path;
    for (int i = 0; i < path.NumSegments; i++)
    {
      Vector2[] points = path.GetBezierPointsInSegment(i);
      Handles.DrawBezier(points[0], points[3], points[1], points[2], Color.green, null, 2);
    }
  }

  void OnEnable()
  {
    creator = (PathCreator)target;
    path = creator.path ?? creator.CreatePath();
    property = serializedObject.FindProperty("path");
  }
}

Moreover, I added a loop field in case you want the curve to be closed, and I added a naive funcionality to remove points by Ctrl+click on the Scene. Summing up, this is just basic stuff, but you could do it as advanced as you want. Also, you can reuse your ControlPoint class with other Components, like a Catmull-Rom spline, geometric shapes, other parametric functions...

Answer 2

The basic question in your post is: 'Is it a good idea to a have a separate Class for the points of a bezier curve?'

Since the curve will be made up of such points and these are more than just two coordinates imo it most certainly is a good idea.

But, as usual when doing class design, let's collect a few use cases, i.e. things a point will be used for or things we expect to do to a point..:

• A point can be added or removed from a curve
• A point can be moved
• Its control point(s) can be moved

Besides the mere location, a point, i.e. an 'anchor point' should have more properties and abilities/methods..:

• It has control points; how these are related to the points is sometimes not exactly the same. Looking at the Unity docs we see that the Handles.DrawLine looks at two points and their 'inner' control poiints. Coming from GDI+ GraphicsPath I see a sequence of points, altenrating between 1 anchor and 2 control points. Imo, this makes an even stronger case for treating the two control points as properties of the anchor point. Since both must be movable they may have a common ancestor or be hooked up to movecontroller class; but I trust you know best how to do that in Unity..

• The property the question really started with was something like bool IsContinuous. When true we need to couple

  • moving a control point to moving the other one in 'the opposite' way.
  • moving the anchor to moving both control points in parallel
• Maybe a property bool IsLocked to prevent moving it
• Maybe a property bool IsProtected to prevent removing it when reducing/simplifying the curve. (Which is hardly needed for constructed curves but very much so for curves from free-hand drawing or tracing with the mouse)
• Maybe a property to know that the point in a group of points which can be edited together.
• Maybe a general marker.
• Maybe a text annotation
• Maybe a type indicator that denotes a break/split in the curve.
• Maybe methods to increase or decrease smoothness vs. pointiness.

Some use cases clearly mostly involve the curve but others don't; and some are useful for both.

So, clearly we have a lot of good reasons to create a clever ÀnchPoint` class..

((I'm a bit tied up but still plan to write my own editor for the GraphicsPath bezier curves. If and when this happens, I'll update the post with things I learned including the class design I come up with..))