c# - 如何使贝塞尔曲线的单个 anchor 连续或不连续

Question

我正在使用以下代码创建贝塞尔曲线。通过在场景 View 中按住 Shift 单击，可以扩展曲线以连接多条贝塞尔曲线。我的代码具有使整个曲线连续或不连续的功能。我意识到我需要让各个点(特别是 anchor )具有此功能。

我认为解决此问题的最理想方法是为具有此功能的点创建一个新类(使点连续或不连续)，因为这可用于添加可能特定于点的其他属性。如何做到这一点？

路径

[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;
    }
}

路径创建器

public class PathCreator : MonoBehaviour {

[HideInInspector]
public Path path;


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

路径编辑器

[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

我认为您的想法很好:您可以编写两个类，分别命名为ControlPoint 和HandlePoint(使它们可序列化)。

ControlPoint 可能代表每条曲线的 p0 和 p3 - 路径确实经过的点。为了连续性，您必须断言一个片段的p3 等于下一个片段的p0。

HandlePoint 可以代表每条曲线的 p1 和 p2 - 曲线的切点并提供方向和倾斜度。对于平滑度，您必须断言一个片段的(p3 - p2).normalized 等于下一个片段的(p1 - p0).normalized部分。 (如果您想要对称平滑度，其中一个的p3 - p2 必须等于另一个的p1 - p0。)

提示 #1:在分配或比较每个线段的点时始终考虑矩阵变换。我建议您在执行操作之前将任何点转换为全局空间。

提示 #2:考虑在线段内的点之间应用约束，因此当您围绕曲线的 p0 或 p3 移动时， p1 或 p2 分别相应地移动相同的量(就像任何图形编辑器软件在贝塞尔曲线上所做的一样)。

---

编辑 -> 代码提供

我做了一个想法的示例实现。实际上，在开始编码之后，我意识到只需一个类 ControlPoint(而不是两个)就可以完成这项工作。 ControlPoint 有 2 条切线。所需的行为由字段 smooth 控制，可以为每个点设置。

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;
  }
}

我还为 ControlPoint 类编写了自定义 PropertyDrawer，因此它可以更好地显示在检查器上。这只是一个天真的实现。您可以大大改进它。

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;
  }
}

我遵循了与您的解决方案相同的架构，但进行了必要的调整以适应 ControlPoint 类，以及其他修复/更改。例如，我将所有点值存储在局部坐标中，因此组件或父级上的变换反射(reflect)在曲线中。

路径.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 几乎是同一回事。

PathCreator.cs

using UnityEngine;

public class PathCreator : MonoBehaviour
{

  public Path path;

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

  void Reset()
  {
    CreatePath();
  }
}

最后，所有的魔法都发生在 PathCreatorEditor 中。这里有两条评论:

1) 我将线条的绘制移动到自定义的 DrawGizmo 静态函数中，这样即使对象不是 Active(即显示在检查员)如果你愿意，你甚至可以让它变得可拾取。我不知道您是否想要这种行为，但您可以轻松恢复；

2) 注意类上的 Handles.matrix = creator.transform.localToWorldMatrix 行。它会自动将点的比例和旋转转换为世界坐标。那里也有关于 PivotRotation 的详细信息。

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");
  }
}

此外，我添加了一个 loop 字段以防您希望曲线闭合，并且我添加了一个简单的功能以通过 Ctrl+click 在场景中删除点. 总而言之，这只是基本的东西，但您可以根据需要进行高级操作。此外，您可以将 ControlPoint 类与其他组件重用，例如 Catmull-Rom 样条、几何形状、其他参数函数...