一、介绍贝塞尔曲线

贝塞尔曲线是一种由四个或更多个控制点确定的光滑曲线。它是由法国数学家Pierre Bézier发明的，为计算机图形学提供了基础。贝塞尔曲线可以用来描述直线和曲线，并且可以通过调整控制点的位置来改变曲线的形状。贝塞尔曲线在计算机图形学、计算机辅助设计（CAD）和计算机动画等领域中广泛应用。

贝塞尔曲线的特点是光滑且可控制。通过调整控制点的位置和数量，可以创建各种形状的曲线，包括直线、曲线、圆弧和复杂的曲线路径。贝塞尔曲线的形状由控制点的位置和相对位置决定，控制点之间的曲线段称为贝塞尔曲线的分段。

贝塞尔曲线有多种类型，包括一次贝塞尔曲线、二次贝塞尔曲线和三次贝塞尔曲线。一次贝塞尔曲线由两个控制点确定，二次贝塞尔曲线由三个控制点确定，三次贝塞尔曲线由四个控制点确定。同类型的贝塞尔曲线具有不同的特性和应用场景。

贝塞尔曲线在计算机图形学中的应用非常广泛。它可以用来创建平滑的曲线路径、绘制复杂的图形和形状、实现动画效果等。在计算机辅助设计中，贝塞尔曲线被用来绘制曲线和曲面，用于建模和设计。在计算机动画中，贝塞尔曲线可以用来控制物体的运动轨迹和形变。

总结起来，贝塞尔曲线是一种由控制点确定的光滑曲线，它在计算机图形学、计算机辅助设计和计算机动画等领域中有广泛的应用。

二、Unity中贝塞尔曲线工具介绍

1.创建一个空物体挂在上BezierSpline.cs脚本组件

2.由上图可知刚创建出来的有两个点和两个手柄组成

3.我们可修改其坐标看下效果

4.这样我们就可以获得这两个点之间的指定数量的点来作为某个物体的运动轨迹

5.增加点

三、脚本构成如下

此工具总共三个脚本构成

1.放在Editor文件夹下的BezierSplineInspector.cs

using UnityEditor;
using UnityEngine;[CustomEditor(typeof(BezierSpline))]
public class BezierSplineInspector : Editor
{private const int stepsPerCurve = 10;private const float directionScale = 0.5f;private const float handleSize = 0.04f;private const float pickSize = 0.06f;private static Color[] modeColors = {Color.white,Color.yellow,Color.cyan};private BezierSpline spline;private Transform handleTransform;private Quaternion handleRotation;private int selectedIndex = -1;public override void OnInspectorGUI(){spline = target as BezierSpline;EditorGUI.BeginChangeCheck();bool loop = EditorGUILayout.Toggle("Loop", spline.Loop);if (EditorGUI.EndChangeCheck()){Undo.RecordObject(spline, "Toggle Loop");EditorUtility.SetDirty(spline);spline.Loop = loop;}if (selectedIndex >= 0 && selectedIndex < spline.ControlPointCount){DrawSelectedPointInspector();}if (GUILayout.Button("Add Curve")){Undo.RecordObject(spline, "Add Curve");spline.AddCurve();EditorUtility.SetDirty(spline);}}private void DrawSelectedPointInspector(){GUILayout.Label("Selected Point");EditorGUI.BeginChangeCheck();Vector3 point = EditorGUILayout.Vector3Field("Position", spline.GetControlPoint(selectedIndex));if (EditorGUI.EndChangeCheck()){Undo.RecordObject(spline, "Move Point");EditorUtility.SetDirty(spline);spline.SetControlPoint(selectedIndex, point);}EditorGUI.BeginChangeCheck();BezierControlPointMode mode = (BezierControlPointMode)EditorGUILayout.EnumPopup("Mode", spline.GetControlPointMode(selectedIndex));if (EditorGUI.EndChangeCheck()){Undo.RecordObject(spline, "Change Point Mode");spline.SetControlPointMode(selectedIndex, mode);EditorUtility.SetDirty(spline);}}private void OnSceneGUI(){spline = target as BezierSpline;handleTransform = spline.transform;handleRotation = Tools.pivotRotation == PivotRotation.Local ?handleTransform.rotation : Quaternion.identity;Vector3 p0 = ShowPoint(0);for (int i = 1; i < spline.ControlPointCount; i += 3){Vector3 p1 = ShowPoint(i);Vector3 p2 = ShowPoint(i + 1);Vector3 p3 = ShowPoint(i + 2);Handles.color = Color.gray;Handles.DrawLine(p0, p1);Handles.DrawLine(p2, p3);Handles.DrawBezier(p0, p3, p1, p2, Color.white, null, 2f);p0 = p3;}ShowDirections();}private void ShowDirections(){Handles.color = Color.green;Vector3 point = spline.GetPoint(0f);Handles.DrawLine(point, point + spline.GetDirection(0f) * directionScale);int steps = stepsPerCurve * spline.CurveCount;for (int i = 1; i <= steps; i++){point = spline.GetPoint(i / (float)steps);Handles.DrawLine(point, point + spline.GetDirection(i / (float)steps) * directionScale);}}private Vector3 ShowPoint(int index){Vector3 point = handleTransform.TransformPoint(spline.GetControlPoint(index));float size = HandleUtility.GetHandleSize(point);if (index == 0){size *= 2f;}Handles.color = modeColors[(int)spline.GetControlPointMode(index)];if (Handles.Button(point, handleRotation, size * handleSize, size * pickSize, Handles.DotCap)){selectedIndex = index;Repaint();}if (selectedIndex == index){EditorGUI.BeginChangeCheck();point = Handles.DoPositionHandle(point, handleRotation);if (EditorGUI.EndChangeCheck()){Undo.RecordObject(spline, "Move Point");EditorUtility.SetDirty(spline);spline.SetControlPoint(index, handleTransform.InverseTransformPoint(point));}}return point;}
}

2.Bezier.cs

using UnityEngine;public static class Bezier
{public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, float t){t = Mathf.Clamp01(t);float oneMinusT = 1f - t;returnoneMinusT * oneMinusT * p0 +2f * oneMinusT * t * p1 +t * t * p2;}public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, float t){return2f * (1f - t) * (p1 - p0) +2f * t * (p2 - p1);}public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t){t = Mathf.Clamp01(t);float OneMinusT = 1f - t;returnOneMinusT * OneMinusT * OneMinusT * p0 +3f * OneMinusT * OneMinusT * t * p1 +3f * OneMinusT * t * t * p2 +t * t * t * p3;}public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t){t = Mathf.Clamp01(t);float oneMinusT = 1f - t;return3f * oneMinusT * oneMinusT * (p1 - p0) +6f * oneMinusT * t * (p2 - p1) +3f * t * t * (p3 - p2);}
}

3.BezierSpline.cs

using UnityEngine;
using System;public class BezierSpline : MonoBehaviour
{[SerializeField]public Vector3[] points;[SerializeField]private BezierControlPointMode[] modes;[SerializeField]private bool loop;public bool Loop{get{return loop;}set{loop = value;if (value == true){modes[modes.Length - 1] = modes[0];SetControlPoint(0, points[0]);}}}public int ControlPointCount{get{return points.Length;}}public Vector3 GetControlPoint(int index){return points[index];}public void SetControlPoint(int index, Vector3 point){if (index % 3 == 0){Vector3 delta = point - points[index];if (loop){if (index == 0){points[1] += delta;points[points.Length - 2] += delta;points[points.Length - 1] = point;}else if (index == points.Length - 1){points[0] = point;points[1] += delta;points[index - 1] += delta;}else{points[index - 1] += delta;points[index + 1] += delta;}}else{if (index > 0){points[index - 1] += delta;}if (index + 1 < points.Length){points[index + 1] += delta;}}}points[index] = point;EnforceMode(index);}public BezierControlPointMode GetControlPointMode(int index){return modes[(index + 1) / 3];}public void SetControlPointMode(int index, BezierControlPointMode mode){int modeIndex = (index + 1) / 3;modes[modeIndex] = mode;if (loop){if (modeIndex == 0){modes[modes.Length - 1] = mode;}else if (modeIndex == modes.Length - 1){modes[0] = mode;}}EnforceMode(index);}private void EnforceMode(int index){int modeIndex = (index + 1) / 3;BezierControlPointMode mode = modes[modeIndex];if (mode == BezierControlPointMode.Free || !loop && (modeIndex == 0 || modeIndex == modes.Length - 1)){return;}int middleIndex = modeIndex * 3;int fixedIndex, enforcedIndex;if (index <= middleIndex){fixedIndex = middleIndex - 1;if (fixedIndex < 0){fixedIndex = points.Length - 2;}enforcedIndex = middleIndex + 1;if (enforcedIndex >= points.Length){enforcedIndex = 1;}}else{fixedIndex = middleIndex + 1;if (fixedIndex >= points.Length){fixedIndex = 1;}enforcedIndex = middleIndex - 1;if (enforcedIndex < 0){enforcedIndex = points.Length - 2;}}Vector3 middle = points[middleIndex];Vector3 enforcedTangent = middle - points[fixedIndex];if (mode == BezierControlPointMode.Aligned){enforcedTangent = enforcedTangent.normalized * Vector3.Distance(middle, points[enforcedIndex]);}points[enforcedIndex] = middle + enforcedTangent;}public int CurveCount{get{return (points.Length - 1) / 3;}}public Vector3 GetPoint(float t){int i;if (t >= 1f){t = 1f;i = points.Length - 4;}else{t = Mathf.Clamp01(t) * CurveCount;i = (int)t;t -= i;i *= 3;}return transform.TransformPoint(Bezier.GetPoint(points[i], points[i + 1], points[i + 2], points[i + 3], t));}public Vector3 GetVelocity(float t){int i;if (t >= 1f){t = 1f;i = points.Length - 4;}else{t = Mathf.Clamp01(t) * CurveCount;i = (int)t;t -= i;i *= 3;}return transform.TransformPoint(Bezier.GetFirstDerivative(points[i], points[i + 1], points[i + 2], points[i + 3], t)) - transform.position;}public Vector3 GetDirection(float t){return GetVelocity(t).normalized;}public void AddCurve(){Vector3 point = points[points.Length - 1];Array.Resize(ref points, points.Length + 3);point.x += 1f;points[points.Length - 3] = point;point.x += 1f;points[points.Length - 2] = point;point.x += 1f;points[points.Length - 1] = point;Array.Resize(ref modes, modes.Length + 1);modes[modes.Length - 1] = modes[modes.Length - 2];EnforceMode(points.Length - 4);if (loop){points[points.Length - 1] = points[0];modes[modes.Length - 1] = modes[0];EnforceMode(0);}}public void Reset(){points = new Vector3[] {new Vector3(1f, 0f, 0f),new Vector3(2f, 0f, 0f),new Vector3(3f, 0f, 0f),new Vector3(4f, 0f, 0f)};modes = new BezierControlPointMode[] {BezierControlPointMode.Free,BezierControlPointMode.Free};}
}public enum BezierControlPointMode
{Free,Aligned,Mirrored
}