曲线绘制

[anhuihulei]

已知一条曲线上的n个点（n>= 3）,现在需要用程序将这条曲线平滑地画出来，并能求出每一点的切矢方向；（现在我只能用二次贝塞尔实现3点的曲线，点大于3时二次曲线如何组合？）；各位朋友能否给我一个解决此问题的办法，这条曲线可以是贝塞尔（2次或3次）、也可以是其他各种样条曲线，若能给一个vc/c#的算法代码帮我我解决此问题，将十分感激；加分很俗气，但一定会加~

[lslsyqyq]

贝塞尔 nurbs都可以 不过我不会

[fengbingchun]

这里有个matlab实现的，效果不错，很方便转成c++或c# http://blog.csdn.net/fengbingchun/article/details/6894692

[潇潇雨云]

using UnityEngine; using System.Collections.Generic; /** Class for representing a Bezier path, and methods for getting suitable points to draw the curve with line segments. */ public class BezierPath { private const int SEGMENTS_PER_CURVE = 10; private const float MINIMUM_SQR_DISTANCE = 0.01f; // This corresponds to about 172 degrees, 8 degrees from a traight line private const float DIVISION_THRESHOLD = -0.99f; private List<Vector3> controlPoints; private int curveCount; //how many bezier curves in this path? /** Constructs a new empty Bezier curve. Use one of these methods to add points: SetControlPoints, Interpolate, SamplePoints. */ public BezierPath() { controlPoints = new List<Vector3>(); } /** Sets the control points of this Bezier path. Points 0-3 forms the first Bezier curve, points 3-6 forms the second curve, etc. */ public void SetControlPoints(List<Vector3> newControlPoints) { controlPoints.Clear(); controlPoints.AddRange(newControlPoints); curveCount = (controlPoints.Count - 1) / 3; } /** Returns the control points for this Bezier curve. */ public List<Vector3> GetControlPoints() { return controlPoints; } /** Calculates a Bezier interpolated path for the given points. */ public void Interpolate(List<Vector3> segmentPoints, float scale) { controlPoints.Clear(); if (segmentPoints.Count < 2) { return; } for (int i = 0; i < segmentPoints.Count; i++) { if (i == 0) // is first { Vector3 p1 = segmentPoints[i]; Vector3 p2 = segmentPoints[i + 1]; Vector3 tangent = (p2 - p1); Vector3 q1 = p1 + scale * tangent; controlPoints.Add(p1); controlPoints.Add(q1); } else if (i == segmentPoints.Count - 1) //last { Vector3 p0 = segmentPoints[i - 1]; Vector3 p1 = segmentPoints[i]; Vector3 tangent = (p1 - p0); Vector3 q0 = p1 - scale * tangent; controlPoints.Add(q0); controlPoints.Add(p1); } else { Vector3 p0 = segmentPoints[i - 1]; Vector3 p1 = segmentPoints[i]; Vector3 p2 = segmentPoints[i + 1]; Vector3 tangent = (p2 - p0).normalized; Vector3 q0 = p1 - scale * tangent * (p1 - p0).magnitude; Vector3 q1 = p1 + scale * tangent * (p2 - p1).magnitude; controlPoints.Add(q0); controlPoints.Add(p1); controlPoints.Add(q1); } } curveCount = (controlPoints.Count - 1) / 3; } /** Sample the given points as a Bezier path. */ public void SamplePoints(List<Vector3> sourcePoints, float minSqrDistance, float maxSqrDistance, float scale) { if(sourcePoints.Count < 2) { return; } Stack<Vector3> samplePoints = new Stack<Vector3>(); samplePoints.Push(sourcePoints[0]); Vector3 potentialSamplePoint = sourcePoints[1]; int i = 2; for (i = 2; i < sourcePoints.Count; i++ ) { if( ((potentialSamplePoint - sourcePoints[i]).sqrMagnitude > minSqrDistance) && ((samplePoints.Peek() - sourcePoints[i]).sqrMagnitude > maxSqrDistance)) { samplePoints.Push(potentialSamplePoint); } potentialSamplePoint = sourcePoints[i]; } //now handle last bit of curve Vector3 p1 = samplePoints.Pop(); //last sample point Vector3 p0 = samplePoints.Peek(); //second last sample point Vector3 tangent = (p0 - potentialSamplePoint).normalized; float d2 = (potentialSamplePoint - p1).magnitude; float d1 = (p1 - p0).magnitude; p1 = p1 + tangent * ((d1 - d2)/2); samplePoints.Push(p1); samplePoints.Push(potentialSamplePoint); Interpolate(new List<Vector3>(samplePoints), scale); } /** Caluclates a point on the path. @param curveIndex The index of the curve that the point is on. For example, the second curve (index 1) is the curve with controlpoints 3, 4, 5, and 6. @param t The paramater indicating where on the curve the point is. 0 corresponds to the "left" point, 1 corresponds to the "right" end point. */ public Vector3 CalculateBezierPoint(int curveIndex, float t) { int nodeIndex = curveIndex * 3; Vector3 p0 = controlPoints[nodeIndex]; Vector3 p1 = controlPoints[nodeIndex + 1]; Vector3 p2 = controlPoints[nodeIndex + 2]; Vector3 p3 = controlPoints[nodeIndex + 3]; return CalculateBezierPoint(t, p0, p1, p2, p3); } /** Gets the drawing points. This implementation simply calculates a certain number of points per curve. */ public List<Vector3> GetDrawingPoints0() { List<Vector3> drawingPoints = new List<Vector3>(); for (int curveIndex = 0; curveIndex < curveCount; curveIndex++) { if (curveIndex == 0) //Only do this for the first end point. //When i != 0, this coincides with the //end point of the previous segment, { drawingPoints.Add(CalculateBezierPoint(curveIndex, 0)); } for (int j = 1; j <= SEGMENTS_PER_CURVE; j++) { float t = j / (float)SEGMENTS_PER_CURVE; drawingPoints.Add(CalculateBezierPoint(curveIndex, t)); } } return drawingPoints; } /** Gets the drawing points. This implementation simply calculates a certain number of points per curve. This is a lsightly different inplementation from the one above. */ public List<Vector3> GetDrawingPoints1() { List<Vector3> drawingPoints = new List<Vector3>(); for (int i = 0; i < controlPoints.Count - 3; i += 3) { Vector3 p0 = controlPoints[i]; Vector3 p1 = controlPoints[i + 1]; Vector3 p2 = controlPoints[i + 2]; Vector3 p3 = controlPoints[i + 3]; if (i == 0) //only do this for the first end point. When i != 0, this coincides with the end point of the previous segment, { drawingPoints.Add(CalculateBezierPoint(0, p0, p1, p2, p3)); } for (int j = 1; j <= SEGMENTS_PER_CURVE; j++) { float t = j / (float)SEGMENTS_PER_CURVE; drawingPoints.Add(CalculateBezierPoint(t, p0, p1, p2, p3)); } } return drawingPoints; } /** This gets the drawing points of a bezier curve, using recursive division, which results in less points for the same accuracy as the above implementation. */ public List<Vector3> GetDrawingPoints2() { List<Vector3> drawingPoints = new List<Vector3>(); for (int curveIndex = 0; curveIndex < curveCount; curveIndex++) { List<Vector3> bezierCurveDrawingPoints = FindDrawingPoints(curveIndex); if (curveIndex != 0) { //remove the fist point, as it coincides with the last point of the previous Bezier curve. bezierCurveDrawingPoints.RemoveAt(0); } drawingPoints.AddRange(bezierCurveDrawingPoints); } return drawingPoints; } List<Vector3> FindDrawingPoints(int curveIndex) { List<Vector3> pointList = new List<Vector3>(); Vector3 left = CalculateBezierPoint(curveIndex, 0); Vector3 right = CalculateBezierPoint(curveIndex, 1); pointList.Add(left); pointList.Add(right); FindDrawingPoints(curveIndex, 0, 1, pointList, 1); return pointList; } /** @returns the number of points added. */ int FindDrawingPoints(int curveIndex, float t0, float t1, List<Vector3> pointList, int insertionIndex) { Vector3 left = CalculateBezierPoint(curveIndex, t0); Vector3 right = CalculateBezierPoint(curveIndex, t1); if ((left - right).sqrMagnitude < MINIMUM_SQR_DISTANCE) { return 0; } float tMid = (t0 + t1) / 2; Vector3 mid = CalculateBezierPoint(curveIndex, tMid); Vector3 leftDirection = (left - mid).normalized; Vector3 rightDirection = (right - mid).normalized; if (Vector3.Dot(leftDirection, rightDirection) > DIVISION_THRESHOLD || Mathf.Abs(tMid - 0.5f) < 0.0001f) { int pointsAddedCount = 0; pointsAddedCount += FindDrawingPoints(curveIndex, t0, tMid, pointList, insertionIndex); pointList.Insert(insertionIndex + pointsAddedCount, mid); pointsAddedCount++; pointsAddedCount += FindDrawingPoints(curveIndex, tMid, t1, pointList, insertionIndex + pointsAddedCount); return pointsAddedCount; } return 0; } /** Caluclates a point on the Bezier curve represented with the four controlpoints given. */ private Vector3 CalculateBezierPoint(float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3) { float u = 1 - t; float tt = t * t; float uu = u * u; float uuu = uu * u; float ttt = tt * t; Vector3 p = uuu * p0; //first term p += 3 * uu * t * p1; //second term p += 3 * u * tt * p2; //third term p += ttt * p3; //fourth term return p; } } c#的

[worldy]

使用PolyBezier函数

[anhuihulei]

引用 4 楼 worldy 的回复:

使用PolyBezier函数

要是知道控制点 我就不需要求找高手了

引用 2 楼 fengbingchun 的回复:

这里有个matlab实现的，效果不错，很方便转成c++或c# http://blog.csdn.net/fengbingchun/article/details/6894692

能否贴出效果先瞅瞅 潇洒雨云 朋友： 我用你的方法试后，在调用时用sample函数对已知的点序列进行抽样，但运行到此函数内部报错，已知点vector3的x、y为屏幕坐标，z传0，报错是“检测到无效代码”（ ((potentialSamplePoint - sourcePoints[i]).sqrMagnitude > minSqrDistance) &&） 这是什么原因呢，是我的unityengine 版本不对，还是 函数传入的参数不对，若是参数不对 又该怎么传参数调用方法，返回点序列的draw函数你那也有0、1、2这 3个，他们有什么区别吗？ 希望你能再次帮助我，谢谢了

[andyboliu]

Mschart控件可以根据数据画曲线，我正在看这方面的资料，不知道对于你的问题是否适用？

[libralibra]

贝塞尔曲线不行,阶次跟点数有关 nurbs可以,阶次跟点数无关,但是你需要找根据型值点反求控制点的算法(为了兼顾效率与性能,一般使用三次nurbs曲线)