三次贝塞尔曲线的弧长始终为零 [英] Cubic bezier curve arc length is always zero

问题描述

我编写了以下代码来计算三次贝塞尔曲线的长度.我的想法来自计算三次贝塞尔曲线的弧长，曲线长度.为什么不起作用?.问题在于它总是产生零长度.

I've written the following code to calculate the length of a cubic bezier curve. I got the idea from Calculate the arclength, curve length of a cubic bezier curve. Why is not working?. The problem is it always produces a length of zero.

public Vector2 SegmentAtPoint(int segmentIndex, float t)
{
    t = Mathf.Clamp01(t);
    float oneMinusT = 1f - t;

    return
        oneMinusT * oneMinusT * oneMinusT * points[segmentIndex * 3] + 
        3f * oneMinusT * oneMinusT * t * points[segmentIndex * 3 + 1] +
        3f * oneMinusT * t * t * points[segmentIndex * 3 + 2] +
        t * t * t * points[segmentIndex * 3 + 3];

}

public float SegmentLength(int segmentIndex)    {
    var steps = 10;
    var t = 1 / steps;
    var sumArc = 0.0f;
    var j = 0.0f;
    var a = new Vector2(0.0f, 0.0f);
    var b = points[segmentIndex * 3];

    var dX = 0.0f;
    var dY = 0.0f;
    var dS = 0.0f;

    for (int i = 0; i < steps; j = j + t)
    {
        a = SegmentAtPoint(segmentIndex, j);

        dX = a.x - b.x;
        dY = a.y - b.y;
        dS = Mathf.Sqrt((dX * dX) + (dY * dY));

        sumArc = sumArc + dS;
        b.x = a.x;
        b.y = a.y;
        i++;
    }

    return sumArc;

}

推荐答案

代码var t = 1 / steps;使还请注意，j = j + t在每个循环后之后执行，因此在第一次迭代时j==0

Also note that j = j + t is executed after every loop, so at the first iteration j==0

此缺陷会导致这样的问题:在第一次迭代中，b和a都相等，因为j仍然保持= 0.因此，您可以按以下间隔计算段长度:0-0, 0-0.1, 0.1-0.2...0.7-0.8,0.8-0.9-忽略0.9-1.0间隔

This flaw causes such problem: both b and a are equal at the first iteration because j still remains =0. So you calculate segment lengths on intervals: 0-0, 0-0.1, 0.1-0.2...0.7-0.8,0.8-0.9 - ignoring 0.9-1.0 interval

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