Question

我一直在查看下面的代码：http://tehc0dez.blogspot.co.uk/2010/04/nice-curves-catmullrom-spline-in-c.html

/// <summary>
/// Calculates interpolated point between two points using Catmull-Rom Spline
/// </summary>
/// <remarks>
/// Points calculated exist on the spline between points two and three.
/// </remarks>/// <param name="p0">First Point</param>
/// <param name="p1">Second Point</param>
/// <param name="p2">Third Point</param>
/// <param name="p3">Fourth Point</param>
/// <param name="t">
/// Normalised distance between second and third point 
/// where the spline point will be calculated
/// </param>
/// <returns>
/// Calculated Spline Point
/// </returns>
static public PointF PointOnCurve(PointF p0, PointF p1, PointF p2, 
                                  PointF p3, float t)
{
    PointF ret = new PointF();
    float t2 = t * t;
    float t3 = t2 * t;
    ret.X = 0.5f * ((2.0f * p1.X) + (-p0.X + p2.X) * t + 
                    (2.0f * p0.X - 5.0f * p1.X + 4 * p2.X - p3.X) * t2 + 
                    (-p0.X + 3.0f * p1.X - 3.0f * p2.X + p3.X) * t3);
    ret.Y = 0.5f * ((2.0f * p1.Y) + (-p0.Y + p2.Y) * t + 
                    (2.0f * p0.Y - 5.0f * p1.Y + 4 * p2.Y - p3.Y) * t2 + 
                    (-p0.Y + 3.0f * p1.Y - 3.0f * p2.Y + p3.Y) * t3);    
    return ret;
}

我不理解的参数是t，它被描述为第二和第三点之间的归一化距离。在这种情况下，我该如何计算归一化距离？

Answer 1

有关Catmull-Rom Spline的更好解释，请查看this page，图1应该可以帮助您。

您有四个点，用于定义样条曲线。 t表示点2和点3之间的位置，应为其计算坐标。 t=0 点2，t=1 点3. t=0.5位于第2点和第3点之间。

为了在屏幕上绘制样条线，您通常要做的是让t从0到1以特定间隔运行，例如0.1。这将为您提供t = 0.1,0.2,0.3，... 0.9的点的精确坐标。您可以选择一个小间隔并为每个结果坐标绘制一个点，或者您可以选择一个更大的间隔并在两个相邻坐标之间绘制一条直线。

如何计算归一化距离？

1 个答案: