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public static class Spline
{
[System.Diagnostics.DebuggerDisplay("({X},{Y})")]
public partial struct Vec2
{
public float X, Y;
public Vec2(float x, float y) {this.X = x; this.Y = y;}
public static implicit operator PointF(Vec2 v) { return new PointF(v.X, v.Y); }
public static implicit operator Vec2(PointF p) { return new Vec2(p.X, p.Y); }
public static Vec2 operator +(Vec2 v1, Vec2 v2) { return new Vec2(v1.X + v2.X, v1.Y + v2.Y); }
public static Vec2 operator -(Vec2 v1, Vec2 v2) { return new Vec2(v1.X - v2.X, v1.Y - v2.Y); }
public static Vec2 operator *(Vec2 v, float f) { return new Vec2(v.X * f, v.Y * f); }
public static Vec2 operator /(Vec2 v, float f) { return new Vec2(v.X / f, v.Y / f); }
}
/// <summary>
/// '贝塞尔'内插。结果不包括头尾点
/// </summary>
public static PointF[] InterpolateBezier(PointF p0, PointF p1, PointF p2, PointF p3, int samples)
{
PointF[] result = new PointF[samples];
for (int i = 0; i < samples; i++)
{
float t = (i + 1) / (samples + 1.0f);
result[i] =
(Vec2)p0 * (1 - t) * (1 - t) * (1 - t) +
(Vec2)p1 * (3 * (1 - t) * (1 - t) * t) +
(Vec2)p2 * (3 * (1 - t) * t * t) +
(Vec2)p3 * (t * t * t);
}
return result;
}
public static PointF[] InterpolateCardinalSpline(PointF p0, PointF p1, PointF p2, PointF p3, int samples)
{
const float tension = 0.5f;
Vec2 u = ((Vec2)p2 - (Vec2)p0) * (tension / 3) + p1;
Vec2 v = ((Vec2)p1 - (Vec2)p3) * (tension / 3) + p2;
return InterpolateBezier(p1, u, v, p2, samples);
}
/// <summary>
/// '基数样条'内插法。 points为通过点,samplesInSegment为两个样本点之间的内插数量。
/// </summary>
public static PointF[] CardinalSpline(PointF[] points, int samplesInSegment)
{
List<PointF> result = new List<PointF>();
for (int i = 0; i < points.Length - 1; i++)
{
result.Add(points[i]);
result.AddRange( InterpolateCardinalSpline(
points[Math.Max(i-1, 0)],
points[i],
points[i+1],
points[Math.Min(i+2, points.Length-1)],
samplesInSegment
));
}
result.Add(points[points.Length - 1]);
return result.ToArray();
}
}
public partial class Form1 : Form
{
protected override void OnPaint(PaintEventArgs e)
{
PointF[] ps = {new PointF(50,50), new PointF(100, 80), new PointF(120, 10), new PointF(200,100)};
// 系统的Graphics.DrawCurve,桃色
e.Graphics.DrawCurve(new Pen(Brushes.PeachPuff, 5), ps);
// 自己取样,蓝色
e.Graphics.DrawLines(Pens.Blue, Spline.CardinalSpline(ps, 10));
}
}