【转】Graphics.DrawCurve的算法

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();
        }
    }

测试方法

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));
    }
}