剑尖拖尾忽密忽疏：等距采样必须保留跨帧余量

public readonly record struct Point(double X, double Y);
public sealed record TrailResult(Point[] Samples, double Carry);

public static class TrailSampler
{
    public static TrailResult Sample(IReadOnlyList<Point> path,
        double spacing, double carry = 0, int maxSamples = 10000)
    {
        if (!double.IsFinite(spacing) || spacing <= 0 ||
            !double.IsFinite(carry) || carry < 0 || carry >= spacing ||
            maxSamples < 0) throw new ArgumentOutOfRangeException();
        if (path.Count == 0) throw new ArgumentException("Empty path");
        foreach (Point p in path)
            if (!double.IsFinite(p.X) || !double.IsFinite(p.Y))
                throw new ArgumentException("Invalid point");
        List<Point> output = new();
        for (int i = 1; i < path.Count; i++)
        {
            Point a = path[i - 1], b = path[i];
            double dx = b.X - a.X, dy = b.Y - a.Y;
            double length = Math.Sqrt(dx * dx + dy * dy);
            if (!double.IsFinite(length)) throw new ArithmeticException();
            if (length == 0) continue;
            double tolerance = spacing * 1e-12;
            double next = spacing - carry;
            while (next <= length + tolerance)
            {
                if (output.Count == maxSamples)
                    throw new InvalidOperationException("Sample budget exceeded");
                double t = Math.Min(next / length, 1);
                output.Add(new(a.X + t * dx, a.Y + t * dy));
                double advanced = next + spacing;
                if (advanced == next || !double.IsFinite(advanced))
                    throw new ArithmeticException();
                next = advanced;
            }
            carry = Math.Max(0, length - (next - spacing));
            if (carry < 0 || carry >= spacing)
                throw new ArithmeticException("Residual lost precision");
        }
        return new(output.ToArray(), carry);
    }
}

日期：2026-10-19；环境：.NET SDK 9.0.202，Release
工作目录：$WORK_DIR
 dotnet build .tmp/daily-labs/2026-10-19-2000/TrailLab.csproj -c Release
 exit=0; warnings=0; errors=0; elapsed=5.50s
 dotnet run --project .tmp/daily-labs/2026-10-19-2000/TrailLab.csproj -c Release --no-build
 exit=0; passed=23; failed=0; skipped=0; elapsed=66.1686ms
 partitions=200; samples_per_straight_path=64
 fixed_samples=[(0.5,0),(1,0),(1.2,0.3),(1.2,0.8),(1.2,1.3)]
 carry≈0.3; reset_per_segment_count=4
 corner_chord≈0.360555; corner_arc=0.5
 missing_corner_length=2.0; missing_corner_count=4