两节骨骼 IK 够不到目标时，先保住骨长

u = T / d
r = clamp(d, |a-b|, a+b)
E = r * u
x = (a*a - b*b + r*r) / (2*r)
h = sqrt(max(0, a*a - x*x))
J = x*u + bend*h*(-u.y, u.x)

public readonly record struct Point(double X, double Y)
{
    public double Length => Math.Sqrt(X * X + Y * Y);
    public static Point operator +(Point a, Point b) => new(a.X + b.X, a.Y + b.Y);
    public static Point operator -(Point a, Point b) => new(a.X - b.X, a.Y - b.Y);
    public static Point operator *(Point a, double s) => new(a.X * s, a.Y * s);
}

public readonly record struct IkResult(Point Joint, Point End, bool Clamped);

public static class TwoBoneIk
{
    public static IkResult Solve(double upper, double lower, Point target, int bend)
    {
        // 输入位于根节点为原点的平面，长度单位保持一致。
        if (!double.IsFinite(upper) || !double.IsFinite(lower) ||
            upper < 1e-3 || lower < 1e-3 || upper > 1e3 || lower > 1e3)
            throw new ArgumentOutOfRangeException(nameof(upper));
        if (!double.IsFinite(target.X) || !double.IsFinite(target.Y) ||
            Math.Abs(target.X) > 1e4 || Math.Abs(target.Y) > 1e4)
            throw new ArgumentOutOfRangeException(nameof(target));
        if (bend != 1 && bend != -1)
            throw new ArgumentOutOfRangeException(nameof(bend));
        double distance = target.Length;
        if (distance < 1e-6)
            throw new ArgumentException("目标过近，无法按当前合同确定朝向", nameof(target));
        Point forward = target * (1 / distance);
        Point side = new(-forward.Y, forward.X);
        double radius = Math.Clamp(distance, Math.Abs(upper - lower), upper + lower);
        double along = (upper * upper - lower * lower + radius * radius) / (2 * radius);
        // 夹紧只吸收可达三角形边界的浮点舍入。
        double height = Math.Sqrt(Math.Max(0, upper * upper - along * along));
        Point joint = forward * along + side * (bend * height);
        return new(joint, forward * radius, radius != distance);
    }
}

double d = 4;
double along = 2 * Math.Clamp((4 + 16 - 1) / (2.0 * 2 * d), -1, 1);
double wrongLower = (new Point(d, 0) - new Point(along, 0)).Length;
if (wrongLower != 2) throw new Exception("反例未复现");
var fixedPose = TwoBoneIk.Solve(2, 1, new Point(4, 0), 1);
if (Math.Abs((fixedPose.End - fixedPose.Joint).Length - 1) > 1e-7)
    throw new Exception("第二段骨长发生变化");

dotnet build "$LAB_DIR/TwoBoneIkLab.csproj" -c Release
dotnet run --project "$LAB_DIR/TwoBoneIkLab.csproj" -c Release --no-build

build exit=0 warnings=0 errors=0 elapsed=00:00:07.80
run exit=0 passed=14 failed=0 skipped=0
assertion_duration_ms=43.6033
sweep_samples=12960 max_length_error=3.410605131648481E-13
normal joint=(1.2,1.6) end=(2,1) clamped=false
far joint=(2,0) end=(3,0) clamped=true
near joint=(2,0) end=(1,0) clamped=true
cosineOnlyLowerLength=2