旋转后的 Mesh 包围盒：只变换最小点和最大点会漏掉角点

namespace BoundsLab;

public readonly record struct V(double X, double Y, double Z)
{
    public bool Finite => double.IsFinite(X) && double.IsFinite(Y) && double.IsFinite(Z);
    public static V operator +(V a, V b) => new(a.X+b.X, a.Y+b.Y, a.Z+b.Z);
    public static V operator -(V a, V b) => new(a.X-b.X, a.Y-b.Y, a.Z-b.Z);
    public static V operator *(V a, double s) => new(a.X*s, a.Y*s, a.Z*s);
    public static V Min(V a, V b) => new(Math.Min(a.X,b.X),Math.Min(a.Y,b.Y),Math.Min(a.Z,b.Z));
    public static V Max(V a, V b) => new(Math.Max(a.X,b.X),Math.Max(a.Y,b.Y),Math.Max(a.Z,b.Z));
    public double Dot(V b) => X*b.X + Y*b.Y + Z*b.Z;
    public V Abs() => new(Math.Abs(X), Math.Abs(Y), Math.Abs(Z));
}

public readonly record struct Box(V Min, V Max);

// 行向量保存矩阵，点按列向量约定进行变换。
public readonly record struct Affine(V RowX, V RowY, V RowZ, V Translation)
{
    public V Apply(V p) => new V(RowX.Dot(p), RowY.Dot(p), RowZ.Dot(p)) + Translation;
    public bool Finite => RowX.Finite && RowY.Finite && RowZ.Finite && Translation.Finite;
}

public static class AffineBounds
{
    public static Box Transform(Box local, Affine a)
    {
        V lo = local.Min, hi = local.Max;
        if (!lo.Finite || !hi.Finite || !a.Finite ||
            lo.X > hi.X || lo.Y > hi.Y || lo.Z > hi.Z)
            throw new ArgumentException("Invalid bounds or affine transform");
        // 先减半再相加，避免同号端点相加溢出。
        V c = lo * 0.5 + hi * 0.5;
        V e = hi * 0.5 - lo * 0.5;
        V wc = a.Apply(c);
        V we = new(a.RowX.Abs().Dot(e), a.RowY.Abs().Dot(e), a.RowZ.Abs().Dot(e));
        Box world = new(wc - we, wc + we);
        if (!world.Min.Finite || !world.Max.Finite)
            throw new ArgumentException("Unrepresentable transformed bounds");
        return world;
    }
}

V p = rotation.Apply(Local.Min), q = rotation.Apply(Local.Max);
Box wrong = new(V.Min(p,q), V.Max(p,q));
V witness = rotation.Apply(new(2,-0.5,0.25));
Check(witness.X > wrong.Max.X);
Check(witness.X <= correct.Max.X + 1e-12);
Check(wrong.Max.X < 1.5 && correct.Max.X > 1.5);

cd "$LAB_ROOT"
dotnet build BoundsLab.csproj -c Release
dotnet run --project BoundsLab.csproj -c Release --no-build

build: exit=0 warnings=0 errors=0
run: exit=0
correctMaxX=1.767767 endpointMaxX=1.060660 witnessX=1.767767
passed=14 failed=0 skipped=0 samples=1807 elapsedMs=37.1372