同一姿态混合后消失：四元数加权前必须对齐半球

using System.Numerics;

public static class QuaternionBlend
{
    public static Quaternion Blend(Quaternion reference, Quaternion[] rotations, float[] weights)
    {
        Validate(reference);
        if (rotations.Length == 0 || rotations.Length != weights.Length)
            throw new ArgumentException("Mismatched blend inputs");
        reference = Quaternion.Normalize(reference);
        double total = 0;
        for (int i = 0; i < weights.Length; i++)
        {
            Validate(rotations[i]);
            if (!float.IsFinite(weights[i]) || weights[i] < 0)
                throw new ArgumentOutOfRangeException(nameof(weights));
            total += weights[i];
        }
        if (total <= 0) throw new ArgumentException("No active weight");
        Quaternion sum = new(0, 0, 0, 0);
        for (int i = 0; i < rotations.Length; i++)
        {
            Quaternion q = Quaternion.Normalize(rotations[i]);
            float dot = Quaternion.Dot(reference, q);
            if (MathF.Abs(dot) <= 1e-6f)
                throw new ArgumentException("Ambiguous hemisphere boundary");
            if (dot < 0) q = -q;
            sum += q * (float)(weights[i] / total);
        }
        if (sum.LengthSquared() <= 1e-12f)
            throw new ArgumentException("Degenerate weighted rotation");
        return Quaternion.Normalize(sum);
    }

    public static Quaternion UnalignedSum(Quaternion[] rotations, float[] weights)
    {
        Quaternion sum = new(0, 0, 0, 0);
        for (int i = 0; i < rotations.Length; i++) sum += rotations[i] * weights[i];
        return sum;
    }

    private static void Validate(Quaternion q)
    {
        float length = q.LengthSquared();
        if (!float.IsFinite(q.X) || !float.IsFinite(q.Y) || !float.IsFinite(q.Z) ||
            !float.IsFinite(q.W) || !float.IsFinite(length) || length <= 1e-12f)
            throw new ArgumentOutOfRangeException(nameof(q));
    }
}

{
  "passed": 23,
  "failed": 0,
  "skipped": 0,
  "samples": 10000,
  "unaligned_length": 0,
  "aligned_rotation": [0, 0, 0.5, 0.8660254],
  "rotated_x": [0.5, 0.8660254, 0],
  "max_component_error": 0
}

dotnet build $WORK_DIR/QuaternionBlendLab.csproj -c Release
dotnet run --project $WORK_DIR/QuaternionBlendLab.csproj -c Release --no-build