动画旋转加权前，先把四元数放到同一半球

using System;
using System.Numerics;

public readonly record struct RotationSample(Quaternion Rotation, float Weight);

public static class QuaternionBlend
{
    public static Quaternion Blend(Quaternion reference, ReadOnlySpan<RotationSample> samples)
    {
        RequireUnit(reference);
        double x = 0, y = 0, z = 0, w = 0, total = 0;
        foreach (var sample in samples)
        {
            RequireUnit(sample.Rotation);
            if (!float.IsFinite(sample.Weight) || sample.Weight < 0)
                throw new ArgumentException("Weights must be finite and nonnegative.");
            var q = sample.Rotation;
            double weight = sample.Weight;
            total += weight;
            if (Quaternion.Dot(reference, q) < 0) weight = -weight;
            x += q.X * weight;
            y += q.Y * weight;
            z += q.Z * weight;
            w += q.W * weight;
        }
        if (total == 0) throw new ArgumentException("Positive total weight required.");
        x /= total; y /= total; z /= total; w /= total;
        double length = Math.Sqrt(x * x + y * y + z * z + w * w);
        if (!double.IsFinite(length) || length < 1e-6)
            throw new ArgumentException("Degenerate rotation blend.");
        return new Quaternion((float)(x / length), (float)(y / length),
            (float)(z / length), (float)(w / length));
    }

    private static void RequireUnit(Quaternion q)
    {
        if (!float.IsFinite(q.X) || !float.IsFinite(q.Y) ||
            !float.IsFinite(q.Z) || !float.IsFinite(q.W) ||
            Math.Abs((double)q.X * q.X + (double)q.Y * q.Y +
                (double)q.Z * q.Z + (double)q.W * q.W - 1) > 1e-4)
            throw new ArgumentException("Finite unit quaternion required.");
    }
}

var q = Quaternion.CreateFromAxisAngle(Vector3.UnitZ, MathF.PI / 2);
var opposite = new Quaternion(-q.X, -q.Y, -q.Z, -q.W);
var raw = (q + opposite) * 0.5f;
var corrected = QuaternionBlend.Blend(q, [new(q, .5f), new(opposite, .5f)]);
if (raw.LengthSquared() != 0 ||
    Vector3.Distance(Vector3.Transform(Vector3.UnitX, corrected), Vector3.UnitY) > 1e-5)
    throw new Exception("Antipodal regression failed.");

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

raw_length_squared=0.000000
corrected_rotated_x=0.000000,1.000000,0.000000
t=0.00 nlerp_degrees=0.000000 slerp_degrees=0.000000
t=0.25 nlerp_degrees=27.795773 slerp_degrees=30.000000
t=0.50 nlerp_degrees=60.000000 slerp_degrees=60.000000
t=0.75 nlerp_degrees=92.204229 slerp_degrees=90.000000
t=1.00 nlerp_degrees=120.000006 slerp_degrees=120.000000
passed=12 failed=0 skipped=0 cases=693 elapsed_ms=46.745