Method GetRotationFromTo

Source/Engine/Core/Math/Quaternion.cpp:406–454

}

void Quaternion::GetRotationFromTo(const Float3& from, const Float3& to, Quaternion& result, const Float3& fallbackAxis)
{
    // Based on Stan Melax's article in Game Programming Gems

    Float3 v0 = from;
    Float3 v1 = to;
    v0.Normalize();
    v1.Normalize();

    // If dot == 1, vectors are the same
    const float d = Float3::Dot(v0, v1);
    if (d >= 1.0f)
    {
        result = Identity;
        return;
    }

    if (d < 1e-6f - 1.0f)
    {
        if (fallbackAxis != Float3::Zero)
        {
            // Rotate 180 degrees about the fallback axis
            RotationAxis(fallbackAxis, PI, result);
        }
        else
        {
            // Generate an axis
            Float3 axis = Float3::Cross(Float3::UnitX, from);
            if (axis.LengthSquared() < ZeroTolerance) // Pick another if colinear
                axis = Float3::Cross(Float3::UnitY, from);
            axis.Normalize();
            RotationAxis(axis, PI, result);
        }
    }
    else
    {
        const float s = Math::Sqrt((1 + d) * 2);
        const float invS = 1 / s;

        Float3 c;
        Float3::Cross(v0, v1, c);

        result.X = c.X * invS;
        result.Y = c.Y * invS;
        result.Z = c.Z * invS;
        result.W = s * 0.5f;
        result.Normalize();
    }
}

void Quaternion::FindBetween(const Float3& from, const Float3& to, Quaternion& result)
{