static float ABFComputeGradAlpha(ABFSystem sys, ABFFace f, ABFHalfEdge e)
{
ABFVertex v = e.Vertex, v1 = e.Next.Vertex, v2 = e.Next.Next.Vertex;
float deriv = (sys.Alpha[e.AngleID] - sys.Beta[e.AngleID]) * sys.Weight[e.AngleID];
deriv += sys.LambdaTriangle[f.AngleID];
if (!v.PVertex.IsBorder)
{
deriv += sys.LambdaPlanar[v.AngleID];
}
if (!v1.PVertex.IsBorder)
{
float product = ABFComputeSinProduct(sys, v1, e.AngleID);
deriv += sys.LambdaLength[v1.AngleID] * product;
}
if (!v2.PVertex.IsBorder)
{
float product = ABFComputeSinProduct(sys, v2, e.AngleID);
deriv += sys.LambdaLength[v2.AngleID] * product;
}
return(deriv);
}
/// <summary>
/// ベクトルの成す角を返す
/// </summary>
/// <param name="v1">先端1</param>
/// <param name="v2">対象点</param>
/// <param name="v3">先端2</param>
/// <returns>点v2における角度</returns>
static float ABFVectorAngle(ABFVertex v1, ABFVertex v2, ABFVertex v3)
{
V3 d1, d2;
d1 = (v1.PVertex.Position - v2.PVertex.Position);
d1.Normalize();
d2 = (v3.PVertex.Position - v2.PVertex.Position);
d2.Normalize();
var cos = d1.Dot(d2) / (d1.LengthSq() * d2.LengthSq());
return((float)Math.Acos(cos));
}
static float ABFComputeSinProduct(ABFSystem sys, ABFVertex v, int aid)
{
ABFHalfEdge e, e1, e2;
float sin1, sin2;
sin1 = sin2 = 1f;
e = v.HEdge;
do
{
e1 = e.Next;
e2 = e.Next.Next;
if (aid == e1.AngleID)
{
/* we are computing a derivative for this angle,
* so we use cos and drop the other part */
sin1 *= sys.Cosine[e1.AngleID];
sin2 = 0f;
}
else
{
sin1 *= sys.Sine[e1.AngleID];
}
if (aid == e2.AngleID)
{
/* see above */
sin1 = 0f;
sin2 *= sys.Cosine[e2.AngleID];
}
else
{
sin2 *= sys.Sine[e2.AngleID];
}
e = e.Next.Next.Pair;
} while (e != v.HEdge);
return(sin1 - sin2);
}