/// <summary>
/// 平面上に分布する点集合が与えられたとき、その点集合が作る多角形の情報を返す
/// 1. 頂点index (originから見て反時計回り)
/// 2. 法線ベクトル
/// 3. 中心座標
/// </summary>
/// <param name="points"></param>
/// <returns></returns>
public static (int[] Indices, V3d Center, V3d Norm) PolygonInfo(IEnumerable <V3d> points, V3d origin)
{
var center = new V3d(points.Average(p => p.X), points.Average(p => p.Y), points.Average(p => p.Z));
var prm = Geometriy.GetPlaneEquationFromPoints(points.Select(p => p.ToVector3DBase()));
var norm = new V3d(prm[0], prm[1], prm[2]);
if (V3d.Dot(norm, (center - origin)) < 0)
{
norm = -norm;
}
//座標変換 (XY平面に投影)
var rot = CreateRotationToZ(norm);
var vXY = points.Select(p => p - center).Select(p => new V2d(rot.M11 * p.X + rot.M12 * p.Y + rot.M13 * p.Z, rot.M21 * p.X + rot.M22 * p.Y + rot.M23 * p.Z)).ToList();
int i = vXY.FindIndex(p => p.LengthSquared == vXY.Max(q => q.LengthSquared));//原点から最も距離の遠い点を選ぶ
//もう一つ点を選び、直線の方程式を産出
List <int> iList = new List <int>(new[] { i });
do
{
for (int j = 0; j < vXY.Count; j++)
{
if (j != i)
{
var V = new V2d(vXY[j].Y - vXY[i].Y, vXY[i].X - vXY[j].X);
var c = vXY[j].X * vXY[i].Y - vXY[i].X * vXY[j].Y;
if (vXY.All(p => V2d.Dot(p, V) + c <= Th))
{
iList.Add(j);
i = j;
break;
}
}
}
} while (i != iList[0]);
return(iList.ToArray(), center, norm);
}
