public static bool operator ==(Vector3d v0, Vector3d v1)
{
return
(Tolerance.IsIgnorable(v0.X - v1.X) &&
Tolerance.IsIgnorable(v0.Y - v1.Y) &&
Tolerance.IsIgnorable(v0.Z - v1.Z));
}
public void Normalize()
{
var norm = Norm;
if (Tolerance.IsIgnorable(norm))
{
return;
}
X = X / norm;
Y = Y / norm;
}
/// <summary>
/// 点が平面上に乗るかどうかを判定します
/// </summary>
/// <param name="point"></param>
/// <returns>true -> 平面上に乗る, false -> 平面上に乗らない</returns>
public bool IsOn(Vector3d point)
{
// 直線と平面との交点計算
var line = new Line(point, Normal);
var intersection = line.GetIntersection(this);
if (!intersection.HasValue)
{
return(false);
}
// 交点と入力点との距離計算
return(Tolerance.IsIgnorable((intersection.Value - point).Norm));
}
/// <summary>
/// 点が多角形の境界or内部に含まれるかを判定します
/// [契約] 点は多角形が成す平面上に乗ると前提します
/// </summary>
/// <param name="point">点</param>
/// <returns></returns>
public bool IsInOrOn(Vector3d point)
{
// 角度の総和法
// \sum_{i} theta_{i} = 2 \pi => in
// \sum_{i} theta_{i} = 0 => out
// Procedure
// (1) 各頂点へのベクトルの計算
// (2) 各角度の計算
// (1)
var vectors = new Vector3d[Points.Length];
for (var i = 0; i < Points.Length; ++i)
{
vectors[i] = Points[i] - point;
if (Tolerance.IsIgnorable(vectors[i].Norm))
{
return(true);
}
}
// (2)
// (r_{i} | r_{i + 1}) = |r_{i}| |r_{i + 1}| cos theta
// theta は鋭角の方
var normal = this.Normal;
var sumAngle = 0d;
for (var i = 0; i < Points.Length; ++i)
{
var i_next = (i + 1) % Points.Length;
var angle =
Math.Acos(
Vector3d.DotProduct(vectors[i], vectors[i_next]) /
(vectors[i].Norm * vectors[i_next].Norm));
// vectors[ i ]×vectors[ i_next ] と normal の方向を比較し，
// 鋭角となる向きが逆行するかどうかを判定
if (Vector3d.ScalarTripletProduct(normal, vectors[i], vectors[i_next]) < 0)
{
angle = -angle;
}
sumAngle += angle;
}
var isIn = sumAngle > Math.PI;
return(isIn);
}
// Norm( v1 )^{2} Norm( v2 )^{2} - (v1 | v2)^{2} が 0 なら平行
public bool AreParallel(Vector2d v)
{
return(Tolerance.IsIgnorable(
(Norm * Norm) * (v.Norm * v.Norm) -
DotProduct(this, v) * DotProduct(this, v)));
}
// (v1 | v2) が 0 なら直角 public bool AreOrthogonal(Vector2d v) => Tolerance.IsIgnorable(DotProduct(this, v));
public static bool operator ==(Vector2d v0, Vector2d v1) => Tolerance.IsIgnorable(v0.X - v1.X) && Tolerance.IsIgnorable(v0.Y - v1.Y);
