| public static Between ( Vector2F v, Vector2F w ) : float | ||
| v | Vector2F | First vector. |
| w | Vector2F | Second vector. |
| 리턴 | float | |
/// <summary>
/// Orthogonally projects <paramref name="v" /> onto a straight line
/// parallel to <paramref name="w" />.
/// </summary>
/// <remarks>
/// See https://en.wikipedia.org/wiki/Vector_projection for details.
/// </remarks>
/// <param name="v">Vector to project.</param>
/// <param name="w">Vector to project onto.</param>
/// <returns>Projected vector.</returns>
public static Vector2F Project(Vector2F v, Vector2F w)
{
return(v.Length * Angle.Cos(Angle.Between(v, w)) * w.Normalize());
}
/// <summary>
/// Decomposes this polygon into triangles.
/// </summary>
/// <remarks>
/// See http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf for details.
/// </remarks>
/// <returns>Triangles composing this polygon.</returns>
public List <Polygon2F> Triangulate()
{
var triangles = new List <Polygon2F>();
var vertices = new List <Vector2F>(this.points);
if (this.IsClockwise())
{
vertices.Reverse();
}
// Remove ears one by one.
var index = 0;
while (vertices.Count > 3)
{
var remainingPolygon = new Polygon2F(vertices);
// Get three consecutive vertices.
var u = vertices[(index - 1 + vertices.Count) % vertices.Count];
var v = vertices[index % vertices.Count];
var w = vertices[(index + 1) % vertices.Count];
// Check if middle vertex is convex.
var vu = u - v;
var vw = w - v;
var angle = Angle.Between(vw, vu);
var convex = angle < Math.PI;
if (!convex)
{
++index;
continue;
}
// Check if line segment lies completely inside the polygon.
var uw = new LineSegment2F(u, w);
if (!remainingPolygon.Contains(uw))
{
++index;
continue;
}
// Check if no other vertices of the polygon are contained in the triangle.
var triangle =
new Polygon2F(new[] { new Vector2F(u.X, u.Y), new Vector2F(v.X, v.Y), new Vector2F(w.X, w.Y) });
var containsOtherVertex =
vertices.Where(other => other != u && other != v && other != w)
.Any(other => triangle.Contains(other));
if (containsOtherVertex)
{
++index;
continue;
}
// Remove ear.
vertices.Remove(v);
triangles.Add(triangle);
}
// Add last triangle.
triangles.Add(new Polygon2F(vertices));
return(triangles);
}
