/// <summary>
/// For each set of three adjacent points A, B, C,
/// find the dot product AB · BC. If the sign of
/// all the dot products is the same, the angles
/// are all positive or negative (depending on the
/// order in which we visit them) so the polygon
/// is convex.
/// </summary>
/// <returns>
/// Return true if the polygon is convex.
/// </returns>
/// <acknowledgment>
/// http://csharphelper.com/blog/2014/07/determine-whether-a-polygon-is-convex-in-c/
/// </acknowledgment>
public static bool IsConvex(PolygonContour2D polygon)
{
var got_negative = false;
var got_positive = false;
var num_points = polygon.Points.Count;
int B, C;
for (var A = 0; A < num_points; A++)
{
B = (A + 1) % num_points;
C = (B + 1) % num_points;
var cross_product = CrossProduct3Vector2DTests.CrossProductVector2D(
polygon.Points[A].X, polygon.Points[A].Y,
polygon.Points[B].X, polygon.Points[B].Y,
polygon.Points[C].X, polygon.Points[C].Y);
if (cross_product < 0)
{
got_negative = true;
}
else
{
got_positive |= cross_product > 0;
}
if (got_negative && got_positive)
{
return(false);
}
}
// If we got this far, the polygon is convex.
return(true);
}
/// <summary>
/// The forms ear.
/// </summary>
/// <param name="polygon">The polygon.</param>
/// <param name="a">The a.</param>
/// <param name="b">The b.</param>
/// <param name="c">The c.</param>
/// <returns>The <see cref="bool"/>. Return true if the three points form an ear.</returns>
/// <acknowledgment>
/// http://csharphelper.com/blog/2014/07/triangulate-a-polygon-in-c/
/// </acknowledgment>
public static bool FormsEar(PolygonContour2D polygon, int a, int b, int c)
{
// See if the angle ABC is concave.
if (Angle3Vector2DTests.AngleVector(
polygon.Points[a].X, polygon.Points[a].Y,
polygon.Points[b].X, polygon.Points[b].Y,
polygon.Points[c].X, polygon.Points[c].Y) > 0)
{
// This is a concave corner so the triangle
// cannot be an ear.
return(false);
}
// Make the triangle A, B, C.
var triangle = new Triangle2D(polygon.Points[a], polygon.Points[b], polygon.Points[c]);
// Check the other points to see
// if they lie in triangle A, B, C.
for (var i = 0; i < polygon.Points.Count; i++)
{
if ((i != a) && (i != b) && (i != c) && triangle.Contains(polygon.Points[i]))
{
// This point is in the triangle
// do this is not an ear.
return(false);
}
}
// This is an ear.
return(true);
}
/// <summary>
/// Find the indexes of three points that form an "ear."
/// </summary>
/// <param name="polygon"></param>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <returns></returns>
/// <acknowledgment>
/// http://csharphelper.com/blog/2014/07/triangulate-a-polygon-in-c/
/// </acknowledgment>
public static Triangle2D FindEar(PolygonContour2D polygon, ref int a, ref int b, ref int c)
{
var num_points = polygon.Points.Count;
for (a = 0; a < num_points; a++)
{
b = (a + 1) % num_points;
c = (b + 1) % num_points;
if (FormsEar(polygon, a, b, c))
{
return(new Triangle2D(polygon.Points[a], polygon.Points[b], polygon.Points[c]));
}
}
//// We should never get here because there should
//// always be at least two ears.
//Debug.Assert(false);
return(new Triangle2D());
}