public static void GetInertia(Vector2[] vertices, out float result)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 0);
if (vertices.Length == 1)
{
result = 0;
return;
}
float denom = 0;
float numer = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; index++, v1 = v2)
{
v2 = vertices[index];
float a, b, c, d;
Vector2.Dot(ref v2, ref v2, out a);
Vector2.Dot(ref v2, ref v1, out b);
Vector2.Dot(ref v1, ref v1, out c);
Vectors2.ZCross(ref v1, ref v2, out d);
d = Math.Abs(d);
numer += d;
denom += (a + b + c) * d;
}
result = denom / (numer * 6);
}
/// <summary>
/// Calculates the area of a polygon.
/// </summary>
/// <param name="vertices">The vertices of the polygon.</param>
/// <param name="result">the area.</param>
public static void GetArea(Vector2[] vertices, out float result)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 2);
float area = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; ++index, v1 = v2)
{
v2 = vertices[index];
float temp;
Vectors2.ZCross(ref v1, ref v2, out temp);
area += temp;
}
result = Math.Abs(area * .5f);
}
/// <summary> Calculates the centroid of a polygon.</summary>
/// <param name="vertices">The vertices of the polygon.</param>
/// <param name="centroid">The centroid of a polygon.</param>
/// <remarks>This is also known as center of gravity/mass.</remarks>
public static void GetCentroid(Vector2[] vertices, out Vector2 centroid)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 2);
centroid = Vector2.Zero;
float temp;
float area = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; ++index, v1 = v2)
{
v2 = vertices[index];
Vectors2.ZCross(ref v1, ref v2, out temp);
area += temp;
centroid.X += ((v1.X + v2.X) * temp);
centroid.Y += ((v1.Y + v2.Y) * temp);
}
temp = 1 / (Math.Abs(area) * 3);
centroid.X *= temp;
centroid.Y *= temp;
}
