public static void TestExtMath()
{
float a = 1f;
float b = 1f + 1e-6f;
float c = 1f + 1e-4f;
Debug.Assert(ExtMathf.Equal(a, b));
Debug.Assert(!ExtMathf.Equal(a, c));
Debug.Assert(ExtMathf.Greater(c, a));
Debug.Assert(!ExtMathf.Greater(b, a));
Debug.Assert(ExtMathf.Less(a, c));
Debug.Assert(!ExtMathf.Less(a, b));
Vector3 A = new Vector3(-1, 0, -1);
Vector3 B = new Vector3(1, 0, 1);
Vector3 C = new Vector3(0, 1, 0);
Vector3 D = new Vector3(0, (1f / 3f), 0);
Debug.Assert(ExtMathf.Centroid(A, B, C) == D);
Vector3 xAxis = new Vector3(Random.Range(-1f, 1f), Random.Range(-1f, 1f), Random.Range(-1f, 1f)).normalized;
Vector3 yAxis;
Vector3 zAxis;
ExtMathf.AxesFromAxis(xAxis, out yAxis, out zAxis);
Debug.Assert(ExtMathf.Equal(Vector3.Cross(yAxis, zAxis).normalized, xAxis));
Debug.Assert(ExtMathf.Equal(Vector3.Cross(zAxis, xAxis).normalized, yAxis));
Debug.Assert(ExtMathf.Equal(Vector3.Cross(xAxis, yAxis).normalized, zAxis));
}
/// <summary>
/// Function returns for given axis min vertex index and breadth along it.
/// </summary>
public int GetAlongAxisData(Vector3 axis, out MinMaxPair breadthData)
{
Pair <int, float> minVertex = new Pair <int, float>(-1, float.MaxValue);
breadthData = new MinMaxPair();
Vector3 centroid = Centroid;
for (int i = 0; i < mDataCloud.Count; i++)
{
Vector3 point = mDataCloud[i];
Vector3 direction = point - centroid;
float distance = Vector3.Dot(direction, axis);
breadthData.CheckAgainst(distance);
if (ExtMathf.Less(distance, minVertex.Second))
{
minVertex.First = i;
minVertex.Second = distance;
}
}
return(minVertex.First);
}
/// <summary>
/// Returns relative position of point 'V' to this Edge, assuming space to be 2D.
/// +1 - point lies above the line.
/// 0 - point lies on the line.
/// -1 - point lies below the line.
/// </summary>
public int CalculateRelative2DPosition(Vector3 P)
{
float d = (P.x - V[0].x) * (V[1].y - V[0].y) - (P.y - V[0].y) * (V[1].x - V[0].x);
return(ExtMathf.Greater(d, 0f) ?
1 : (ExtMathf.Less(d, 0f) ?
-1 : 0));
}
/// <summary>
/// Returns relative position of point 'V' to this Triangle.
/// +1 - point lies in front of the triangle.
/// 0 - point lies on the triangle.
/// -1 - point lies behind the triangle.
/// </summary>
public int CalculateRelativePosition(Vector3 P)
{
float distance = CalculateDistance(P);
return(ExtMathf.Greater(distance, 0f) ?
1 : (ExtMathf.Less(distance, 0f) ?
-1 : 0));
}
/// <summary>
/// Function for each axis returns it's min vertex index and breadth along it.
/// </summary>
public void GetAlongAxesData(
Vector3 xAxis, Vector3 yAxis, Vector3 zAxis,
out Pair <int, MinMaxPair> xAxisData,
out Pair <int, MinMaxPair> yAxisData,
out Pair <int, MinMaxPair> zAxisData
)
{
Pair <int, float> minVertexX = new Pair <int, float>(0, float.MaxValue);
Pair <int, float> minVertexY = new Pair <int, float>(0, float.MaxValue);
Pair <int, float> minVertexZ = new Pair <int, float>(0, float.MaxValue);
MinMaxPair breadthX = new MinMaxPair();
MinMaxPair breadthY = new MinMaxPair();
MinMaxPair breadthZ = new MinMaxPair();
Vector3 centroid = Centroid;
for (int i = 0; i < mDataCloud.Count; i++)
{
Vector3 point = mDataCloud[i];
Vector3 direction = point - centroid;
float xDistance = Vector3.Dot(direction, xAxis);
float yDistance = Vector3.Dot(direction, yAxis);
float zDistance = Vector3.Dot(direction, zAxis);
breadthX.CheckAgainst(xDistance);
breadthY.CheckAgainst(yDistance);
breadthZ.CheckAgainst(zDistance);
if (ExtMathf.Less(xDistance, minVertexX.Second))
{
minVertexX.First = i;
minVertexX.Second = xDistance;
}
if (ExtMathf.Less(yDistance, minVertexY.Second))
{
minVertexY.First = i;
minVertexY.Second = yDistance;
}
if (ExtMathf.Less(zDistance, minVertexZ.Second))
{
minVertexZ.First = i;
minVertexZ.Second = zDistance;
}
}
xAxisData = new Pair <int, MinMaxPair>(minVertexX.First, breadthX);
yAxisData = new Pair <int, MinMaxPair>(minVertexY.First, breadthY);
zAxisData = new Pair <int, MinMaxPair>(minVertexZ.First, breadthZ);
}