//Vertices need to be reduced to 2D
//see Akenine-Möller, Tomas; Haines, Eric; Hoffman, Naty (2016): Real-Time Rendering, p. 754
/// <summary>
/// Tests if a point/vertex lies inside or outside a face - Only use this if you know the face AND vertex lie in the same plane and this plane is parallel to xy or xz or yz!
/// </summary>
/// <param name="geometry">The geometry the polygon (here: face) belongs to.</param>
/// <param name="face">The faces to be tested. It will not be Reduced2D!</param>
/// <param name="v">The vertex to be tested.</param>
/// <returns></returns>
public static bool IsPointInPolygon(this Geometry geometry, Face face, float3 v)
{
var inside = false;
var faceVerts = geometry.GetFaceVertices(face.Handle).ToList();
var v1 = geometry.GetVertexByHandle(faceVerts.Last().Handle);
var v1Pos = geometry.Get2DVertPos(face, v1.Handle);
var y0 = v1Pos.y >= v.y;
foreach (var vert in faceVerts)
{
var e1Pos = geometry.Get2DVertPos(face, vert.Handle);
var y1 = e1Pos.y >= v.y;
if (y0 != y1)
{
if ((e1Pos.y - v.y) * (v1Pos.x - e1Pos.x) >=
(e1Pos.x - v.x) * (v1Pos.y - e1Pos.y) == y1)
{
inside = !inside;
}
}
y0 = y1;
v1Pos = e1Pos;
}
return(inside);
}
private static bool IsPolygonRightOfVert(Geometry geometry, Face face, IList <HalfEdge> faceHalfEdges, Vertex vert)
{
var prevV = GetPrevVertex(face, faceHalfEdges, vert);
var nextV = GetNextVertex(face, faceHalfEdges, vert);
var redPrevPos = geometry.Get2DVertPos(face, prevV.Handle);
var redNextPos = geometry.Get2DVertPos(face, nextV.Handle);
return(redPrevPos.y > redNextPos.y);
}
//Vertices need to be reduced to 2D.
/// <summary>
/// Determines if the angle between two vectors, formed by three vertices, is greater or equal 180°.
/// The first vector will be created from v1 and v2, the second from v2 and v3.
/// </summary>
/// <param name="geom">The geometry the vertices belong to.</param>
/// <param name="face">The face the vertices belong to.</param>
/// <param name="v1">Vertex one</param>
/// <param name="v2">Vertex two</param>
/// <param name="v3">Vertex three</param>
/// <returns></returns>
public static bool IsAngleGreaterOrEqualPi(this Geometry geom, Face face, Vertex v1, Vertex v2, Vertex v3)
{
var v1Pos = geom.Get2DVertPos(face, v1.Handle);
var v2Pos = geom.Get2DVertPos(face, v2.Handle);
var v3Pos = geom.Get2DVertPos(face, v3.Handle);
var firstVec = v1Pos - v2Pos;
var secondVec = v3Pos - v2Pos;
var cross = firstVec.x * secondVec.y - firstVec.y * secondVec.x; //Z component of the cross product.
var dot = float3.Dot(firstVec, secondVec);
var angle = (float)System.Math.Atan2(cross, dot);
return(angle <= 0);
}
//Vertices need to be reduced to 2D.
/// <summary>
/// Determines whether the angle between two vectors formed by three vertices is greater than 180 °.
/// The first vector will be created from v1 and v2, the second from v2 and v3.
/// </summary>
/// <param name="geom">The geometry the vertices belong to.</param>
/// <param name="face">The face the vertices belong to.</param>
/// <param name="v1">Vertex one</param>
/// <param name="v2">Vertex two</param>
/// <param name="v3">Vertex three</param>
/// <returns></returns>
public static bool IsAngleGreaterPi(this Geometry geom, Face face, Vertex v1, Vertex v2, Vertex v3)
{
var v1Pos = geom.Get2DVertPos(face, v1.Handle);
var v2Pos = geom.Get2DVertPos(face, v2.Handle);
var v3Pos = geom.Get2DVertPos(face, v3.Handle);
var firstVec = v1Pos - v2Pos;
var secondVec = v3Pos - v2Pos;
var det = firstVec.x * secondVec.y - firstVec.y * secondVec.x; //determinant / Z component of the cross product / sine / y
var dot = float3.Dot(firstVec, secondVec); // cosine / x
var angle = (float)System.Math.Atan2(det, dot);
if ((angle * -1).Equals(M.Pi))
{
return(false);
}
return(angle < 0);
}
//Vertices need to be reduced to 2D.
private static IList <Vertex> GetSortedVertices(Geometry geometry, Face face, IEnumerable <Vertex> unsortedVerts)
{
var sorted = new List <Vertex>();
sorted.AddRange(unsortedVerts);
sorted.Sort(delegate(Vertex a, Vertex b)
{
var redA = geometry.Get2DVertPos(face, a.Handle);
var redB = geometry.Get2DVertPos(face, b.Handle);
var ydiff = -1 * redA.y.CompareTo(redB.y);
if (ydiff != 0)
{
return(ydiff);
}
return(redA.x.CompareTo(redB.x));
});
return(sorted);
}
//Vertices need to be reduced to 2D.
private static bool IsUnderVert(Face face, Vertex middle, Vertex neighbour)
{
var redMiddle = _geometry.Get2DVertPos(face, middle.Handle);
var redNeighbour = _geometry.Get2DVertPos(face, neighbour.Handle);
if (redMiddle.y > redNeighbour.y)
{
return(true);
}
if (redMiddle.y.Equals(redNeighbour.y) && redMiddle.x < redNeighbour.x)
{
return(true);
}
return(false);
}
