public Geometry Intersection(Edge edge)
{
// If no coplanar, cannot intersect
if (!edge.IsCoplanarTo(this.Origin, this.Direction))
{
return(null);
}
// Intersection can be an Edge or null
if (this.Direction.IsParallelTo(edge.Direction))
{
bool containsStart = this.Contains(edge.StartVertex);
bool containsEnd = this.Contains(edge.EndVertex);
if (!containsStart && !containsEnd)
{
return(null);
}
else if (containsStart)
{
return(Edge.ByStartVertexEndVertex(edge.StartVertex, this.Origin));
}
else
{
return(Edge.ByStartVertexEndVertex(this.Origin, edge.EndVertex));
}
}
// No coincident nor same extremes
var b = this.Direction;
var a = edge.Direction;
var c = Vector.ByTwoVertices(edge.StartVertex, this.Origin);
var cxb = c.Cross(b);
var axb = a.Cross(b);
var dot = cxb.Dot(axb);
double t = (dot) / Math.Pow(axb.Length, 2);
if (t < 0 && !t.AlmostEqualTo(0))
{
return(null);
}
if (t > 1 && !t.AlmostEqualTo(1))
{
return(null);
}
var intersection = edge.StartVertex.Translate(edge.Direction.Scale(t));
return(this.Contains(intersection) ? intersection : null);
}
/// <summary>
/// TODO: To be reviewed
/// Returns the orientation of vertices p1-p2-p3
/// 0 => Vertices are colinear
/// 1 => Counterclock-wise, left turn
/// -1 => Clock-wise, right turn
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
/// <param name="plane"></param>
/// <returns></returns>
internal static int Orientation(Vertex p1, Vertex p2, Vertex p3, string plane = "xy")
{
// See https://www.geeksforgeeks.org/orientation-3-ordered-points/
// for details of below formula.
double value = 0;
switch (plane)
{
case "xy":
value = (p2.X - p1.X) * (p3.Y - p2.Y) - (p2.Y - p1.Y) * (p3.X - p2.X);
break;
case "xz":
value = (p2.X - p1.X) * (p3.Z - p2.Z) - (p2.Z - p1.Z) * (p3.X - p2.X);
break;
case "yz":
value = (p2.Y - p1.Y) * (p3.Z - p2.Z) - (p2.Z - p1.Z) * (p3.Y - p2.Y);
break;
default:
throw new Exception("Plane not defined");
}
//Rounding due to floating point error.
if (value.AlmostEqualTo(0))
{
return(0);
} //Points are colinear
return((value > 0) ? 1 : -1); //Counter clock or clock wise
}
public static List <Vertex> ConvexHull(List <Vertex> vertices)
{
var verticesCount = vertices.Count();
//If less than 3, cannot be created
if (verticesCount < 3)
{
throw new ArgumentOutOfRangeException("vertices", verticesCount, "No ConvexHull can be created with less than 3 vertices");
}
// TODO: Check if they are colinear
//if (Vertex.Colinear(vertices))
//{
// throw new ArgumentException("Vertices are colinear", "vertices");
//}
Vertex minVertex = Vertex.MinimumVertex(vertices);
List <Vertex> sorted = Vertex.OrderByRadianAndDistance(vertices, minVertex);
Stack <Vertex> stack = new Stack <Vertex>();
// Adding fist vertex to stack.
stack.Push(minVertex);
//First vertex on sorted should be the minVertex itself
// so just skip it.
for (int i = 1; i < verticesCount; i++)
{
int nextIndex = (i + 1) % verticesCount;
var vertex = sorted[i];
var nextVertex = sorted[nextIndex];
double vertexAngle = Vertex.RadAngle(minVertex, vertex);
double nextVertexAngle = Vertex.RadAngle(minVertex, nextVertex);
// If the angle is same as next, skip as we'll only use the fartest
// vertex with same angle.
if (vertexAngle.AlmostEqualTo(nextVertexAngle))
{
continue;
}
// If stack is still less than 3, keep adding.
if (stack.Count < 3)
{
stack.Push(vertex);
}
else
{
// While it is not a left turn, remove top on stack
while (Vertex.Orientation(GetNextToTop <Vertex>(stack), stack.Peek(), vertex) != 1)
{
stack.Pop();
}
stack.Push(vertex);
}
}
return(stack.Reverse().ToList());
}
public override IResultValue Evaluate()
{
IResultValue num1 = First.Evaluate();
IResultValue num2 = Second.Evaluate();
double d1 = (double)num1.ToDecimal();
double d2 = (double)num2.ToDecimal();
return(new ResultBoolean(!d1.AlmostEqualTo(d2)));
}
/// <summary>
/// Determins if a Vertex lies on the left-hand side of an edge on the XY plane.
/// 1 => for vertex left of the edge
/// 0 => for vertex on the edge
/// -1 => for vertex right of the edege
/// </summary>
/// <param name="edge"></param>
/// <param name="vertex"></param>
/// <returns>
///
/// </returns>
public int IsLeftFrom(Edge edge)
{
double value = (edge.EndVertex.X - edge.StartVertex.X) * (this.Y - edge.StartVertex.Y) - (edge.EndVertex.Y - edge.StartVertex.Y) * (this.X - edge.StartVertex.X);
if (value.AlmostEqualTo(0))
{
return(0);
}
return(value > 0 ? 1 : -1);
}
/// <summary>
/// TODO: To be reviewed
/// </summary>
/// <param name="centre"></param>
/// <param name="vertex"></param>
/// <returns></returns>
public static double RadAngle(Vertex centre, Vertex vertex)
{
//Rad angles http://math.rice.edu/~pcmi/sphere/drg_txt.html
double dx = vertex.X - centre.X;
double dy = vertex.Y - centre.Y;
bool onYAxis = dx.AlmostEqualTo(0);
bool onXAxis = dy.AlmostEqualTo(0);
//TODO: Implement Z angle? that would becom UV coordinates.
//double dz = vertex.point.Z - centre.point.Z;
if (onYAxis && onXAxis)
{
return(0);
}
if (onYAxis) // both Vertices on Y axis
{
if (dy < 0) //vertex below X axis
{
return(Math.PI * 3 / 2);
}
else//vertex above X Axis
{
return(Math.PI / 2);
}
}
if (onXAxis) // both Vertices on X Axis
{
if (dx < 0) // vertex on the left of Y axis
{
return(Math.PI);
}
else//vertex on the right of Y axis
{
return(0);
}
}
if (dx < 0)
{
return(Math.PI + Math.Atan(dy / dx));
}
if (dy < 0)
{
return(2 * Math.PI + Math.Atan(dy / dx));
}
return(Math.Atan(dy / dx));
}
public string VolumeToSymbol(double d)
{
if (d.AlmostEqualTo(0))
{
return("\uE198");
}
if (d < 33.333333)
{
return("\uE993");
}
if (d < 66.66666667)
{
return("\uE994");
}
return("\uE995");
}
protected override void OnPaint(PaintEventArgs e)
{
base.OnPaint(e);
if (!_oldScaleFactor.AlmostEqualTo(ScaleFactor))
{
Image = ScaleImage(_originalImage);
}
if (!DesignMode && !ShowBorder)
{
return;
}
var pen = new Pen(Color.FromArgb(45, 68, 108), 1);
var rectangle = new Rectangle(0, 0, Size.Width - 1, Size.Height - 1);
e.Graphics.DrawRectangle(pen, rectangle);
}
/// <summary>
/// Checks if the given Vertex is contained on the Ray.
/// </summary>
/// <param name="vertex"></param>
/// <returns></returns>
public bool Contains(Vertex vertex)
{
// If the Vector from Ray's origin to the given
// vertex is parallel to Ray's Direction, return true.
var vector = Vector.ByTwoVertices(this.Origin, vertex);
if (!this.Direction.IsParallelTo(vector))
{
return(false);
}
// Need to check if point falls on the visible path of Ray.
// Vertex = Origin + t * Direction; t = (V-O)/D
// If t < 0, it doesn't
double t = Double.PositiveInfinity;
if (this.Direction.X != 0)
{
t = (vertex.X - this.Origin.X) / this.Direction.X;
}
else if (this.Direction.Y != 0)
{
t = (vertex.Y - this.Origin.Y) / this.Direction.Y;
}
else if (this.Direction.Z != 0)
{
t = (vertex.Z - this.Origin.Z) / this.Direction.Z;
}
else
{
throw new Exception("Something when wrong, contact Author");
}
return(t > 0 && !t.AlmostEqualTo(0));
}
/// <summary>
/// Checks if the polygon is convex
/// </summary>
/// <returns></returns>
public bool IsConvex()
{
//https://math.stackexchange.com/questions/1743995/determine-whether-a-polygon-is-convex-based-on-its-vertices/1745427#1745427
double wSign = 0; // First non-zero orientation
int xSign = 0;
int xFirstSign = 0;
int xFlips = 0;
int ySign = 0;
int yFirstSign = 0;
int yFlips = 0;
int vertexCount = this.Vertices.Count();
Vertex current = this.Vertices[vertexCount - 2];
Vertex next = this.Vertices[vertexCount - 1];
for (int i = 0; i < vertexCount; i++)
{
var prev = current;
current = next;
next = this.Vertices[i];
// Previous edge vector
double prevX = current.X - prev.X;
double prevY = current.Y - prev.Y;
// Next edge vector
double nextX = next.X - current.X;
double nextY = next.Y - current.Y;
if (!nextX.AlmostEqualTo(0))
{
if (nextX > 0)
{
if (xSign == 0)
{
xFirstSign = 1;
}
else if (xSign < 0)
{
xFlips += 1;
}
xSign = 1;
}
else // nextX < 0
{
if (xSign == 0)
{
xFirstSign = -1;
}
else if (xSign > 0)
{
xFlips += 1;
}
xSign = -1;
}
}
if (xFlips > 2)
{
return(false);
}
if (!nextY.AlmostEqualTo(0))
{
if (nextY > 0)
{
if (ySign == 0)
{
yFirstSign = 1;
}
else if (ySign < 0)
{
yFlips += 1;
}
ySign = 1;
}
else // nextY < 0
{
if (ySign == 0)
{
yFirstSign = -1;
}
else if (ySign > 0)
{
yFlips += 1;
}
ySign = -1;
}
}
if (yFlips > 2)
{
return(false);
}
// Find out the orientation of this pair of edges
// and ensure ir does not differ from previous ones
double w = prevX * nextY - nextX * prevY;
bool wIsZero = w.AlmostEqualTo(0);
bool wSignIsZero = wSign.AlmostEqualTo(0);
if (wSignIsZero && !wIsZero)
{
wSign = w;
}
else if (!wSignIsZero && !wIsZero)
{
if ((wSign > 0 && w < 0) || (wSign > 0 && w < 0))
{
return(false);
}
}
}
// Final/wraparound sign flips
if (xSign != 0 && xFirstSign != 0 && xSign != xFirstSign)
{
xFlips += 1;
}
if (ySign != 0 && yFirstSign != 0 && ySign != yFirstSign)
{
yFlips += 1;
}
// Concave polygons have two sign flips along each axis
if (xFlips != 2 || yFlips != 2)
{
return(false);
}
// This is a convex polygon
return(true);
}
public void AlmostEqualTo(double num1, double num2, double tolerance, bool expected)
{
Assert.Equal(expected, num1.AlmostEqualTo(num2, tolerance));
}
public static bool IsLowerEqualThan(this double value1, double value2, double precision = 0.000001)
{
return(value1 < value2 || value1.AlmostEqualTo(value2, precision));
}
public GeometryBase Intersection(Edge other)
{
// http://mathworld.wolfram.com/Line-LineIntersection.html
if (!this.BoundingBox.Intersects(other.BoundingBox))
{
return(null);
}
if (!this.IsCoplanarTo(other))
{
return(null);
}
if (this.Equals(other))
{
return(this);
} // Issues if same polygon id???
var a = this.Direction;
var b = other.Direction;
if (a.IsParallelTo(b))
{
// Fully contains the test edge
if (other.StartVertex.OnEdge(this) && other.EndVertex.OnEdge(this))
{
return(other);
}
// Is fully contained by test edge
else if (this.StartVertex.OnEdge(other) && this.EndVertex.OnEdge(other))
{
return(this);
}
// Not fully inclusive but overlapping
else if (this.StartVertex.OnEdge(other) || this.EndVertex.OnEdge(other))
{
Vertex[] vertices = new Vertex[4]
{
this.StartVertex,
this.EndVertex,
other.StartVertex,
other.EndVertex
};
var sorted = vertices.OrderBy(v => v.Y).ThenBy(v => v.X).ThenBy(v => v.Z).ToList();
return(Edge.ByStartVertexEndVertex(sorted[1], sorted[2]));
}
// Not intersecting
else
{
return(null);
}
}
// No parallels but intersecting on one of the extreme vertices
if (other.Contains(this.StartVertex))
{
return(this.StartVertex);
}
else if (other.Contains(this.EndVertex))
{
return(this.EndVertex);
}
// No coincident nor same extremes
var c = Vector.ByTwoVertices(this.StartVertex, other.StartVertex);
var cxb = c.Cross(b);
var axb = a.Cross(b);
var dot = cxb.Dot(axb);
// If dot == 0 it means that other edge contains at least a vertex from this edge
// and they are parallel or perpendicular. Cannot be parallel as that was tested before.
// It might also mean they don't intersect but the would if extending the projections
double s = (dot) / Math.Pow(axb.Length, 2);
if (s.AlmostEqualTo(0))
{
if (this.StartVertex.OnEdge(other))
{
return(this.StartVertex);
}
else if (this.EndVertex.OnEdge(other))
{
return(this.EndVertex);
}
else if (other.StartVertex.OnEdge(this))
{
return(other.StartVertex);
}
else if (other.EndVertex.OnEdge(this))
{
return(other.EndVertex);
}
else
{
return(null);
}
}
// s > 1, means that "intersection" vertex is not on either edge
// s == NaN means they are parallels so never intersect
if (s < 0 || s > 1 || Double.IsNaN(s))
{
return(null);
}
Vertex intersection = this.StartVertex.Translate(a.Scale(s));
if (intersection.Equals(other.StartVertex))
{
return(other.StartVertex);
}
if (intersection.Equals(other.EndVertex))
{
return(other.EndVertex);
}
if (!intersection.OnEdge(other))
{
return(null);
}
return(intersection);
}