public gEdge(gVertex start, gVertex end)
{
StartVertex = start;
EndVertex = end;
Length = StartVertex.DistanceTo(EndVertex);
Direction = gVector.ByTwoVertices(StartVertex, EndVertex);
}
internal gVertex Translate(gVector vector, double distance)
{
gVector normalized = vector.Normalized();
gVector distVector = normalized * distance;
return(this.Translate(distVector));
}
public bool IsCoplanarTo(gEdge edge)
{
// http://mathworld.wolfram.com/Coplanar.html
gVector a = this.Direction;
gVector b = edge.Direction;
gVector c = gVector.ByTwoVertices(this.StartVertex, edge.StartVertex);
return(c.Dot(a.Cross(b)) == 0);
}
public double DistanceTo(gEdge edge)
{
// http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
gVector v1 = gVector.ByTwoVertices(this, edge.StartVertex);
gVector v2 = gVector.ByTwoVertices(this, edge.EndVertex);
gVector numerator = v1.Cross(v2);
gVector denominator = gVector.ByTwoVertices(edge.EndVertex, edge.StartVertex);
return(numerator.Length / denominator.Length);
}
public gVector Cross(gVector vector)
{
double x = (this.Y * vector.Z) - (this.Z * vector.Y);
double y = (this.Z * vector.X) - (this.X * vector.Z);
double z = (this.X * vector.Y) - (this.Y * vector.X);
double angle = ToRadians(this.Angle(vector));
double length = this.Length * vector.Length * Math.Sin(angle);
return(new gVector(x, y, z, length));
}
public double Angle(gVector vector)
{
double dot = this.Dot(vector);
double cos = dot / (this.Length * vector.Length);
if (cos > 1)
{
return(ToDegrees(Math.Acos(1)));
}
else if (cos < -1)
{
return(ToDegrees(Math.Acos(-1)));
}
else
{
return(ToDegrees(Math.Acos(cos)));
}
}
public bool OnEdge(gVertex start, gVertex end)
{
if (this.Equals(start) || this.Equals(end))
{
return(true);
}
// https://www.lucidarme.me/check-if-a-point-belongs-on-a-line-segment/
gVector startEnd = gVector.ByTwoVertices(start, end);
gVector startMid = gVector.ByTwoVertices(start, this);
gVector endMid = gVector.ByTwoVertices(this, end);
if (!startMid.IsParallelTo(endMid))
{
return(false);
} // Not aligned
double dotAC = startEnd.Dot(startMid);
double dotAB = startEnd.Dot(startEnd);
return(0 <= dotAC && dotAC <= dotAB);
}
public double DistanceTo(gEdge edge)
{
// http://mathworld.wolfram.com/Line-LineDistance.html
if (this.IsCoplanarTo(edge))
{
var distances = new double[4] {
StartVertex.DistanceTo(edge),
EndVertex.DistanceTo(edge),
edge.StartVertex.DistanceTo(this),
edge.EndVertex.DistanceTo(this)
};
return(distances.Min());
}
else
{
var a = this.Direction;
var b = edge.Direction;
var c = gVector.ByTwoVertices(this.StartVertex, edge.StartVertex);
gVector cross = a.Cross(b);
double numerator = c.Dot(cross);
double denominator = cross.Length;
return(Math.Abs(numerator) / Math.Abs(denominator));
}
}
internal gVertex Translate(gVector vector)
{
return(gVertex.ByCoordinates(this.X + vector.X, this.Y + vector.Y, this.Z + vector.Z));
}
public double Dot(gVector vector)
{
return((this.X * vector.X) + (this.Y * vector.Y) + (this.Z * vector.Z));
}
public bool IsParallelTo(gVector vector)
{
var dot = this.Normalized().Dot(vector.Normalized());
return(Threshold(dot, 1));
}
