/// <summary>
/// returns a pnt rotated from angle degrees around the axis
/// </summary>
/// <param name="angle">in defree</param>
/// <param name="axis"></param>
/// <returns></returns>
public Pnt Rotate(double angle, Pnt axis)
{
Pnt p = this;
p.Rotated(angle, axis);
return(p);
}
public Edge(Edge e)
{
v = e.v;
this.p1 = e.p1;
this.p2 = e.p2;
this.pts = e.pts;
}
// constructors
public Edge(List <gp_Pnt> pts)
{
this.pts = ToPnt(pts);
p1 = ToPnt(pts[0]);
p2 = ToPnt(pts[1]);
v = ToPnt(pts[1]) - ToPnt(pts[0]);
}
// comparison
public bool IsEqual(Pnt p2)
{
if (this.x == p2.x && this.y == p2.y && this.z == p2.z)
{
return(true);
}
return(false);
}
public Pnt(Pnt p)
{
x = p.x;
y = p.y;
z = p.z;
d.Clear();
d.Add(p.x);
d.Add(p.y);
d.Add(p.z);
}
/// <summary>
/// modifies the edge
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
public void Replace(Pnt p1, Pnt p2)
{
v = p2 - p1;
this.pts.Clear();
this.pts.Add(p1);
this.pts.Add(p2);
this.p1 = p1;
this.p2 = p2;
}
}//*/
/// <summary>
/// we want to know if the vertex "what" already exists in our list of unique vertices "from"
/// </summary>
/// <param name="from"> the list of unique vertices</param>
/// <param name="what"> the vertex we are looking at</param>
/// <returns>returns the index of the vertex or -1 if it is the first time we see that vertex</returns>
public int ExistsIn(List <Pnt> from, Pnt what)
{
for (int i = 0; i < from.Count; i++)
{
if (from[i].x == what.x && from[i].y == what.y && from[i].z == what.z)
{
return(i);
}
}
return(-1);
}//*/
public Edge(gp_Pnt p1, gp_Pnt p2)
{
v = ToPnt(p2) - ToPnt(p1);
this.pts.Clear();
this.pts.Add(ToPnt(p1));
this.pts.Add(ToPnt(p2));
this.p1 = ToPnt(p1);
this.p2 = ToPnt(p2);
}
public Edge(Pnt p1, Pnt p2)
{
v = p2 - p1;
this.pts.Clear();
this.pts.Add(p1);
this.pts.Add(p2);
this.p1 = p1;
this.p2 = p2;
}
/// <summary>
/// modifies the edge
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
public void Replace(gp_Pnt p1, gp_Pnt p2)
{
v = ToPnt(p2) - ToPnt(p1);
this.pts.Clear();
this.pts.Add(ToPnt(p1));
this.pts.Add(ToPnt(p2));
this.p1 = ToPnt(p1);
this.p2 = ToPnt(p2);
}
/// <summary>
/// signed angle between two vectors defined by p1 and p2
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="axis">normale of the plane defined by the two vectors</param>
/// <returns></returns>
public static double SignedAngle(Pnt p1, Pnt p2, Pnt axis)
{
double angle = Math.Acos(DotProduct(Normalize(p1), Normalize(p2)));
Pnt cross = Cross(p1, p2);
if (DotProduct(axis, cross) < 0)
{ // Or > 0
angle = -angle;
}
return(angle * 360 / (2 * Math.PI)); // in degree
}
/// <summary>
/// retrieves the index of the vertex (pt)
/// </summary>
/// <param name="pt"> the vertex for which we want to know the index</param>
/// <returns>returns the index of pt</returns>
public int RetrievesIndex(Pnt pt)
{
// if we don't know that vertex, we add it to the vertices
if (ExistsIn(vertices, pt) == -1)
{
vertices.Add(pt);
return(vertices.Count - 1);
}
else
{
// otherwise we get the index of that already known vertex
return(ExistsIn(vertices, pt));
}
}//*/
/// <summary>
/// rotate this from the angle "angle" around the axis "axis"
/// </summary>
/// <param name="angle">in degree</param>
/// <param name="axis"></param>
public void Rotated(double angle, Pnt axis)
{
angle = angle * Math.PI / 180; // converting to radians
double rx = x * (Math.Cos(angle) + axis.x * axis.x * (1 - Math.Cos(angle))) + y * (axis.x * axis.y * (1 - Math.Cos(angle)) - axis.z * Math.Sin(angle)) + z * (axis.x * axis.z * (1 - Math.Cos(angle)) + axis.y * Math.Sin(angle));
double ry = x * (axis.y * axis.x * (1 - Math.Cos(angle)) + axis.z * Math.Sin(angle)) + y * (Math.Cos(angle) + axis.y * axis.y * (1 - Math.Cos(angle))) + z * (axis.y * axis.z * (1 - Math.Cos(angle)) - axis.x * Math.Sin(angle));
double rz = x * (axis.z * axis.x * (1 - Math.Cos(angle) - axis.y * Math.Sin(angle))) + y * (axis.z * axis.y * (1 - Math.Cos(angle)) + axis.x * Math.Sin(angle)) + z * (Math.Cos(angle) + axis.z * axis.z * (1 - Math.Cos(angle)));
x = rx;
y = ry;
z = rz;
d.Clear();
d.Add(rx);
d.Add(ry);
d.Add(rz);
}
/// <summary>
/// angle between two edges
/// </summary>
/// <param name="e"></param>
/// <param name="axis"></param>
/// <returns></returns>
public double Angle(Edge e, Pnt axis)
{
return(this.v.IsEqual(e.v) ? 0 : Pnt.SignedAngle(v, e.v, axis));
}
/// <summary>
/// angle between the two vectors
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <returns></returns>
public static double Angle(Pnt p1, Pnt p2)
{
double angle = Math.Acos(DotProduct(Normalize(p1), Normalize(p2)));
return(angle * 360 / (2 * Math.PI)); // in degree;
}
/// <summary>
/// dot product of the two vectors
/// </summary>
/// <param name="e1"></param>
/// <param name="e2"></param>
/// <returns></returns>
public static double DotProduct(Pnt e1, Pnt e2)
{
return(e1.x * e2.x + e1.y * e2.y + e1.z * e2.z);
}
/// <summary>
/// dot product between this and the vector e2
/// </summary>
/// <param name="e2"></param>
/// <returns></returns>
public double DotProduct(Pnt e2)
{
return(x * e2.x + y * e2.y + z * e2.z);
}
/// <summary>
/// returns the distance between this and pt
/// </summary>
/// <param name="pt"></param>
/// <returns></returns>
public double Distance(Pnt pt)
{
return(Math.Sqrt((x - pt.x) * (x - pt.x) + (y - pt.y) * (y - pt.y) + (z - pt.z) * (z - pt.z)));
}
/// <summary>
/// cross product between the two vectors
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <returns></returns>
public static Pnt Cross(Pnt p1, Pnt p2)
{
return(new Pnt(p1.y * p2.z - p1.z * p2.y, p1.z * p2.x - p1.x * p2.z, p1.x * p2.y - p1.y * p2.x));
}
/// <summary>
/// normalization of the vector
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Pnt Normalize(Pnt p)
{
double L = Math.Sqrt(p.x * p.x + p.y * p.y + p.z * p.z);
return(L == 0 ? p : p / L);
}