public Point3D cross(Point3D p)
{
return new Point3D(
Y * p.Z - Z * p.Y,
Z * p.X - X * p.Z,
X * p.Y - Y * p.X );
}
public void parallelPath(ref List<double> EastingExp, ref List<double> NorthingExp, double displacement)
{
///////////////////////////////////////////////////////////////////////////////////////////////////////
//find a parallel path to the path stored in the polygonMath object
//strategy:
// consider the segments before and after the current ith point
// find two points on these two segments that are equidistance from ith point
// Form a line between these two points
// The midpoint of this line and the original point form a bisector of the adjacent line
// Move along this Bisector, outward, from the point by the desired epansion distance
// take care with three edge vertices that are in a perfect line
////////////////////////////////////////////////////////////////////////////////////////////////////////
Point3D s1 = new Point3D();
Point3D s2 = new Point3D();
Point3D u1 = new Point3D();
Point3D u2 = new Point3D();
double magP=0.0, magM=0.0;
//take care of the interior points -- start-end points are special cases
for (int i = 0; i < numLatLonPoints; i++)
{
if (i < numLatLonPoints - 1) //exclude last point fro below test
{
//note: X to the North, Y to the east and Z is down (right hand rule)
double delXP = Northing[i + 1] - Northing[i];
double delYP = Easting[i + 1] - Easting[i];
magP = Math.Sqrt(delXP * delXP + delYP * delYP);
//vector along segment
s2 = new Point3D(delXP, delYP, 0.0);
//unit vector orthogonal to and to the left of i->i+1 segment
u2 = s2.unit(magP, s2.cross(new Point3D(0.0, 0.0, 1.0)));
}
if (i > 0) //exclude first point from below test
{
//test to see if the i-1->i point segment has zero length
double delXM = Northing[i] - Northing[i-1];
double delYM = Easting[i] - Easting[i-1];
magM = Math.Sqrt(delXM * delXM + delYM * delYM);
//vector along segment
s1 = new Point3D(delXM, delYM, 0.0);
//unit vector orthogonal to and to the left of ith segment
u1 = s1.unit(magM, s1.cross(new Point3D(0.0, 0.0, 1.0)));
}
//handle the special cases for the first and last
if (i == 0 ) //first point
{
NorthingExp.Add(Northing[i] + displacement * u2.X);
EastingExp.Add(Easting[i] + displacement * u2.Y);
continue;
}
else if ( i == (numLatLonPoints - 1)) //last point
{
NorthingExp.Add(Northing[i] + displacement * u1.X);
EastingExp.Add(Easting[i] + displacement * u1.Y);
continue;
}
//compute theta -- signed angle between unit vectors
double sinTheta = u1.cross(u2).Z; //sign indicates the direction of the turn (to right or to left)
double cosTheta = u1.dot(u2); //should be positve if the abs(angle change) is < 90 deg
//gives an angle between +/- 90 deg
double theta = Math.Atan2(sinTheta, cosTheta);
//force the angle to be between 0-180 deg;
//if (theta < 0) theta += Math.PI / 2.0;
//two cases depending on the angle between the two neighbor segments
//parallel path always placed the left of the input path
//TODO -- need to offer an option of right or left or centered parallel paths
if (sinTheta > 0)
{
//compute point on the parallel path -- partallel path segments are parallel to input path segments
NorthingExp.Add(Northing[i] + displacement * ((u1.X + u2.X) / 2.0) / Math.Cos(theta / 2.0 ) );
EastingExp.Add(Easting[i] + displacement * ((u1.Y + u2.Y) / 2.0) / Math.Cos(theta / 2.0 ) );
}
else
{
//compute point on the parallel path -- partallel path segments are parallel to input path segments
double beta = Math.PI - theta; //also restricted to 0-180 deg
NorthingExp.Add(Northing[i] + displacement * ((u1.X + u2.X) / 2.0) / Math.Cos(theta / 2.0));
EastingExp.Add(Easting[i] + displacement * ((u1.Y + u2.Y) / 2.0) / Math.Cos(theta / 2.0));
}
}
}
public Point3D unit(double magnitude, Point3D p)
{
return new Point3D( p.X/magnitude, p.Y/magnitude, p.Z/magnitude);
}
public double dot(Point3D p)
{
return X * p.X + Y * p.Y + Z * p.Z;
}