public bool isfEqual(XYPT q)
{
bool bxeq = (x == q.x ? true : false);
bool byeq = (y == q.y ? true : false);
return(bxeq && byeq);
}
public bool PointInPolygon(XYPT point)
{
int i, j;
bool inside = false;
int nvert = m_points.Count;
for (i = 0, j = nvert - 1; i < nvert; j = i++)
{
if (((m_points[i].YY > point.YY) != (m_points[j].YY > point.YY)) &&
(point.XX < (m_points[j].XX - m_points[i].XX) * (point.YY - m_points[i].YY) / (m_points[j].YY - m_points[i].YY) + m_points[i].XX))
{
inside = !inside;
}
}
// check if point is over segments of polygon
if (inside != true)
{
for (int k = 0; k < nvert; k++)
{
if (PointOnLineSegment(m_points[(k + 1) % nvert], m_points[k], point))
{
return(true);
}
}
}
return(inside);
}
public Line(XYPT pt1, XYPT pt2)
{
m_points = new List <XYPT>()
{
pt1, pt2
};
}
public void RemovePoint(XYPT p)
{
if (ContainsPoint(p))
{
m_points.Remove(p);
}
}
/// <summary>
/// <para> Imagine a list of column vectors, each bearing a list of XY-points, essentially a 2d matrix. </para>
/// <para> This utility returns the largest X and largest Y value in each row. </para>
/// </summary>
/// <param name="list"> A list of lists of XYPTs </param>
/// <returns></returns>
public static XYPT[] MaximumVector(List <List <XYPT> > list)
{
/* Example:
*
* List[0] List[1] List[2] double[] Array
* List[0][0] [1][0] [2][0] ==> [0].x = Max{ [0][0].x, [1][0].x, [2][0].x }; [0].y = Max{ [0][0].y, [1][0].y, [2][0].y }
* [0][1] [1][1] [2][1] ==> [1].x = Max{ [1][0].x, [1][1].x, [2][1].x }; [1].y = Max{ [0][1].y, [1][1].y, [2][1].y }
* [0][2] [1][2] [2][2] ==> [2].x = Max{ [2][0].x, [1][2].x, [2][2].x }; [2].y = Max{ [0][2].y, [1][2].y, [2][2].y }
* [0][3] [1][3] [2][3] ==> [3].x = Max{ [3][0].x, [1][3].x, [2][3].x }; [3].y = Max{ [0][3].y, [1][3].y, [2][3].y }
* [0][4] [1][4] [2][4] ==> [4].x = Max{ [4][0].x, [1][4].x, [2][4].x }; [4].y = Max{ [0][4].y, [1][4].y, [2][4].y }
*/
int mVectors = list.Count;
XYPT[] maximum = new XYPT[0];
int nRowsMax = 0;
if (mVectors <= 0)
{
return(maximum);
}
for (int iRow = 0; iRow < mVectors; iRow++)
{
if (nRowsMax < list[iRow].Count)
{
nRowsMax = list[iRow].Count;
}
}
// Create the array of sums
maximum = new XYPT[nRowsMax];
if (nRowsMax <= 0)
{
return(maximum);
}
for (int iRow = 0; iRow < nRowsMax; iRow++)
{
maximum[iRow] = -XYPT.MaxValue; // Set to the largest negative double.
for (int jCol = 0; jCol < mVectors; jCol++)
{
int nXYPTs = list[jCol].Count;
if (1 <= nXYPTs && nXYPTs <= nRowsMax)
{
XYPT p = list[jCol][iRow];
if (maximum[iRow].x < p.x)
{
maximum[iRow].x = p.x;
}
if (maximum[iRow].y < p.y)
{
maximum[iRow].y = p.y;
}
}
}
} // for( int iRow = 0 ; iRow < nRowsMax ; iRow++ )
return(maximum);
} // public static double[] MaximumVectorYs( List<List<XYPT>> list )
public XYPT Moved(XYPT displacement)
{
XYPT asif = this; // asif == "As If"
asif.x += displacement.x;
asif.y += displacement.y;
return(asif);
}
public XYPT MidwayPointTo(XYPT p2)
{
XYPT p;
p.x = 0.5f * (this.x + p2.x);
p.y = 0.5f * (this.y + p2.y);
return(p);
}
public XYPT Midpt(XYPT p2)
{
XYPT p;
p.x = 0.5f * (this.x + p2.x);
p.y = 0.5f * (this.y + p2.y);
return(p);
}
public XYPT Moved(double r, double phi)
{
XYPT asif = this; // asif == "As If"
asif.x += r * Math.Cos(phi);
asif.y += r * Math.Sin(phi);
return(asif);
}
public void AddPoint(XYPT p)
{
if (m_points == null)
{
m_points = new List <XYPT>();
}
m_points.Add(p);
}
/// <summary>
/// Returns q rotated relative p (origin).
/// </summary>
/// <param name="q"> The point being rotated. </param>
/// <param name="phi"> The angle of rotation (in radians). </param>
/// <returns></returns>
public XYPT Rotated(XYPT q, double phi)
{
double cp = Math.Cos(phi);
double sp = Math.Sin(phi);
double dx = q.x - x;
double dy = q.y - y;
return(new XYPT(x + (dx * cp) - (dy * sp),
y + (dx * sp) + (dy * cp)));
}
public bool ContainsPoint(XYPT p)
{
if (m_points == null)
{
m_points = new List <XYPT>();
return(false);
}
return(m_points.Contains(p));
}
public double AngleTo02π(XYPT p)
{
XYPT q = p - this; double φ = Math.Atan2(q.y, q.x);
if (φ < 0)
{
φ += Math.PI * 2;
}
return(φ);
}
/// <summary>
/// Rotates p relative q.
/// </summary>
/// <param name="q"> The point being rotated. </param>
/// <param name="phi"> The angle of rotation (in radians). </param>
/// <returns></returns>
public void rotateRel(XYPT q, double phi)
{
double cp = Math.Cos(phi);
double sp = Math.Sin(phi);
double dx = x - q.x;
double dy = y - q.y;
x = q.x + (dx * cp) - (dy * sp);
y = q.y + (dx * sp) + (dy * cp);
}
/// <summary>
/// Rotates q relative p.
/// </summary>
/// <param name="q"> The point being rotated. </param>
/// <param name="phi"> The angle of rotation (in radians). </param>
/// <returns></returns>
public void rotate(ref XYPT q, double phi)
{
double cp = Math.Cos(phi);
double sp = Math.Sin(phi);
double dx = q.x - x;
double dy = q.y - y;
q.x = x + (dx * cp) - (dy * sp);
q.y = y + (dx * sp) + (dy * cp);
}
public void minimize(XYPT q)
{
if (q.x < this.x)
{
this.x = q.x;
}
if (q.y < this.y)
{
this.x = q.y;
}
}
public void maximize(XYPT q)
{
if (this.x < q.x)
{
this.x = q.x;
}
if (this.y < q.y)
{
this.x = q.y;
}
}
private XYPT GetCenter()
{
XYPT center = new XYPT();
foreach (var point in m_points)
{
center.x += point.x;
center.y += point.y;
}
center /= Count;
return(center);
}
public bool Pt2LinePt(XYPT pt1, XYPT pt2, XYPT pPerp, out XYPT pDrop, double epsilon = 0.001)
{
double dx = pt2.x - pt1.x;
double dy = pt2.y - pt1.y;
if ((dx == 0.0) && (dy == 0.0))
{
pDrop.x = pt1.x;
pDrop.y = pt1.y;
return(true);
}
if (Math.Abs(dy) <= Math.Abs(dx))
{
double m = dy / dx; // Slope of line
double b = pt1.y - m * pt1.x; // Y-Intercept
// Find the point on (x1,y1)-(x2,y2) that is closest to (x,y)
double tmp = (pPerp.y - b) * m + pPerp.x;
pDrop.x = tmp / (m * m + 1);
pDrop.y = m * pDrop.x + b;
}
else
{
double m = dx / dy; // Inverse slope of line
double b = pt1.x - m * pt1.y; // X-Intercept
// Find the point on (x1,y1)-(x2,y2) that is closest to (x,y).
double tmp = (pPerp.x - b) * m + pPerp.y;
pDrop.y = tmp / (m * m + 1);
pDrop.x = m * pDrop.y + b;
}
// x and y are the points on (x1,y1)-(x2,y2) such that
// (x,y)-(xr,yr) is perpendicular to (x1,y1)-(x2,y2).
bool b1 = (pt1.x <= pDrop.x + epsilon) && (pDrop.x <= pt2.x + epsilon);
bool b2 = (pt2.x <= pDrop.x + epsilon) && (pDrop.x <= pt1.x + epsilon);
bool b3 = (pt1.y <= pDrop.y + epsilon) && (pDrop.y <= pt2.y + epsilon);
bool b4 = (pt2.y <= pDrop.y + epsilon) && (pDrop.y <= pt1.y + epsilon);
if ((b1 || b2) && (b3 || b4))
{
return(true);
}
else
{
return(false);
}
}
public static XYPT sum(List <XYPT> listXYPT)
{
int n = listXYPT.Count;
XYPT s = new XYPT(0, 0);
if (n <= 0)
{
return(s);
}
for (int i = 0; i < n; i++)
{
s += listXYPT[i];
}
return(s);
}
public static XYPT sum(XYPT[] array)
{
int n = array.GetLength(0);
XYPT s = new XYPT(0, 0);
if (n <= 0)
{
return(s);
}
for (int i = 0; i < n; i++)
{
s += array[i];
}
return(s);
}
public static XYPT average(List <XYPT> listXYPT)
{
int n = listXYPT.Count;
XYPT sum = new XYPT(0, 0);
if (n <= 0)
{
return(sum);
}
for (int i = 0; i < n; i++)
{
sum += listXYPT[i];
}
return(sum / n);
}
public static XYPT average(XYPT[] array)
{
int n = array.GetLength(0);
XYPT sum = new XYPT(0, 0);
if (n <= 0)
{
return(sum);
}
for (int i = 0; i < n; i++)
{
sum += array[i];
}
return(sum / n);
}
/// <summary>
/// checks if 2 points are the same
/// </summary>
/// <param name="obj"></param>
/// <returns></returns>
public override bool Equals(object obj)
{
if (obj == null || GetType() != obj.GetType())
{
return(false);
}
if (obj is XYPT)
{
XYPT xyPoint = (XYPT)obj;
return(this.x == xyPoint.x &&
this.y == xyPoint.y);
}
else
{
return(false);
}
}
public bool PointOnLineSegment(XYPT pt1, XYPT pt2, XYPT pt, double epsilon = 0.001)
{
if (pt.XX - Math.Max(pt1.XX, pt2.XX) > epsilon ||
Math.Min(pt1.XX, pt2.XX) - pt.XX > epsilon ||
pt.YY - Math.Max(pt1.YY, pt2.YY) > epsilon ||
Math.Min(pt1.YY, pt2.YY) - pt.YY > epsilon)
{
return(false);
}
if (Math.Abs(pt2.XX - pt1.XX) < epsilon)
{
return(Math.Abs(pt1.XX - pt.XX) < epsilon || Math.Abs(pt2.XX - pt.XX) < epsilon);
}
if (Math.Abs(pt2.YY - pt1.YY) < epsilon)
{
return(Math.Abs(pt1.YY - pt.YY) < epsilon || Math.Abs(pt2.YY - pt.YY) < epsilon);
}
double x = pt1.XX + (pt.YY - pt1.YY) * (pt2.XX - pt1.XX) / (pt2.YY - pt1.YY);
double y = pt1.YY + (pt.XX - pt1.XX) * (pt2.YY - pt1.YY) / (pt2.XX - pt1.XX);
return(Math.Abs(pt.XX - x) < epsilon || Math.Abs(pt.YY - y) < epsilon);
}
public void swapWith(ref XYPT q)
{
XYPT t = this; this = q; q = t;
}
public bool isNearlySameAs(XYPT q, double sepToler)
{
return(this.DistTo(q) <= sepToler);
}
public void move(XYPT displacement)
{
x += displacement.x;
y += displacement.y;
}
public bool NearlyEquals(XYPT q, double sepToler)
{
return(this.DistTo(q) <= sepToler);
}
/// <summary>
/// <para> Imagine a list of column vectors, each bearing a list of XY-points, essentially a 2d matrix. </para>
/// <para> This utility averages points in the same row. </para>
/// </summary>
/// <param name="list"> A list of lists of XYPTs </param>
/// <returns></returns>
public static XYPT[] averageVectors(List <List <XYPT> > list)
{
/* Example:
*
* List[0] List[1] List[2] XYPT[] Array
*
* List[0][0] [1][0] [2][0] ==> [0] = ( [0][0] + [1][0] + [2][0] ) / 3
* [0][1] [1][1] [2][1] ==> [1] = ( [0][1] + [1][1] + [2][1] ) / 3
* [0][2] [1][2] [2][2] ==> [2] = ( [0][2] + [1][2] + [2][2] ) / 3
* [0][3] [1][3] [2][3] ==> [3] = ( [0][3] + [1][3] + [2][3] ) / 3
* [0][4] [1][4] [2][4] ==> [4] = ( [0][4] + [1][4] + [2][4] ) / 3
*/
int mVectors = list.Count;
XYPT[] sum = new XYPT[0];
int nRowsMax = 0;
int[] n;
if (mVectors <= 0)
{
return(sum);
}
for (int iRow = 0; iRow < mVectors; iRow++)
{
if (nRowsMax < list[iRow].Count)
{
nRowsMax = list[iRow].Count;
}
}
// Create the array of sums
sum = new XYPT[nRowsMax];
if (nRowsMax <= 0)
{
return(sum);
}
n = new int[nRowsMax];
for (int iRow = 0; iRow < nRowsMax; iRow++)
{
sum[iRow] = XYPT.ZeroZero; // Zero the sums.
for (int jCol = 0; jCol < mVectors; jCol++)
{
int nXYPTs = list[jCol].Count;
if (1 <= nXYPTs && nXYPTs <= nRowsMax)
{
n[iRow]++;
sum[iRow] += list[jCol][iRow];
}
}
}
for (int iRow = 0; iRow < nRowsMax; iRow++)
{
sum[iRow] /= n[iRow];
}
return(sum);
}