/// <summary>
/// Gets the circumference of a closed polygon.
/// </summary>
/// <param name="closedPolygon">The closed polygon.</param>
/// <returns>The circumference of the given closed polygon.</returns>
public static double GetClosedPolygonCircumference(IEnumerable <IntPoint> closedPolygon)
{
IntPoint firstPoint = default;
IntPoint previous = default;
double sum = 0.0;
var numberOfPoints = 0;
foreach (var pt in closedPolygon)
{
if (0 == numberOfPoints)
{
firstPoint = pt;
}
else
{
sum += Math.Sqrt((double)(Int128.Int128Mul(pt.X - previous.X, pt.X - previous.X) + Int128.Int128Mul(pt.Y - previous.Y, pt.Y - previous.Y)));
}
previous = pt;
++numberOfPoints;
}
if (numberOfPoints == 0)
{
throw new ArgumentException("Polygon is empty (has no point at all)", nameof(closedPolygon));
}
else
{
var pt = firstPoint;
sum += Math.Sqrt((double)(Int128.Int128Mul(pt.X - previous.X, pt.X - previous.X) + Int128.Int128Mul(pt.Y - previous.Y, pt.Y - previous.Y)));
return(sum);
}
}
/// <summary>
/// Calculates the 2nd moments of the given closed polygon. The polygon
/// has to be non-selfintersecting!
/// </summary>
/// <param name="closedPolygon">The closed polygon.</param>
/// <returns>The second moments, Ixx, Iyy, and Ixy, of the given polygon (with respect to the origin (x=0, y=0)).</returns>
/// <seealso href="https://en.wikipedia.org/wiki/Second_moment_of_area"/>
public static (double Ixx, double Iyy, double Ixy) GetClosedPolygonSecondMoments(IEnumerable <IntPoint> closedPolygon)
{
IntPoint firstPoint = default;
IntPoint previous = default;
var numberOfPoints = 0;
double sumX = 0;
double sumY = 0;
double sumXY = 0;
Int128 s;
foreach (var pt in closedPolygon)
{
if (numberOfPoints == 0)
{
firstPoint = pt;
}
else
{
s = (Int128.Int128Mul(previous.X, pt.Y) - Int128.Int128Mul(previous.Y, pt.X));
sumX += (Pow2(previous.Y) + previous.Y * pt.Y + Pow2(pt.Y)) * (double)s;
sumY += (Pow2(previous.X) + previous.X * pt.X + Pow2(pt.X)) * (double)s;
sumXY += (previous.X * pt.Y + 2 * previous.X * previous.Y + 2 * pt.X * pt.Y + pt.X * previous.Y) * (double)s;
}
previous = pt;
++numberOfPoints;
}
if (numberOfPoints == 0)
{
throw new ArgumentException("Polygon is empty (has no point at all)", nameof(closedPolygon));
}
else if (numberOfPoints == 1)
{
return(0, 0, 0);
}
else if (numberOfPoints == 2)
{
return(0, 0, 0);
}
else
{
s = (Int128.Int128Mul(previous.X, firstPoint.Y) - Int128.Int128Mul(previous.Y, firstPoint.X));
var pt = firstPoint;
sumX += (Pow2(previous.Y) + previous.Y * pt.Y + Pow2(pt.Y)) * (double)s;
sumY += (Pow2(previous.X) + previous.X * pt.X + Pow2(pt.X)) * (double)s;
sumXY += (previous.X * pt.Y + 2 * previous.X * previous.Y + 2 * pt.X * pt.Y + pt.X * previous.Y) * (double)s;
sumX /= 6;
sumY /= 6;
sumXY /= 12;
return(sumX, sumY, sumXY);
}
}
/// <summary>
/// Calculate the center of gravity (centroid) of the given closed polygon. The polygon
/// has to be non-selfintersecting!
/// </summary>
/// <param name="closedPolygon">The closed polygon.</param>
/// <returns>The center of gravity of the given polygon.</returns>
/// <seealso href="https://en.wikipedia.org/wiki/Centroid"/>
public static PointD2D GetClosedPolygonCentroid(IEnumerable <IntPoint> closedPolygon)
{
IntPoint firstPoint = default;
IntPoint previous = default;
var numberOfPoints = 0;
double sumX = 0;
double sumY = 0;
Int128 s;
var sumS = new Int128(0);
foreach (var pt in closedPolygon)
{
if (numberOfPoints == 0)
{
firstPoint = pt;
}
else
{
s = (Int128.Int128Mul(previous.X, pt.Y) - Int128.Int128Mul(previous.Y, pt.X));
sumS += s;
sumX += (previous.X + pt.X) * (double)s;
sumY += (previous.Y + pt.Y) * (double)s;
}
previous = pt;
++numberOfPoints;
}
if (numberOfPoints == 0)
{
throw new ArgumentException("Polygon is empty (has no point at all)", nameof(closedPolygon));
}
else if (numberOfPoints == 1)
{
return(new PointD2D(firstPoint.X, firstPoint.Y));
}
else if (numberOfPoints == 2)
{
return(new PointD2D((firstPoint.X + previous.X) / 2, (firstPoint.Y + previous.Y) / 2));
}
else
{
s = (Int128.Int128Mul(previous.X, firstPoint.Y) - Int128.Int128Mul(previous.Y, firstPoint.X));
sumS += s;
sumX += (previous.X + firstPoint.X) * (double)s;
sumY += (previous.Y + firstPoint.Y) * (double)s;
sumX /= (3 * (double)sumS);
sumY /= (3 * (double)sumS);
return(new PointD2D(sumX, sumY));
}
}
/// <summary>
/// Gets the area of a closed polygon.
/// </summary>
/// <param name="closedPolygon">The points forming a closed polygon.</param>
/// <returns>The polygon area. The value is signed. The sign is positive if the polygon is counter-clockwise (in a coordinate system in which x is to the right and y is up).</returns>
public static double GetClosedPolygonArea(IEnumerable <IntPoint> closedPolygon)
{
IntPoint firstPoint = default;
IntPoint previous = default;
var sum = new Int128(0);
var numberOfPoints = 0;
foreach (var pt in closedPolygon)
{
if (0 == numberOfPoints)
{
firstPoint = pt;
}
else
{
sum += (Int128.Int128Mul(previous.X, pt.Y) - Int128.Int128Mul(previous.Y, pt.X));
}
previous = pt;
++numberOfPoints;
}
if (numberOfPoints == 0)
{
throw new ArgumentException("Polygon is empty (has no point at all)", nameof(closedPolygon));
}
else if (numberOfPoints == 1)
{
return(0);
}
else if (numberOfPoints == 2)
{
return(0);
}
else
{
sum += (Int128.Int128Mul(previous.X, firstPoint.Y) - Int128.Int128Mul(previous.Y, firstPoint.X));
return((double)sum / 2.0);
}
}
public static bool PointOnLineSegment(IntPoint pt,
IntPoint linePt1, IntPoint linePt2, bool UseFullRange)
{
if (UseFullRange)
{
return(((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
(((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
((Int128.Int128Mul((pt.X - linePt1.X), (linePt2.Y - linePt1.Y)) ==
Int128.Int128Mul((linePt2.X - linePt1.X), (pt.Y - linePt1.Y))))));
}
else
{
return(((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
(((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
((pt.X - linePt1.X) * (linePt2.Y - linePt1.Y) ==
(linePt2.X - linePt1.X) * (pt.Y - linePt1.Y))));
}
}
