/// <summary>
/// Algorithm to find a minimal bounding rectangle (MBR) such that the MBR corresponds to a rectangle
/// with smallest possible area completely enclosing the polygon.
/// <para>From 'A Fast Algorithm for Generating a Minimal Bounding Rectangle' by Lennert D. Den Boer.</para>
/// </summary>
/// <param name="polygon">
/// Polygon P is assumed to be both simple and convex, and to contain no duplicate (coincident) vertices.
/// The vertices of P are assumed to be in strict cyclic sequential order, either clockwise or
/// counter-clockwise relative to the origin P0.
/// </param>
internal static PdfRectangle ParametricPerpendicularProjection(IReadOnlyList <PdfPoint> polygon)
{
if (polygon == null || polygon.Count == 0)
{
throw new ArgumentException("ParametricPerpendicularProjection(): polygon cannot be null and must contain at least one point.");
}
if (polygon.Count < 4)
{
if (polygon.Count == 1)
{
return(new PdfRectangle(polygon[0], polygon[0]));
}
else if (polygon.Count == 2)
{
return(new PdfRectangle(polygon[0], polygon[1]));
}
else
{
PdfPoint p3 = polygon[0].Add(polygon[1].Subtract(polygon[2]));
return(new PdfRectangle(p3, polygon[1], polygon[0], polygon[2]));
}
}
PdfPoint[] MBR = new PdfPoint[0];
double Amin = double.MaxValue;
double tmin = 1;
double tmax = 0;
double smax = 0;
int j = 1;
int k = 0;
int l = -1;
PdfPoint Q = new PdfPoint();
PdfPoint R0 = new PdfPoint();
PdfPoint R1 = new PdfPoint();
PdfPoint u = new PdfPoint();
int nv = polygon.Count;
while (true)
{
var Pk = polygon[k];
PdfPoint v = polygon[j].Subtract(Pk);
double r = 1.0 / v.DotProduct(v);
for (j = 0; j < nv; j++)
{
if (j == k)
{
continue;
}
PdfPoint Pj = polygon[j];
u = Pj.Subtract(Pk);
double t = u.DotProduct(v) * r;
PdfPoint Pt = new PdfPoint(t * v.X + Pk.X, t * v.Y + Pk.Y);
u = Pt.Subtract(Pj);
double s = u.DotProduct(u);
if (t < tmin)
{
tmin = t;
R0 = Pt;
}
if (t > tmax)
{
tmax = t;
R1 = Pt;
}
if (s > smax)
{
smax = s;
Q = Pt;
l = j;
}
}
if (l == -1)
{
// All points are colinear - rectangle has no area (need more tests)
var bottomLeft = polygon.OrderBy(p => p.X).ThenBy(p => p.Y).First();
var topRight = polygon.OrderByDescending(p => p.Y).OrderByDescending(p => p.X).First();
return(new PdfRectangle(bottomLeft, topRight, bottomLeft, topRight));
}
PdfPoint PlMinusQ = polygon[l].Subtract(Q);
PdfPoint R2 = R1.Add(PlMinusQ);
PdfPoint R3 = R0.Add(PlMinusQ);
u = R1.Subtract(R0);
double A = u.DotProduct(u) * smax;
if (A < Amin)
{
Amin = A;
MBR = new[] { R0, R1, R2, R3 };
}
k++;
j = k;
if (j == nv)
{
j = 0;
}
if (k == nv)
{
break;
}
}
return(new PdfRectangle(MBR[2], MBR[3], MBR[1], MBR[0]));
}
/// <summary>
/// Algorithm to find a minimal bounding rectangle (MBR) such that the MBR corresponds to a rectangle
/// with smallest possible area completely enclosing the polygon.
/// <para>From 'A Fast Algorithm for Generating a Minimal Bounding Rectangle' by Lennert D. Den Boer.</para>
/// </summary>
/// <param name="polygon">
/// Polygon P is assumed to be both simple and convex, and to contain no duplicate (coincident) vertices.
/// The vertices of P are assumed to be in strict cyclic sequential order, either clockwise or
/// counter-clockwise relative to the origin P0.
/// </param>
private static PdfRectangle ParametricPerpendicularProjection(IReadOnlyList <PdfPoint> polygon)
{
if (polygon == null || polygon.Count == 0)
{
throw new ArgumentException("ParametricPerpendicularProjection(): polygon cannot be null and must contain at least one point.", nameof(polygon));
}
else if (polygon.Count == 1)
{
return(new PdfRectangle(polygon[0], polygon[0]));
}
else if (polygon.Count == 2)
{
return(new PdfRectangle(polygon[0], polygon[1]));
}
PdfPoint[] MBR = new PdfPoint[0];
double Amin = double.PositiveInfinity;
int j = 1;
int k = 0;
PdfPoint Q = new PdfPoint();
PdfPoint R0 = new PdfPoint();
PdfPoint R1 = new PdfPoint();
PdfPoint u = new PdfPoint();
while (true)
{
PdfPoint Pk = polygon[k];
PdfPoint v = polygon[j].Subtract(Pk);
double r = 1.0 / v.DotProduct(v);
double tmin = 1;
double tmax = 0;
double smax = 0;
int l = -1;
for (j = 0; j < polygon.Count; j++)
{
PdfPoint Pj = polygon[j];
u = Pj.Subtract(Pk);
double t = u.DotProduct(v) * r;
PdfPoint Pt = new PdfPoint(t * v.X + Pk.X, t * v.Y + Pk.Y);
u = Pt.Subtract(Pj);
double s = u.DotProduct(u);
if (t < tmin)
{
tmin = t;
R0 = Pt;
}
if (t > tmax)
{
tmax = t;
R1 = Pt;
}
if (s > smax)
{
smax = s;
Q = Pt;
l = j;
}
}
if (l != -1)
{
PdfPoint PlMinusQ = polygon[l].Subtract(Q);
PdfPoint R2 = R1.Add(PlMinusQ);
PdfPoint R3 = R0.Add(PlMinusQ);
u = R1.Subtract(R0);
double A = u.DotProduct(u) * smax;
if (A < Amin)
{
Amin = A;
MBR = new[] { R0, R1, R2, R3 };
}
}
k++;
j = k + 1;
if (j == polygon.Count)
{
j = 0;
}
if (k == polygon.Count)
{
break;
}
}
return(new PdfRectangle(MBR[2], MBR[3], MBR[1], MBR[0]));
}
