private static double[] IntersectT(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
// if the bounding boxes do not intersect, they cannot intersect
var bezierBbox = bezierCurve.GetBoundingRectangle();
if (!bezierBbox.HasValue)
{
return(null);
}
if (bezierBbox.Value.Left > Math.Max(p1.X, p2.X) || Math.Min(p1.X, p2.X) > bezierBbox.Value.Right)
{
return(null);
}
if (bezierBbox.Value.Top < Math.Min(p1.Y, p2.Y) || Math.Max(p1.Y, p2.Y) < bezierBbox.Value.Bottom)
{
return(null);
}
double A = (p2.Y - p1.Y);
double B = (p1.X - p2.X);
double C = p1.X * (p1.Y - p2.Y) + p1.Y * (p2.X - p1.X);
double alpha = bezierCurve.StartPoint.X * A + bezierCurve.StartPoint.Y * B;
double beta = 3.0 * (bezierCurve.FirstControlPoint.X * A + bezierCurve.FirstControlPoint.Y * B);
double gamma = 3.0 * (bezierCurve.SecondControlPoint.X * A + bezierCurve.SecondControlPoint.Y * B);
double delta = bezierCurve.EndPoint.X * A + bezierCurve.EndPoint.Y * B;
double a = -alpha + beta - gamma + delta;
double b = 3 * alpha - 2 * beta + gamma;
double c = -3 * alpha + beta;
double d = alpha + C;
var solution = SolveCubicEquation(a, b, c, d);
return(solution.Where(s => !double.IsNaN(s)).Where(s => s >= -epsilon && (s - 1) <= epsilon).OrderBy(s => s).ToArray());
}
/// <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>
/// Whether the line segment contains the point.
/// </summary>
public static bool Contains(this PdfPath.Line line, PdfPoint point)
{
return(Contains(line.From, line.To, point));
}
/// <summary>
/// Whether the line segment contains the point.
/// </summary>
public static bool Contains(this PdfLine line, PdfPoint point)
{
return(Contains(line.Point1, line.Point2, point));
}
internal PdfRectangle(PdfPoint point1, PdfPoint point2) : this(point1.X, point1.Y, point2.X, point2.Y)
{
}
/// <summary>
/// Get the <see cref="PdfPoint"/> that is the intersection of two lines.
/// </summary>
public static PdfPoint?Intersect(this Line line, Line other)
{
// if the bounding boxes do not intersect, the lines cannot intersect
var thisLineBbox = line.GetBoundingRectangle();
if (!thisLineBbox.HasValue)
{
return(null);
}
var lineBbox = other.GetBoundingRectangle();
if (!lineBbox.HasValue)
{
return(null);
}
if (!thisLineBbox.Value.IntersectsWith(lineBbox.Value))
{
return(null);
}
var eq1 = GetSlopeIntercept(line.From, line.To);
var eq2 = GetSlopeIntercept(other.From, other.To);
if (double.IsNaN(eq1.Slope) && double.IsNaN(eq2.Slope))
{
return(null); // both lines are vertical (hence parallel)
}
if (eq1.Slope == eq2.Slope)
{
return(null); // both lines are parallel
}
var intersection = new PdfPoint();
if (double.IsNaN(eq1.Slope))
{
var x = eq1.Intercept;
var y = eq2.Slope * x + eq2.Intercept;
intersection = new PdfPoint(x, y);
}
else if (double.IsNaN(eq2.Slope))
{
var x = eq2.Intercept;
var y = eq1.Slope * x + eq1.Intercept;
intersection = new PdfPoint(x, y);
}
else
{
var x = (eq2.Intercept - eq1.Intercept) / (eq1.Slope - eq2.Slope);
var y = eq1.Slope * x + eq1.Intercept;
intersection = new PdfPoint(x, y);
}
// check if the intersection point belongs to both segments
// (for the moment we only know it belongs to both lines)
if (!line.Contains(intersection))
{
return(null);
}
if (!other.Contains(intersection))
{
return(null);
}
return(intersection);
}
/// <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]));
}
private static bool IntersectsWith(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
return(Intersect(bezierCurve, p1, p2).Length > 0);
}
/// <summary>
/// Create a new <see cref="Line"/>.
/// </summary>
public Line(PdfPoint from, PdfPoint to)
{
From = from;
To = to;
}
/// <summary>
/// Create a Bezier curve at the provided points.
/// </summary>
public BezierCurve(PdfPoint startPoint, PdfPoint firstControlPoint, PdfPoint secondControlPoint, PdfPoint endPoint)
{
StartPoint = startPoint;
FirstControlPoint = firstControlPoint;
SecondControlPoint = secondControlPoint;
EndPoint = endPoint;
}
/// <summary>
/// Create a new <see cref="Move"/> path command.
/// </summary>
/// <param name="location"></param>
public Move(PdfPoint location)
{
Location = location;
}
/// <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]));
}
double[] MBR = new double[8];
double Amin = double.PositiveInfinity;
int j = 1;
int k = 0;
double QX = double.NaN;
double QY = double.NaN;
double R0X = double.NaN;
double R0Y = double.NaN;
double R1X = double.NaN;
double R1Y = double.NaN;
while (true)
{
PdfPoint Pk = polygon[k];
PdfPoint Pj = polygon[j];
double vX = Pj.X - Pk.X;
double vY = Pj.Y - Pk.Y;
double r = 1.0 / (vX * vX + vY * vY);
double tmin = 1;
double tmax = 0;
double smax = 0;
int l = -1;
double uX;
double uY;
for (j = 0; j < polygon.Count; j++)
{
Pj = polygon[j];
uX = Pj.X - Pk.X;
uY = Pj.Y - Pk.Y;
double t = (uX * vX + uY * vY) * r;
double PtX = t * vX + Pk.X;
double PtY = t * vY + Pk.Y;
uX = PtX - Pj.X;
uY = PtY - Pj.Y;
double s = uX * uX + uY * uY;
if (t < tmin)
{
tmin = t;
R0X = PtX;
R0Y = PtY;
}
if (t > tmax)
{
tmax = t;
R1X = PtX;
R1Y = PtY;
}
if (s > smax)
{
smax = s;
QX = PtX;
QY = PtY;
l = j;
}
}
if (l != -1)
{
PdfPoint Pl = polygon[l];
double PlMinusQX = Pl.X - QX;
double PlMinusQY = Pl.Y - QY;
double R2X = R1X + PlMinusQX;
double R2Y = R1Y + PlMinusQY;
double R3X = R0X + PlMinusQX;
double R3Y = R0Y + PlMinusQY;
uX = R1X - R0X;
uY = R1Y - R0Y;
double A = (uX * uX + uY * uY) * smax;
if (A < Amin)
{
Amin = A;
MBR = new[] { R0X, R0Y, R1X, R1Y, R2X, R2Y, R3X, R3Y };
}
}
k++;
j = k + 1;
if (j == polygon.Count)
{
j = 0;
}
if (k == polygon.Count)
{
break;
}
}
return(new PdfRectangle(new PdfPoint(MBR[4], MBR[5]),
new PdfPoint(MBR[6], MBR[7]),
new PdfPoint(MBR[2], MBR[3]),
new PdfPoint(MBR[0], MBR[1])));
}
public PdfRectangle(PdfPoint point1, PdfPoint point2) : this(point1.X, point1.Y, point2.X, point2.Y)
{
}
/// <summary>
/// Whether the line formed by <paramref name="p11"/> and <paramref name="p12"/>
/// intersects the line formed by <paramref name="p21"/> and <paramref name="p22"/>.
/// </summary>
public static bool IntersectsWith(PdfPoint p11, PdfPoint p12, PdfPoint p21, PdfPoint p22)
{
return((ccw(p11, p12, p21) != ccw(p11, p12, p22)) &&
(ccw(p21, p22, p11) != ccw(p21, p22, p12)));
}
/// <summary>
/// Return true if the points are in counter-clockwise order.
/// </summary>
/// <param name="point1">The first point.</param>
/// <param name="point2">The second point.</param>
/// <param name="point3">The third point.</param>
private static bool ccw(PdfPoint point1, PdfPoint point2, PdfPoint point3)
{
return((point2.X - point1.X) * (point3.Y - point1.Y) > (point2.Y - point1.Y) * (point3.X - point1.X));
}
private static bool ParallelTo(PdfPoint p11, PdfPoint p12, PdfPoint p21, PdfPoint p22)
{
return(Math.Abs((p12.Y - p11.Y) * (p22.X - p21.X) - (p22.Y - p21.Y) * (p12.X - p11.X)) < epsilon);
}
/// <summary>
/// Get the dot product of both points.
/// </summary>
/// <param name="point1">The first point.</param>
/// <param name="point2">The second point.</param>
public static double DotProduct(this PdfPoint point1, PdfPoint point2)
{
return(point1.X * point2.X + point1.Y * point2.Y);
}
private static PdfPoint[] Intersect(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
var ts = IntersectT(bezierCurve, p1, p2);
if (ts == null || ts.Length == 0)
{
return(EmptyArray <PdfPoint> .Instance);
}
List <PdfPoint> points = new List <PdfPoint>();
foreach (var t in ts)
{
PdfPoint point = new PdfPoint(
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.X,
bezierCurve.FirstControlPoint.X,
bezierCurve.SecondControlPoint.X,
bezierCurve.EndPoint.X,
t),
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.Y,
bezierCurve.FirstControlPoint.Y,
bezierCurve.SecondControlPoint.Y,
bezierCurve.EndPoint.Y,
t));
if (Contains(p1, p2, point))
{
points.Add(point);
}
}
return(points.ToArray());
}
/// <summary>
/// Get a point with the summed coordinates of both points.
/// </summary>
/// <param name="point1">The first point.</param>
/// <param name="point2">The second point.</param>
public static PdfPoint Add(this PdfPoint point1, PdfPoint point2)
{
return(new PdfPoint(point1.X + point2.X, point1.Y + point2.Y));
}
private static (double Slope, double Intercept) GetSlopeIntercept(PdfPoint point1, PdfPoint point2)
{
if (Math.Abs(point1.X - point2.X) > epsilon)
{
var slope = (point2.Y - point1.Y) / (point2.X - point1.X);
var intercept = point2.Y - slope * point2.X;
return(slope, intercept);
}
else
{
// vertical line special case
return(double.NaN, point1.X);
}
}
/// <summary>
/// Get a point with the substracted coordinates of both points.
/// </summary>
/// <param name="point1">The first point.</param>
/// <param name="point2">The second point.</param>
public static PdfPoint Subtract(this PdfPoint point1, PdfPoint point2)
{
return(new PdfPoint(point1.X - point2.X, point1.Y - point2.Y));
}
private static (double Slope, double Intercept) GetSlopeIntercept(PdfPoint point1, PdfPoint point2)
{
if ((point1.X - point2.X) != 0) // vertical line special case
{
var slope = (double)((point2.Y - point1.Y) / (point2.X - point1.X));
var intercept = (double)point2.Y - slope * (double)point2.X;
return(slope, intercept);
}
else
{
return(double.NaN, (double)point1.X);
}
}
/// <summary>
/// Create a new <see cref="PdfLine"/>.
/// </summary>
/// <param name="point1">First point of the line.</param>
/// <param name="point2">Second point of the line.</param>
public PdfLine(PdfPoint point1, PdfPoint point2)
{
Point1 = point1;
Point2 = point2;
}
