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- fix minimum area rectangle algo and make it public

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- add tests
- tidy up code
This commit is contained in:
BobLd
2020-03-15 15:04:03 +00:00
committed by Eliot Jones
parent bd6b03c2e8
commit c1a1fa1f7f
2 changed files with 517 additions and 63 deletions
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121
src/UglyToad.PdfPig/Geometry/GeometryExtensions.cs
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@@ -65,57 +65,45 @@
/// 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)
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.");
throw new ArgumentException("ParametricPerpendicularProjection(): polygon cannot be null and must contain at least one point.", nameof(polygon));
}
if (polygon.Count < 4)
else if (polygon.Count == 1)
{
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]);
}
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.MaxValue;
double tmin = 1;
double tmax = 0;
double smax = 0;
double Amin = double.PositiveInfinity;
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 Pk = polygon[k];
PdfPoint v = polygon[j].Subtract(Pk);
double r = 1.0 / v.DotProduct(v);
for (j = 0; j < nv; j++)
double tmin = 1;
double tmax = 0;
double smax = 0;
int l = -1;
for (j = 0; j < polygon.Count; j++)
{
if (j == k) continue;
PdfPoint Pj = polygon[j];
u = Pj.Subtract(Pk);
double t = u.DotProduct(v) * r;
@@ -143,37 +131,48 @@
}
}
if (l == -1)
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);
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;
u = R1.Subtract(R0);
if (A < Amin)
{
Amin = A;
MBR = new[] { R0, R1, R2, R3 };
double A = u.DotProduct(u) * smax;
if (A < Amin)
{
Amin = A;
MBR = new[] { R0, R1, R2, R3 };
}
}
k++;
j = k;
j = k + 1;
if (j == nv) j = 0;
if (k == nv) break;
if (j == polygon.Count) j = 0;
if (k == polygon.Count) break;
}
return new PdfRectangle(MBR[2], MBR[3], MBR[1], MBR[0]);
}
/// <summary>
/// Algorithm to find the (oriented) minimum area rectangle (MAR) by first finding the convex hull of the points
/// and then finding its MAR.
/// </summary>
/// <param name="points">The points.</param>
public static PdfRectangle MinimumAreaRectangle(IEnumerable<PdfPoint> points)
{
if (points == null || points.Count() == 0)
{
throw new ArgumentException("MinimumAreaRectangle(): points cannot be null and must contain at least one point.", nameof(points));
}
return ParametricPerpendicularProjection(GrahamScan(points.Distinct()).ToList());
}
/// <summary>
/// Algorithm to find the oriented bounding box (OBB) by first fitting a line through the points to get the slope,
/// then rotating the points to obtain the axis-aligned bounding box (AABB), and then rotating back the AABB.
@@ -241,10 +240,10 @@
if (points.Count() < 3) return points;
Func<PdfPoint, PdfPoint, double> polarAngle = (PdfPoint point1, PdfPoint point2) =>
double polarAngle(PdfPoint point1, PdfPoint point2)
{
return Math.Atan2(point2.Y - point1.Y, point2.X - point1.X) % Math.PI;
};
}
Stack<PdfPoint> stack = new Stack<PdfPoint>();
var sortedPoints = points.OrderBy(p => p.Y).ThenBy(p => p.X).ToList();
@@ -607,25 +606,25 @@
{
if (!IntersectsWith(p11, p12, p21, p22)) return null;
var eq1 = GetSlopeIntercept(p11, p12);
var eq2 = GetSlopeIntercept(p21, p22);
var (Slope1, Intercept1) = GetSlopeIntercept(p11, p12);
var (Slope2, Intercept2) = GetSlopeIntercept(p21, p22);
if (double.IsNaN(eq1.Slope))
if (double.IsNaN(Slope1))
{
var x = eq1.Intercept;
var y = eq2.Slope * x + eq2.Intercept;
var x = Intercept1;
var y = Slope2 * x + Intercept2;
return new PdfPoint(x, y);
}
else if (double.IsNaN(eq2.Slope))
else if (double.IsNaN(Slope2))
{
var x = eq2.Intercept;
var y = eq1.Slope * x + eq1.Intercept;
var x = Intercept2;
var y = Slope1 * x + Intercept1;
return new PdfPoint(x, y);
}
else
{
var x = (eq2.Intercept - eq1.Intercept) / (eq1.Slope - eq2.Slope);
var y = eq1.Slope * x + eq1.Intercept;
var x = (Intercept2 - Intercept1) / (Slope1 - Slope2);
var y = Slope1 * x + Intercept1;
return new PdfPoint(x, y);
}
}
@@ -875,7 +874,7 @@
else // Casus irreducibilis
{
// François Viète's formula
Func<double, double, double, double> vietTrigonometricSolution = (p_, q_, k) => 2.0 * Math.Sqrt(-p_ / 3.0)
double vietTrigonometricSolution(double p_, double q_, double k) => 2.0 * Math.Sqrt(-p_ / 3.0)
* Math.Cos(OneThird * Math.Acos((3.0 * q_) / (2.0 * p_) * Math.Sqrt(-3.0 / p_)) - (2.0 * Math.PI * k) / 3.0);
double p = Q * 3.0; // (3.0 * a * c - b * b) / (3.0 * aSquared);