Created
July 31, 2013 10:05
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Find largest convex area within a given shape
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/* | |
* Proof of concept for | |
* http://stackoverflow.com/a/17967201/1468366 | |
* http://math.stackexchange.com/a/456233/35416 | |
* | |
* Note: This code was written ONLY to get this single example image. | |
* It makes a number of implicit assumptions, and therefore won't be | |
* fit for general applications without some modifications. | |
* Furthermore, speedy coding was considered more important than | |
* performance at run time. | |
* | |
* 2013-07-31 Martin von Gagern | |
*/ | |
import java.awt.*; | |
import java.awt.geom.*; | |
import javax.swing.*; | |
import java.util.*; | |
import java.util.List; | |
class MX455687a extends JPanel { | |
Path2D.Double p, fp, convexParts, concaveParts; | |
List<Point2D.Double> pts; | |
List<Integer> inflectionPoints; | |
MX455687a() { | |
setPreferredSize(new Dimension(600, 600)); | |
initPath(); | |
flatten(); | |
findInflections(); | |
composeParts(); | |
opt(); | |
} | |
void initPath() { | |
double x, y; | |
p = new Path2D.Double(); | |
// These coordinates come from Inkscape. | |
p.moveTo(x = 237.68304, y = 996.48825-452.36218); | |
p.curveTo(x + 6.51879, y - 1.8326, | |
x + 21.80476, y - 7.8128, | |
x = x + 33.96883, y = y - 13.2891); | |
p.curveTo(x + 35.39892, y - 15.9369, | |
x + 57.77364, y - 20.8704, | |
x = x + 95.533, y = y - 21.0644); | |
p.curveTo(x + 17.94058, y - 0.092, | |
x + 46.49802, y + 1.5691, | |
x = x + 65.58485, y = y + 3.8151); | |
p.curveTo(x + 42.7117, y + 5.0265, | |
x + 67.20049, y + 3.9623, | |
x = x + 83.80193, y = y - 3.6408); | |
p.curveTo(x + 16.30881, y - 7.4692, | |
x + 26.86538, y - 17.33109, | |
x = x + 33.85875, y = y - 31.63035); | |
p.curveTo(x + 8.9218, y - 18.24244, | |
x + 9.37729, y - 36.65979, | |
x = x + 1.83938, y = y - 74.37299); | |
p.curveTo(x - 4.18125, y - 20.91934, | |
x - 6.16273, y - 37.79353, | |
x = x - 6.28951, y = y - 53.56106); | |
p.curveTo(x - 0.16743, y - 20.82869, | |
x + 0.39748, y - 24.26443, | |
x = x + 5.93532, y = y - 36.09556); | |
p.curveTo(x + 3.66125, y - 7.82194, | |
x + 11.82786, y - 18.98987, | |
x = x + 20.32519, y = y - 27.79488); | |
p.curveTo(x + 18.95025, y - 19.63646, | |
x + 23.84825, y - 30.72434, | |
x = x + 23.58954, y = y - 53.40104); | |
p.curveTo(595.26225, 635.6563-452.36218, | |
553.20055, 577.42-452.36218, | |
x = 499.75728, y = 552.43576-452.36218); | |
p.curveTo(x - 16.60094, y - 7.7608, | |
x - 23.50652, y - 8.25737, | |
x = x - 83.26282, y = y - 5.98713); | |
p.curveTo(x - 28.66827, y + 1.08916, | |
x - 44.1929, y - 3.69973, | |
x = x - 77.79958, y = y - 23.99885); | |
p.curveTo(x - 32.27854, y - 19.49689, | |
x - 40.26394, y - 22.01741, | |
x = x - 53.60573, y = y - 16.9202); | |
p.curveTo(x - 19.38047, y + 7.40425, | |
x - 23.91467, y + 17.04982, | |
x = x - 34.82266, y = y + 74.07759); | |
p.curveTo(x - 6.2155, y + 32.49513, | |
x - 13.92691, y + 50.61982, | |
x = x - 28.24379, y = y + 66.38345); | |
p.curveTo(x - 19.25485, y + 21.2006, | |
x - 38.95949, y + 30.19284, | |
x = x - 110.92011, y = y + 50.61855); | |
p.curveTo(x - 27.286991, y + 7.74529, | |
x - 56.347896, y + 16.65699, | |
x = x - 64.579815, y = y + 19.80378); | |
p.curveTo(16.76242, 727.7893-452.36218, | |
1.8467711, 745.44327-452.36218, | |
4.4516545, 766.20783-452.36218); | |
p.curveTo(7.6378213, 791.60621-452.36218, | |
16.690734, 807.26349-452.36218, | |
74.13503, 886.72752-452.36218); | |
p.curveTo(150.96578, 993.00915-452.36218, | |
180.22006, 1012.6424-452.36218, | |
237.68304, 996.48825-452.36218); | |
p.closePath(); | |
} | |
void flatten() { | |
fp = new Path2D.Double(); | |
fp.append(p.getPathIterator(null, 0.1), false); | |
pts = new ArrayList<Point2D.Double>(); | |
double[] coords = new double[6]; | |
for (PathIterator pi = fp.getPathIterator(null); | |
!pi.isDone(); pi.next()) { | |
if (pi.currentSegment(coords) != PathIterator.SEG_CLOSE) | |
pts.add(new Point2D.Double(coords[0], coords[1])); | |
} | |
} | |
void findInflections() { | |
inflectionPoints = new ArrayList<Integer>(); | |
Point2D.Double a = pts.get(pts.size() - 2); | |
Point2D.Double b = pts.get(0), c; | |
double oldDet = -1, det; | |
// negative det means convex due to the orientation of the path | |
// the initial vertex has negative det due to the starting point | |
for (int i = 1; i != pts.size(); ++i) { | |
c = pts.get(i); | |
det = a.x*b.y + b.x*c.y + c.x*a.y - a.y*b.x - b.y*c.x - c.y*a.x; | |
if (det * oldDet < 0) { | |
System.out.println("At " + i + "/" + pts.size() + | |
" from " + oldDet + " to " + det); | |
inflectionPoints.add(det < 0 ? i - 1 : i); | |
} | |
a = b; | |
b = c; | |
oldDet = det; | |
} | |
} | |
void composeParts() { | |
convexParts = new Path2D.Double(); | |
concaveParts = new Path2D.Double(); | |
Point2D.Double p; | |
int begin, end; | |
for (int i = 0; i < inflectionPoints.size(); i += 2) { | |
begin = inflectionPoints.get(i); | |
end = inflectionPoints.get(i + 1); | |
p = pts.get(begin); | |
concaveParts.moveTo(p.x, p.y); | |
for (int j = begin + 1; j <= end; ++j) { | |
p = pts.get(j); | |
concaveParts.lineTo(p.x, p.y); | |
} | |
} | |
for (int i = 1; i < inflectionPoints.size() - 1; i += 2) { | |
begin = inflectionPoints.get(i); | |
end = inflectionPoints.get(i + 1); | |
p = pts.get(begin); | |
convexParts.moveTo(p.x, p.y); | |
for (int j = begin + 1; j <= end; ++j) { | |
p = pts.get(j); | |
convexParts.lineTo(p.x, p.y); | |
} | |
} | |
begin = inflectionPoints.get(inflectionPoints.size() - 1); | |
end = pts.size(); | |
p = pts.get(begin); | |
convexParts.moveTo(p.x, p.y); | |
for (int j = begin + 1; j < end; ++j) { | |
p = pts.get(j); | |
convexParts.lineTo(p.x, p.y); | |
} | |
end = inflectionPoints.get(0); | |
for (int j = 0; j <= end; ++j) { | |
p = pts.get(j); | |
convexParts.lineTo(p.x, p.y); | |
} | |
} | |
double bestValue; | |
Shape bestShape; | |
List<Line2D> lines, bestLines; | |
void opt() { | |
bestValue = 0; | |
lines = new ArrayList<Line2D>(); | |
opt(0, new Area(fp)); | |
} | |
void opt(int i, Area a1) { | |
if (i == inflectionPoints.size()) { | |
double a = area(a1); | |
if (a > bestValue) { | |
bestValue = a; | |
bestShape = a1; | |
bestLines = new ArrayList<Line2D>(lines); | |
} | |
return; | |
} | |
int begin = inflectionPoints.get(i), end = inflectionPoints.get(i + 1); | |
Point2D.Double a = pts.get(begin - 1), b; | |
for (int j = begin; j <= end + 1; ++j) { | |
b = pts.get(j); | |
double f = 1200/a.distance(b); | |
double dx = f*(b.x - a.x), dy = f*(b.y - a.y); | |
Path2D.Double p = new Path2D.Double(); | |
p.moveTo(a.x - dx , a.y - dy ); | |
p.lineTo(a.x - dx + dy, a.y - dy - dx); | |
p.lineTo(a.x + dx + dy, a.y + dy - dx); | |
p.lineTo(a.x + dx , a.y + dy ); | |
p.closePath(); | |
Area a2 = new Area(a1); | |
a2.intersect(new Area(p)); | |
lines.add(new Line2D.Double(a.x - dx, a.y - dy, | |
a.x + dx, a.y + dy)); | |
opt(i + 2, a2); | |
lines.remove(lines.size() - 1); | |
a = b; | |
} | |
} | |
double area(Shape s) { | |
double total = 0, part = 0; | |
double[] coords = new double[6]; | |
Point2D.Double initial = null; | |
double ax = 0, ay = 0, bx, by; | |
for (PathIterator pi = s.getPathIterator(null); | |
!pi.isDone(); pi.next()) { | |
switch (pi.currentSegment(coords)) { | |
case PathIterator.SEG_MOVETO: | |
ax = coords[0]; | |
ay = coords[1]; | |
initial = new Point2D.Double(ax, ay); | |
part = 0; | |
break; | |
case PathIterator.SEG_CLOSE: | |
bx = initial.x; | |
by = initial.y; | |
part += ax*by - bx*ay; | |
total += part; | |
part = 0; | |
ax = bx; | |
ay = by; | |
break; | |
case PathIterator.SEG_LINETO: | |
bx = coords[0]; | |
by = coords[1]; | |
part += ax*by - bx*ay; | |
ax = bx; | |
ay = by; | |
break; | |
default: | |
throw new IllegalArgumentException("Non-flat shape"); | |
} | |
} | |
if (total < 0) | |
total = -total; | |
return total; | |
} | |
@Override public void paintComponent(Graphics g) { | |
Graphics2D g2d = (Graphics2D)g; | |
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING, | |
RenderingHints.VALUE_ANTIALIAS_ON); | |
g2d.setRenderingHint(RenderingHints.KEY_STROKE_CONTROL, | |
RenderingHints.VALUE_STROKE_PURE); | |
g2d.setColor(Color.WHITE); | |
g2d.fillRect(0, 0, getWidth(), getHeight()); | |
g2d.setColor(new Color(128, 255, 128)); | |
g2d.fill(bestShape); | |
g2d.setColor(Color.BLUE); | |
g2d.setStroke(new BasicStroke(1.25f)); | |
for (Line2D l: bestLines) | |
g2d.draw(l); | |
g2d.setStroke(new BasicStroke(2.f)); | |
g2d.setColor(Color.BLACK); | |
g2d.draw(convexParts); | |
g2d.setColor(Color.RED); | |
g2d.draw(concaveParts); | |
} | |
public static void main(String[] args) { | |
JFrame f = new JFrame(); | |
f.getContentPane().add(new MX455687a()); | |
f.pack(); | |
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); | |
f.setVisible(true); | |
} | |
} |
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