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QuadGraph.pde
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Tue, Nov 19, 11:45

QuadGraph.pde
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import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.ArrayList;
import java.util.Map;
class QuadGraph {
boolean verbose=false;
List<int[]> cycles = new ArrayList<int[]>();
int[][] graph;
List<PVector> findBestQuad(List<PVector> lines, int width, int height, int max_quad_area, int min_quad_area, boolean verbose) {
this.verbose=verbose;
build(lines, width, height); //<>//
findCycles(verbose);
ArrayList<PVector> bestQuad=new ArrayList<PVector>();
float bestQuadArea=0;
for (int [] cy : cycles) {
ArrayList<PVector> quad= new ArrayList<PVector>();
PVector l1 = lines.get(cy[0]);
PVector l2 = lines.get(cy[1]);
PVector l3 = lines.get(cy[2]);
PVector l4 = lines.get(cy[3]);
quad.add(intersection(l1, l2));
quad.add(intersection(l2, l3));
quad.add(intersection(l3, l4));
quad.add(intersection(l4, l1));
quad=sortCorners(quad);
PVector c1 = quad.get(0);
PVector c2 = quad.get(1);
PVector c3 = quad.get(2);
PVector c4 = quad.get(3);
if (isConvex(c1, c2, c3, c4) &&
nonFlatQuad(c1, c2, c3, c4)) {
float quadArea=validArea(c1, c2, c3, c4, max_quad_area, min_quad_area);
if (quadArea>0 && quadArea>bestQuadArea) {
bestQuadArea=quadArea;
bestQuad=quad;
}
}
}
if (bestQuadArea>0)
return bestQuad;
else
return new ArrayList<PVector>();
}
void build(List<PVector> lines, int width, int height) {
int n = lines.size();
// The maximum possible number of edges is n * (n - 1)/2
graph = new int[n * (n - 1)/2][2];
int idx =0;
for (int i = 0; i < lines.size(); i++) {
for (int j = i + 1; j < lines.size(); j++) {
if (intersect(lines.get(i), lines.get(j), width, height)) {
graph[idx][0]=i;
graph[idx][1]=j;
idx++;
}
}
}
}
/** Returns true if polar lines 1 and 2 intersect
* inside an area of size (width, height)
*/
boolean intersect(PVector line1, PVector line2, int width, int height) {
double sin_t1 = Math.sin(line1.y);
double sin_t2 = Math.sin(line2.y);
double cos_t1 = Math.cos(line1.y);
double cos_t2 = Math.cos(line2.y);
float r1 = line1.x;
float r2 = line2.x;
double denom = cos_t2 * sin_t1 - cos_t1 * sin_t2;
int x = (int) ((r2 * sin_t1 - r1 * sin_t2) / denom);
int y = (int) ((-r2 * cos_t1 + r1 * cos_t2) / denom);
if (0 <= x && 0 <= y && width >= x && height >= y)
return true;
else
return false;
}
PVector intersection(PVector line1, PVector line2) {
double sin_t1 = Math.sin(line1.y);
double sin_t2 = Math.sin(line2.y);
double cos_t1 = Math.cos(line1.y);
double cos_t2 = Math.cos(line2.y);
float r1 = line1.x;
float r2 = line2.x;
double denom = cos_t2 * sin_t1 - cos_t1 * sin_t2;
int x = (int) ((r2 * sin_t1 - r1 * sin_t2) / denom);
int y = (int) ((-r2 * cos_t1 + r1 * cos_t2) / denom);
return new PVector(x,y);
}
void findCycles(boolean verbose) {
cycles.clear();
for (int i = 0; i < graph.length; i++) {
for (int j = 0; j < graph[i].length; j++) {
findNewCycles(new int[] {graph[i][j]});
}
}
if (verbose) {
for (int[] cy : cycles) {
String s = "" + cy[0];
for (int i = 1; i < cy.length; i++) {
s += "," + cy[i];
}
System.out.println(s);
}
}
}
void findNewCycles(int[] path)
{
int n = path[0];
int x;
int[] sub = new int[path.length + 1];
for (int i = 0; i < graph.length; i++)
for (int y = 0; y <= 1; y++)
if (graph[i][y] == n)
// edge refers to our current node
{
x = graph[i][(y + 1) % 2];
if (!visited(x, path))
// neighbor node not on path yet
{
sub[0] = x;
System.arraycopy(path, 0, sub, 1, path.length);
// explore extended path
findNewCycles(sub);
} else if ((path.length == 4) && (x == path[path.length - 1]))
// cycle found
{
int[] p = normalize(path);
int[] inv = invert(p);
if (isNew(p) && isNew(inv))
{
cycles.add(p);
}
}
}
}
// check of both arrays have same lengths and contents
Boolean equals(int[] a, int[] b)
{
Boolean ret = (a[0] == b[0]) && (a.length == b.length);
for (int i = 1; ret && (i < a.length); i++)
{
if (a[i] != b[i])
{
ret = false;
}
}
return ret;
}
// create a path array with reversed order
int[] invert(int[] path)
{
int[] p = new int[path.length];
for (int i = 0; i < path.length; i++)
{
p[i] = path[path.length - 1 - i];
}
return normalize(p);
}
// rotate cycle path such that it begins with the smallest node
int[] normalize(int[] path)
{
int[] p = new int[path.length];
int x = smallest(path);
int n;
System.arraycopy(path, 0, p, 0, path.length);
while (p[0] != x)
{
n = p[0];
System.arraycopy(p, 1, p, 0, p.length - 1);
p[p.length - 1] = n;
}
return p;
}
// compare path against known cycles
// return true, iff path is not a known cycle
Boolean isNew(int[] path)
{
Boolean ret = true;
for (int[] p : cycles)
{
if (equals(p, path))
{
ret = false;
break;
}
}
return ret;
}
// return the int of the array which is the smallest
int smallest(int[] path)
{
int min = path[0];
for (int p : path)
{
if (p < min)
{
min = p;
}
}
return min;
}
// check if vertex n is contained in path
Boolean visited(int n, int[] path)
{
Boolean ret = false;
for (int p : path)
{
if (p == n)
{
ret = true;
break;
}
}
return ret;
}
/** Check if a quad is convex or not.
*
* Algo: take two adjacent edges and compute their cross-product.
* The sign of the z-component of all the cross-products is the
* same for a convex polygon.
*
* See http://debian.fmi.uni-sofia.bg/~sergei/cgsr/docs/clockwise.htm
* for justification.
*
* @param c1
*/
boolean isConvex(PVector c1, PVector c2, PVector c3, PVector c4) {
PVector v21= PVector.sub(c1, c2);
PVector v32= PVector.sub(c2, c3);
PVector v43= PVector.sub(c3, c4);
PVector v14= PVector.sub(c4, c1);
float i1=v21.cross(v32).z;
float i2=v32.cross(v43).z;
float i3=v43.cross(v14).z;
float i4=v14.cross(v21).z;
if ( (i1>0 && i2>0 && i3>0 && i4>0)
|| (i1<0 && i2<0 && i3<0 && i4<0))
return true;
else if(verbose)
System.out.println("Eliminating non-convex quad");
return false;
}
/** Compute the area of a quad, and check it lays within a specific range
*/
float validArea(PVector c1, PVector c2, PVector c3, PVector c4, float max_area, float min_area) {
float i1=c1.cross(c2).z;
float i2=c2.cross(c3).z;
float i3=c3.cross(c4).z;
float i4=c4.cross(c1).z;
float area = Math.abs(0.5f * (i1 + i2 + i3 + i4));
if (area < max_area && area > min_area){
return area;
}
return 0;
}
/** Compute the (cosine) of the four angles of the quad, and check they are all large enough
* (the quad representing our board should be close to a rectangle)
*/
boolean nonFlatQuad(PVector c1, PVector c2, PVector c3, PVector c4) {
// cos(70deg) ~= 0.3
float min_cos = 0.5f;
PVector v21= PVector.sub(c1, c2);
PVector v32= PVector.sub(c2, c3);
PVector v43= PVector.sub(c3, c4);
PVector v14= PVector.sub(c4, c1);
float cos1=Math.abs(v21.dot(v32) / (v21.mag() * v32.mag()));
float cos2=Math.abs(v32.dot(v43) / (v32.mag() * v43.mag()));
float cos3=Math.abs(v43.dot(v14) / (v43.mag() * v14.mag()));
float cos4=Math.abs(v14.dot(v21) / (v14.mag() * v21.mag()));
if (cos1 < min_cos && cos2 < min_cos && cos3 < min_cos && cos4 < min_cos)
return true;
else {
if(verbose)
System.out.println("Flat quad");
return false;
}
}
ArrayList<PVector> sortCorners(ArrayList<PVector> quad) {
// 1 - Sort corners so that they are ordered clockwise
PVector a = quad.get(0);
PVector b = quad.get(2);
PVector center = new PVector((a.x+b.x)/2, (a.y+b.y)/2);
Collections.sort(quad, new CWComparator(center));
// 2 - Sort by upper left most corner
PVector origin = new PVector(0, 0);
float distToOrigin = 1000;
for (PVector p : quad) {
if (p.dist(origin) < distToOrigin) distToOrigin = p.dist(origin);
}
while (quad.get(0).dist(origin) != distToOrigin)
Collections.rotate(quad, 1);
return quad;
}
}
class CWComparator implements Comparator<PVector> {
PVector center;
public CWComparator(PVector center) {
this.center = center;
}
@Override
public int compare(PVector b, PVector d) {
if (Math.atan2(b.y-center.y, b.x-center.x)<Math.atan2(d.y-center.y, d.x-center.x))
return -1;
else return 1;
}
}

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