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border.cpp
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#include "border.h"
/* Cell geometry parameter calculation
*
* TODO: Fix full[0], [1] and [2] EVERYWHERE
*
* */
void pre_cell_geometry(double array[5], gasCell cell, int i, int j) {
double full[5];
full[0] = M_PI*(2*(j-axis_j)+0.5)*pow(dr,2)*dx;
full[1] = M_PI*(2*(j-axis_j)+1)*pow(dr,2);
full[2] = M_PI*(2*(j-axis_j)+1)*pow(dr,2);
full[3] = 2*M_PI*(j-axis_j)*dr*dx;
full[4] = 2*M_PI*(j-axis_j+1)*dr*dx;
switch (cell.type) {
case 0:
array[0] = 1;
array[1] = 1;
array[2] = 1;
array[3] = 1;
array[4] = 1;
break;
case 1:
array[0] = (2*M_PI * (j*dr + (cell.r_1*dr + cell.r_2*dr)/2) * (cell.r_1*dr + cell.r_2*dr)/2 * dx) / full[0] ;
array[1] = (M_PI * (2*j*dr*cell.r_1*dr + pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = (M_PI * (2*j*dr*cell.r_2*dr + pow(cell.r_2*dr, 2))) / full[2] ;
array[3] = 1;
array[4] = 0;
// array[0] = ((j-1)*(cell.r_1+cell.r_2) + cell.r_1*cell.r_2 +
// pow(cell.r_2-cell.r_1, 2)/3) / (2*j-1);
// array[1] = cell.r_1 * (j-1+cell.r_1/2) / (j-0.5);
// array[2] = cell.r_2 * (j-1+cell.r_2/2) / (j-0.5);
// array[3] = 1;
// array[4] = 0;
break;
case 2:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI * (j*dr + (cell.r_1*dr + cell.r_2*dr)/2) * (cell.r_1*dr + cell.r_2*dr)/2 * dx) / full[0] ;
array[1] = (M_PI * (2*(j+1)*dr*cell.r_1*dr - pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = (M_PI * (2*(j+1)*dr*cell.r_2*dr - pow(cell.r_2*dr, 2))) / full[2] ;
array[3] = 0;
array[4] = 1;
break;
case 3:
array[0] = (2*M_PI * (j*dr + dr/2) * (cell.x_1*dx + cell.x_2*dx)/2 * dr) / full[0] ;
array[1] = 1;
array[2] = 0;
array[3] = (2*M_PI*j*cell.x_1*dx*dr) / full[3] ;
array[4] = (2*M_PI*(j+1)*cell.x_2*dx*dr) / full[4] ;
// array[0] = (j*cell.x_2 + (j-1)*cell.x_1 - (cell.x_2 - cell.x_1)/3) / (2*j-1);
// array[1] = 1;
// array[2] = 0;
// array[3] = cell.x_1;
// array[4] = cell.x_2;
break;
case 4:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI * (j*dr + dr/2) * (cell.x_1*dx + cell.x_2*dx)/2 * dr) / full[0] ;
array[1] = 0;
array[2] = 1;
array[3] = (2*M_PI*j*(dx - cell.x_1*dx)*dr) / full[3] ;
array[4] = (2*M_PI*j*(dx - cell.x_2*dx)*dr) / full[4] ;
break;
case 5:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI*(j*dr + cell.r_1*dr + (dr-cell.r_1*dr)/2) * (dr-cell.r_1*dr)*cell.x_2*dx/2) / full[0] ;
array[1] = (M_PI*(2*j*dr*cell.r_1*dr + pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = 1;
array[3] = 1;
array[4] = (2*M_PI*j*(dx-cell.x_2*dx)*dr) / full[4] ;
break;
case 6:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI*(j*dr + cell.r_1*dr/2) * cell.r_1*dr*cell.x_1*dx / 2) / full[0] ;
array[1] = (M_PI*(2*(j+1)*dr*cell.r_1*dr - pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = 1;
array[3] = (2*M_PI*j*(dx - cell.x_1*dx)*dr) / full[3] ;
array[4] = 1;
break;
case 7:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI*(j*dr + cell.r_1*dr/2)*cell.r_1*dr * (dx - cell.x_1*dx)/2) / full[0] ;
array[1] = 1;
array[2] = (M_PI*(2*(j+1)*dr*cell.r_2*dr - pow(cell.r_2*dr,2))) / full[2] ;
array[3] = (2*M_PI*j*cell.x_1*dx*dr) / full[3] ;
array[4] = 1;
break;
case 8:
array[0] = (2*M_PI*(j*dr + dr/2)*dx*dr - 2*M_PI*(j*dr + cell.r_1*dr + (dr - cell.r_1*dr)/2) * (dr - cell.r_1*dr)*(dx - cell.x_2*dx)/2) / full[0] ;
array[1] = 1;
array[2] = (M_PI*(2*j*dr*cell.r_1*dr - pow(cell.r_1*dr,2))) / full[2] ;
array[3] = 1;
array[4] = (2*M_PI*(j+1)*cell.x_2*dx*dr) / full[4] ;
break;
case 9:
array[0] = (2*M_PI*(j*dr + cell.r_1*dr + (dr-cell.r_1*dr)/2) * (dr-cell.r_1*dr)*cell.x_2*dx/2) / full[0] ;
array[1] = (2*M_PI*j*pow(dr,2)*dx - M_PI*(2*j*dr*cell.r_1*dr + pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = 0;
array[3] = 0;
array[4] = (2*M_PI*j*pow(dr,2)*dx - 2*M_PI*j*(dx-cell.x_2*dx)*dr) / full[4] ;
break;
case 10:
array[0] = (2*M_PI*(j*dr + cell.r_1*dr/2) * cell.r_1*dr*cell.x_1*dx / 2) / full[0] ;
array[1] = (M_PI * (2*j*dr*cell.r_1*dr + pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = 0;
array[3] = (2*M_PI*j*cell.x_1*dx*dr) / full[3];
array[4] = 0;
// array[0] = cell.x_1*cell.r_1*(j-1 + cell.r_1/3) / (2*j-1);
// array[1] = cell.r_1 * (j-1 + cell.r_1/2) / (j-0.5);
// array[2] = 0;
// array[3] = cell.x_1;
// array[4] = 0;
break;
case 11:
array[0] = (2*M_PI*(j*dr + cell.r_1*dr/2)*cell.r_1*dr * (dx - cell.x_1*dx)/2) / full[0] ;
array[1] = 0;
array[2] = (2*M_PI*j*pow(dr,2)*dx - M_PI*(2*(j+1)*dr*cell.r_2*dr - pow(cell.r_2*dr,2))) / full[2] ;
array[3] = (2*M_PI*j*pow(dr,2)*dx - 2*M_PI*j*cell.x_1*dx*dr) / full[3] ;
array[4] = 0;
break;
case 12:
array[0] = (2*M_PI*(j*dr + cell.r_1*dr + (dr - cell.r_1*dr)/2) * (dr - cell.r_1*dr)*(dx - cell.x_2*dx)/2) / full[0] ;
array[1] = 0;
array[2] = (2*M_PI*j*pow(dr,2)*dx - M_PI*(2*j*dr*cell.r_1*dr - pow(cell.r_1*dr,2))) / full[2] ;
array[3] = 0;
array[4] = (2*M_PI*j*pow(dr,2)*dx - 2*M_PI*(j+1)*cell.x_2*dx*dr) / full[4] ;
break;
case 13:
array[0] = 1;
array[1] = 1;
array[2] = 1;
array[3] = 1;
array[4] = 0;
break;
case 14:
array[0] = 1;
array[1] = 1;
array[2] = 1;
array[3] = 0;
array[4] = 1;
break;
case 15:
array[0] = 1;
array[1] = 0;
array[2] = 1;
array[3] = 1;
array[4] = 0;
break;
case 16:
array[0] = 1;
array[1] = 0;
array[2] = 1;
array[3] = 0;
array[4] = 1;
break;
case 17:
array[0] = 1;
array[1] = 0;
array[2] = 1;
array[3] = 1;
array[4] = 1;
break;
case 18:
array[0] = 0;
array[1] = 0;
array[2] = 0;
array[3] = 0;
array[4] = 0;
break;
case 19:
array[0] = 1;
array[1] = 1;
array[2] = 0;
array[3] = 1;
array[4] = 1;
break;
case 20:
array[0] = 1;
array[1] = 1;
array[2] = 0;
array[3] = 1;
array[4] = 0;
break;
case 21:
array[0] = 1;
array[1] = 1;
array[2] = 0;
array[3] = 0;
array[4] = 1;
break;
case 22:
array[0] = (2*M_PI*(j*dr + cell.r_1*dr/2) * cell.r_1*dr*cell.x_1*dx / 2) / full[0] ;
array[1] = (M_PI * (2*j*dr*cell.r_1*dr + pow(cell.r_1*dr, 2))) / full[1] ;
array[2] = 0;
array[3] = (2*M_PI*j*cell.x_1*dx*dr) / full[3];
array[4] = 0;
// array[0] = ((j-1)*(cell.r_1+cell.r_2) + cell.r_1*cell.r_2 +
// pow(cell.r_2-cell.r_1, 2)/3) / (2*j-1);
// array[1] = cell.r_1 * (j-1+cell.r_1/2) / (j-0.5);
// array[2] = 0;
// array[3] = 1;
// array[4] = 0;
break;
default:
break;
}
}
double polygonArea(double *X, double *Y, int points) {
double area=0. ;
int i, j=points-1 ;
for (i=0; i<points; i++) {
area+=(X[j]+X[i])*(Y[j]-Y[i]); j=i; }
return area*.5; }
void getLineAngle(cell2d cell, int i, int j, int n, Line2D& line,
LineAngle2D& angle, bool debug) {
line.ybegin = j+1;
line.yend = j;
line.xbegin = i;
line.xend = i+1;
/* TODO: here i assume we have angle from left top to right bottom */
switch (cell.at(n).at(i).at(j).type) {
case 1:
line.xbegin = i*dx;
line.xend = (i+1)*dx;
line.ybegin = j*dr + cell.at(n).at(i).at(j).r_1*dr;
line.yend = j*dr + cell.at(n).at(i).at(j).r_2*dr;
break;
case 3:
line.xbegin = i*dx + cell.at(n).at(i).at(j).x_2*dx;
line.xend = i*dx + cell.at(n).at(i).at(j).x_1*dx;
line.ybegin = (j+1)*dr;
line.yend = j*dr;
break;
case 8:
line.xbegin = i*dx + cell.at(n).at(i).at(j).x_2*dx;
line.xend = (i+1)*dx;
line.ybegin = (j+1)*dr;
line.yend = j*dr + cell.at(n).at(i).at(j).r_2*dr;
break;
case 10:
line.xbegin = i*dx;
line.xend = i*dx + cell.at(n).at(i).at(j).x_1*dx;
line.ybegin = j*dr + cell.at(n).at(i).at(j).r_1*dr;
line.yend = j*dr;
break;
case 22:
line.xbegin = i*dx;
line.xend = (i+1)*dx;
line.ybegin = j*dr + cell.at(n).at(i).at(j).r_1*dr;
line.yend = j*dr + cell.at(n).at(i).at(j).r_2*dr;
break;
default:
break;
}
angle.cos_a = (line.xend - line.xbegin) / sqrt(pow(line.yend-line.ybegin,2)+pow(line.xend-line.xbegin,2));
angle.sin_a = (line.yend - line.ybegin) / sqrt(pow(line.yend-line.ybegin,2)+pow(line.xend-line.xbegin,2));
angle.cos_2a = pow(angle.cos_a,2) - pow(angle.sin_a,2);
angle.sin_2a = 2*angle.cos_a*angle.sin_a;
if (debug) {
printf("x_1 = %4.4f, r_1 = %4.4f, x_2 = %4.4f, r_2 = %4.4f\n",
cell.at(n).at(i).at(j).x_1,cell.at(n).at(i).at(j).r_1,
cell.at(n).at(i).at(j).x_2,cell.at(n).at(i).at(j).r_2);
printf("Line begin = %4.4f:%4.4f, line end = %4.4f:%4.4f, line angle = %4.4f\n",
line.xbegin,line.ybegin, line.xend,line.yend,
asin(angle.sin_a)*180/M_PI);
getchar();
}
}
void setVertices(int weightCell, Point2D vertices[4], bool debug, int i, int j) {
int curI = i;
int curJ = j;
if (weightCell == 0) {
curI = i+1;
curJ = j;
} else if (weightCell == 1) {
curI = i;
curJ = j+1;
} else if (weightCell == 2) {
curI = i+1;
curJ = j+1;
}
// (curI+0.5)*dx returns us to the center of the cell
vertices[0].x = (curI)*dx;
vertices[1].x = (curI+1)*dx;
vertices[2].x = (curI+1)*dx;
vertices[3].x = (curI)*dx;
vertices[0].y = (curJ)*dr;
vertices[1].y = (curJ)*dr;
vertices[2].y = (curJ+1)*dr;
vertices[3].y = (curJ+1)*dr;
if (debug) {
printf("Orig vertices at i = %d, j = %d, weightCell = %d\n",
i,j,weightCell);
for (unsigned int idx2 = 0; idx2 < 4; idx2++)
printf("%d: %4.4f:%4.4f\n", idx2, vertices[idx2].x, vertices[idx2].y);
getchar();
}
}
void getMirrorVerts(Point2D vertices[4], Int2D vertices_ij[4],
Line2D line, LineAngle2D angle, bool debug, int i, int j) {
for (unsigned int idx = 0; idx < 4; idx++) {
double dist = (
(line.xend - line.xbegin) * (line.ybegin - vertices[idx].y) -
(line.xbegin - vertices[idx].x) * (line.yend - line.ybegin)
) / sqrt(pow(line.xend-line.xbegin,2)+pow(line.yend-line.ybegin,2));
double diffX = 2 * dist * angle.sin_a;
double diffY = 2 * dist * angle.cos_a;
vertices[idx].x -= diffX;
vertices[idx].y += diffY;
vertices_ij[idx].i = floor(vertices[idx].x/dx);
vertices_ij[idx].j = floor(vertices[idx].y/dr);
if (debug) {
printf("Point %u, distance total: %4.4f, x: %4.4f, y: %4.4f\n", idx,dist,diffX,diffY);
}
}
if (debug) {
printf("Vertices at i = %d, j = %d\n", i,j);
for (unsigned int idx2 = 0; idx2 < 4; idx2++)
printf("%d: %4.4f:%4.4f\n", idx2, vertices[idx2].x, vertices[idx2].y);
printf("Vertices_ij at i = %d, j = %d\n", i,j);
for (unsigned int idx2 = 0; idx2 < 4; idx2++)
printf("%d: %d:%d\n", idx2, vertices_ij[idx2].i, vertices_ij[idx2].j);
getchar();
}
}
bool onCross(double x, double y) {
double deltaX = pow(10,-6)*dx;
double deltaY = pow(10,-6)*dx;
double delta = pow(10,-5)*dx;
return (fmod(x+deltaX,dx) < delta && fmod(y+deltaY,dr) < delta);
}
std::vector <TPoint2D> getExtPoints(Point2D vertices[4],
Int2D vertices_ij[4], bool debug) {
/**
* Axis intersections and point types
*
* Point types:
* 0 - vertex
* 1 - axis intersection
* 2 - internal point
*
**/
std::vector <TPoint2D> result;
for (int idx1 = 0; idx1 < 4; idx1++) {
TPoint2D point;
point.x = vertices[idx1].x; point.y = vertices[idx1].y;
point.type = 0;
result.push_back(point);
if (debug) {
std::string cross = onCross(point.x, point.y) ? "true" : "false";
printf("onCross returned %s for point %6.6f:%6.6f\n",
cross.c_str(), point.x, point.y);
}
if (onCross(point.x,point.y)) {
continue;
}
if (fabs(fmod(point.x, dx)) < pow(10,-6) && fabs(fmod(point.y, dr)) < pow(10,-6)) continue;
int idx2 = idx1 != 3 ? idx1 + 1 : 0;
// One intersection point on Y axis
if (vertices_ij[idx1].i != vertices_ij[idx2].i && vertices_ij[idx1].j == vertices_ij[idx2].j) {
double interX = floor(fmax(vertices[idx1].x,vertices[idx2].x)/dx)*dx;
double interY = vertices[idx2].y + (interX - vertices[idx2].x) * (vertices[idx2].y - vertices[idx1].y) / (vertices[idx2].x - vertices[idx1].x);
point.x = interX; point.y = interY; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
} else
// One intersection point on X axis
if (vertices_ij[idx1].i == vertices_ij[idx2].i && vertices_ij[idx1].j != vertices_ij[idx2].j) {
unsigned int idx_max = vertices[idx1].y > vertices[idx2].y ? idx1 : idx2;
double interY = floor(vertices[idx_max].y/dr)*dr;
double interX = vertices[idx2].x + (interY - vertices[idx2].y) * (vertices[idx2].x - vertices[idx1].x) / (vertices[idx2].y - vertices[idx1].y);
point.x = interX; point.y = interY; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
} else
// If has 2 intersection result - first serve the closest one (because triangle gen is buggy)
if (vertices_ij[idx1].i != vertices_ij[idx2].i && vertices_ij[idx1].j != vertices_ij[idx2].j) {
double interX1 = floor(fmax(vertices[idx1].x,vertices[idx2].x)/dx)*dx;
double interY1 = vertices[idx2].y + (interX1 - vertices[idx2].x) * (vertices[idx2].y - vertices[idx1].y) / (vertices[idx2].x - vertices[idx1].x);
double interY2 = floor(fmax(vertices[idx1].y,vertices[idx2].y)/dr)*dr;
double interX2 = vertices[idx2].x + (interY2 - vertices[idx2].y) * (vertices[idx2].x - vertices[idx1].x) / (vertices[idx2].y - vertices[idx1].y);
if (pow(vertices[idx1].x-interX1,2) + pow(vertices[idx1].y-interY1,2) < pow(vertices[idx1].x-interX2,2) + pow(vertices[idx1].y-interY2,2)) {
point.x = interX1; point.y = interY1; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
point.x = interX2; point.y = interY2 ; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
} else {
point.x = interX2; point.y = interY2; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
point.x = interX1; point.y = interY1; point.type = 1;
if (!onCross(point.x,point.y)) {
result.push_back(point);
}
}
}
}
return result;
}
Int2D getMaxDifference(unsigned int max_i_point[2], unsigned int max_j_point[2],
Int2D vertices_ij[4], bool debug, int i, int j) {
Int2D max_diff;
max_diff.i = -1;
max_diff.j = -1;
for (unsigned int idx2 = 0; idx2 < 4; idx2++) {
for (unsigned int idx3 = 0; idx3 < 4; idx3++) {
if (vertices_ij[idx2].i - vertices_ij[idx3].i > max_diff.i) {
max_diff.i = vertices_ij[idx2].i - vertices_ij[idx3].i;
max_i_point[0] = idx2;
max_i_point[1] = idx3;
}
if (vertices_ij[idx2].j - vertices_ij[idx3].j > max_diff.j) {
max_diff.j = vertices_ij[idx2].j - vertices_ij[idx3].j;
max_j_point[0] = idx2;
max_j_point[1] = idx3;
}
}
}
if (debug) {
printf("Cell %d:%d\n", i,j);
printf("max_diff.i = %d, max_i_points : %d, %d\n",
max_diff.i,max_i_point[0],max_i_point[1]);
printf("max_diff.j = %d, max_j_points : %d, %d\n",
max_diff.j,max_j_point[0],max_j_point[1]);
}
return max_diff;
}
std::vector <TPoint2D> clearDoubles(std::vector <TPoint2D> points) {
//~ bool changed = true;
//~ while (changed) {
//~ changed = false;
//~ for (unsigned int idx = 0; idx < points.size(); idx++) {
//~ for (unsigned int idx2 = 0; idx2 < points.size(); idx2++) {
//~ if (fabs(points.at(idx2).x - points.at(idx).x) < pow(10,-6) &&
//~ fabs(points.at(idx2).y - points.at(idx).y) < pow(10,-6) &&
//~ points.at(idx).type != 2 &&
//~ idx2 != idx) {
//~ points.erase(points.begin()+idx2);
//~ changed = true;
//~ }
//~ }
//~ }
//~ }
//~
return points;
}
double getDiff(std::vector <TPoint2D> points, unsigned int idx1,
unsigned int idx2, bool byX) {
if (byX) {
return floor(points.at(idx1).x/dx) - floor(points.at(idx2).x/dx);
} else {
return floor(points.at(idx1).y/dr) - floor(points.at(idx2).y/dr);
}
}
/*
* nvert: Number of vertices in the polygon. Whether to repeat the first vertex at the end.
* vertx, verty: Arrays containing the x- and y-coordinates of the polygon's vertices.
* testx, testy: X- and y-coordinate of the test point.
*/
int pnpoly(int nvert, float *vertx, float *verty, float testx, float testy)
{
int i, j, c = 0;
for (i = 0, j = nvert-1; i < nvert; j = i++) {
if ( ((verty[i]>testy) != (verty[j]>testy)) &&
(testx < (vertx[j]-vertx[i]) * (testy-verty[i]) / (verty[j]-verty[i]) + vertx[i]) )
c = !c;
}
return c;
}
std::vector <TPoint2D> getIntPoints(std::vector <TPoint2D> points,
Point2D vertices[4], Int2D max_diff, unsigned int max_i_point[2],
unsigned int max_j_point[2], bool debug) {
TPoint2D point;
if (max_diff.i == 1 && max_diff.j == 1) {
double internalX = floor(fmax(fmax(vertices[0].x,vertices[1].x),fmax(vertices[2].x,vertices[3].x))/dx)*dx;
double internalY = floor(fmax(fmax(vertices[0].y,vertices[1].y),fmax(vertices[2].y,vertices[3].y))/dr)*dr;
point.x = internalX; point.y = internalY; point.type = 2;
points.push_back(point);
} else {
int i0 = floor(points.at(max_i_point[0]).x/dx);
int i1 = floor(points.at(max_i_point[1]).x/dx);
int j0 = floor(points.at(max_j_point[0]).y/dr);
int j1 = floor(points.at(max_j_point[1]).y/dr);
int minI = i0 < i1 ? i0 : i1;
int maxI = i0 > i1 ? i0 : i1;
int minJ = j0 < j1 ? j0 : j1;
int maxJ= j0 > j1 ? j0 : j1;
float vertx[4]; float verty[4]; int nvert = 4;
for (int idx = 0; idx < 4; idx++) {
vertx[idx] = vertices[idx].x;
verty[idx] = vertices[idx].y;
}
for (int i = minI-1; i <= maxI+1; i++) {
for (int j = minJ-1; j <= maxJ+1; j++) {
int ans = pnpoly(nvert, vertx, verty, i*dx, j*dr);
if (ans == 1) {
if (debug)
printf("pnpoly returned %d on point %d:%d\n", ans, i, j);
point.x = i*dx; point.y = j*dr; point.type = 2;
points.push_back(point);
}
}
}
}
return points;
}
std::vector <Int2D> makeCells(Int2D vertices_ij[4],
unsigned int max_i_point[2], unsigned int max_j_point[2], bool debug) {
std::vector <Int2D> cells;
unsigned int i_left, i_right, j_top, j_bottom = 0;
// Left and right
i_left = vertices_ij[max_i_point[0]].i;
i_right = vertices_ij[max_i_point[1]].i;
if (i_left > i_right) {
unsigned int tmp = i_left;
i_left = i_right;
i_right = tmp;
}
// Top and bottom
j_bottom = vertices_ij[max_j_point[0]].j;
j_top = vertices_ij[max_j_point[1]].j;
if (j_bottom > j_top) {
unsigned int tmp = j_bottom;
j_bottom = j_top;
j_top = tmp;
}
if (debug)
printf("\nWe have the following cells: \n");
// Make cells
for (unsigned int idx2 = i_left; idx2 <= i_right; idx2++) {
for (unsigned int idx3 = j_bottom; idx3 <= j_top; idx3++) {
Int2D newCell;
newCell.i = idx2; newCell.j = idx3;
cells.push_back(newCell);
if (debug)
printf("Cell %u: %d:%d\n", (unsigned int)(cells.size()-1), idx2, idx3);
}
}
return cells;
}
std::vector <TPoint2D> getPointsInCell(unsigned int idx,
std::vector <TPoint2D> points, std::vector <Int2D> cells,
bool debug) {
std::vector <TPoint2D> pointsInCell;
double delta = pow(10,-10);
for (unsigned int idx2 = 0; idx2 < points.size(); idx2++) {
bool rule[4];
rule[0] = points.at(idx2).x > cells.at(idx).i*dx - delta;
rule[1] = points.at(idx2).x < (cells.at(idx).i+1)*dx + delta;
rule[2] = points.at(idx2).y > cells.at(idx).j*dr - delta;
rule[3] = points.at(idx2).y < (cells.at(idx).j+1)*dr + delta;
if (rule[0] && rule[1] && rule[2] && rule[3]) {
pointsInCell.push_back(points.at(idx2));
if (debug)
printf("Cell %u: %4.4f:%4.4f, type %d \n",
idx,points.at(idx2).x,points.at(idx2).y,
points.at(idx2).type);
}
}
return pointsInCell;
}
static bool IsOnSegment(double xi, double yi, double xj, double yj,
double xk, double yk) {
return (xi <= xk || xj <= xk) && (xk <= xi || xk <= xj) &&
(yi <= yk || yj <= yk) && (yk <= yi || yk <= yj);
}
static char ComputeDirection(double xi, double yi, double xj, double yj,
double xk, double yk) {
double a = (xk - xi) * (yj - yi);
double b = (xj - xi) * (yk - yi);
return a < b ? -1 : a > b ? 1 : 0;
}
/** Do line segments (x1, y1)--(x2, y2) and (x3, y3)--(x4, y4) intersect? */
bool DoLineSegmentsIntersect(double x1, double y1, double x2, double y2,
double x3, double y3, double x4, double y4) {
char d1 = ComputeDirection(x3, y3, x4, y4, x1, y1);
char d2 = ComputeDirection(x3, y3, x4, y4, x2, y2);
char d3 = ComputeDirection(x1, y1, x2, y2, x3, y3);
char d4 = ComputeDirection(x1, y1, x2, y2, x4, y4);
return (((d1 > 0 && d2 < 0) || (d1 < 0 && d2 > 0)) &&
((d3 > 0 && d4 < 0) || (d3 < 0 && d4 > 0))) ||
(d1 == 0 && IsOnSegment(x3, y3, x4, y4, x1, y1)) ||
(d2 == 0 && IsOnSegment(x3, y3, x4, y4, x2, y2)) ||
(d3 == 0 && IsOnSegment(x1, y1, x2, y2, x3, y3)) ||
(d4 == 0 && IsOnSegment(x1, y1, x2, y2, x4, y4));
}
std::vector <TPoint2D> fixIntPointID(std::vector <TPoint2D> pointsInCell,
bool debug) {
if (debug)
printf("We have an internal point!\n");
unsigned int intIdx = 100;
TPoint2D intPoint;
for (unsigned int idx2 = 0; idx2 < pointsInCell.size(); idx2++) {
if (pointsInCell.at(idx2).type == 2) {
intIdx = idx2;
intPoint = pointsInCell.at(idx2);
break;
}
}
// If none found - return
if (intIdx == 100)
return pointsInCell;
for (unsigned int idx2 = 0; idx2 < pointsInCell.size(); idx2++) {
Point2D l1[2];
l1[0].x = pointsInCell.at(intIdx).x;
l1[0].y = pointsInCell.at(intIdx).y;
l1[1].x = pointsInCell.at(idx2).x;
l1[1].y = pointsInCell.at(idx2).y;
bool intersect = false;
for (unsigned int idx3 = 0; idx3 < pointsInCell.size(); idx3++) {
for (unsigned int idx4 = 0; idx4 < pointsInCell.size(); idx4++) {
if (idx3 != idx4 && idx3 != intIdx && idx3 != idx2
&& idx4 != intIdx && idx4 != idx2) {
Point2D l2[2];
l2[0].x = pointsInCell.at(idx3).x;
l2[0].y = pointsInCell.at(idx3).y;
l2[1].x = pointsInCell.at(idx4).x;
l2[1].y = pointsInCell.at(idx4).y;
intersect = DoLineSegmentsIntersect(l1[0].x,l1[0].y,l1[1].x,l1[1].y,
l2[0].x,l2[0].y,l2[1].x,l2[1].y);
}
}
}
if (!intersect && idx2 != 0) {
if (debug)
printf("point will be placed between %u and %u\n", idx2, idx2+1);
std::vector<TPoint2D>::iterator it = pointsInCell.begin();
pointsInCell.erase(it+intIdx);
pointsInCell.insert(it+idx2+1, intPoint);
break;
}
}
return pointsInCell;
}
Vector2dVector triangulateCell(std::vector <TPoint2D> points, bool debug) {
Vector2dVector a;
Vector2dVector result;
for (unsigned int idx = 0; idx < points.size(); idx++) {
a.push_back( Vector2d(points.at(idx).x, points.at(idx).y) );
}
if (debug) {
printf("Size of point vector %u\n", (unsigned int) a.size());
printf("Area from triangulate = %6.6f\n", Triangulate::Area(a));
}
Triangulate::Process(a, result);
return result;
}
double triangleArea(double dX0, double dY0, double dX1, double dY1, double dX2, double dY2)
{
double dArea = ((dX1 - dX0)*(dY2 - dY0) - (dX2 - dX0)*(dY1 - dY0))/2.0;
return (dArea > 0.0) ? dArea : -dArea;
}
/**
* The Graham scan is a method of computing the convex hull of a finite set of points
* in the plane with time complexity O(n log n). It is named after Ronald Graham, who
* published the original algorithm in 1972. The algorithm finds all vertices of
* the convex hull ordered along its boundary. It may also be easily modified to report
* all input points that lie on the boundary of their convex hull.
*/
/**
* Returns a convex hull given an unordered array of points.
*/
// public static function convexHull(data:Array):Array
// {
// return findHull( order(data) );
// }
/**
* Orders an array of points counterclockwise.
*/
std::vector <TPoint2D> fixPointOrder(std::vector <TPoint2D> points, bool debug) {
// first run through all the points and find the upper left
TPoint2D p = points.front();
int n = points.size();
for (int i = 1; i < n; i++) {
if (points.at(i).y > p.y)
{
p = points.at(i);
}
else if (points.at(i).y == p.y && points.at(i).x < p.x)
{
p = points.at(i);
}
}
if (debug)
printf("Top left point is at %6.6f:%6.6f\n", p.x, p.y);
// next find all the cotangents of the angles made by the point P and the
// other points
std::vector <CPoint2D> sorted;
// we need arrays for positive and negative values, because Array.sort
// will put sort the negatives backwards.
std::vector <CPoint2D> pos;
std::vector <CPoint2D> neg;
// add points back in order
for (int i = 0; i < n; i++)
{
double a = points.at(i).x - p.x - 0.00001*dx;
double b = points.at(i).y - p.y - 0.00001*dr;
double cot = b/a;
if (cot < 0) {
CPoint2D cPoint;
cPoint.point = points.at(i);
cPoint.cot = cot;
neg.push_back(cPoint);
} else {
CPoint2D cPoint;
cPoint.point = points.at(i);
cPoint.cot = cot;
pos.push_back(cPoint);
}
}
// sort the arrays
std::sort(pos.begin(), pos.end(), lesserCot());
std::sort(neg.begin(), neg.end(), lesserCot());
neg.insert(neg.end(), pos.begin(), pos.end());
sorted = neg;
std::vector <TPoint2D> ordered;
ordered.push_back(p);
for (int i = 0; i < n; i++)
{
if (p.x == sorted.at(i).point.x && p.y == sorted.at(i).point.y)
continue;
ordered.push_back(sorted.at(i).point);
}
return ordered;
}
/**
*
*/
double direction(TPoint2D p1, TPoint2D p2, TPoint2D p3) {
// > 0 is right turn
// == 0 is collinear
// < 0 is left turn
// we only want right turns, usually we want right turns, but
// flash's grid is flipped on y.
return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
}
/**
* Given an array of points ordered counterclockwise, findHull will
* filter the points and return an array containing the vertices of a
* convex polygon that envelopes those points.
*/
std::vector <TPoint2D> findHull(std::vector <TPoint2D> points) {
int n = points.size();
std::vector <TPoint2D> hull;
hull.push_back(points.at(0)); // add the pivot
hull.push_back(points.at(1)); // makes first vector
if (n > 3) {
for (int i = 2; i < n; i++) {
while (direction(hull.at(hull.size() - 2), hull.at(hull.size() - 1), points.at(i)) >= 0)
hull.pop_back();
hull.push_back(points.at(i));
}
}
return hull;
}
WeightVector wightVectorsCalc(cell2d& cell, int i, int j, int n, bool debug) {
/**
* Transform points from center of the cell
*
* [3] +---+ [2]
* | |
* [0] +---+ [1]
*
* | cos(a) -sin(a) |
* R(-a) = | |
* | sin(a) cos(a) |
*
* weightCell[0] is i+1 cell (X), [1] is j+1 (Y), [2] is i+1,j+1
*
**/
if (debug)
printf("\n\n**************************************************\n\n");
Point2D vertices[4];
Int2D vertices_ij[4];
Line2D line;
LineAngle2D angle;
WeightVector result;
std::vector <TPoint2D> points;
unsigned int max_i_point[2] = {0};
unsigned int max_j_point[2] = {0};
Int2D max_diff;
double origArea = dx*dr;
std::vector <Int2D> cells;
for (unsigned int weightCell = 0; weightCell < 3; weightCell++) {
// First, we'll set original cell's vertices
setVertices(weightCell, vertices, debug, i, j);
// Determining line begin-end points and angle
getLineAngle(cell, i, j, n, line, angle, debug);
cell.at(n).at(i).at(j).angle = angle;
// Getting mirrored over line vertices array
getMirrorVerts(vertices, vertices_ij, line, angle, debug, i, j);
// Getting all points of intersection between mirrored cell and grid
points = getExtPoints(vertices, vertices_ij, debug);
// Getting maximum i and j difference between mirrored vertices
max_diff = getMaxDifference(max_i_point, max_j_point,
vertices_ij, debug, i, j);
// Cleaning points from doubles (occures sometimes)
points = clearDoubles(points);
// Getting internal points (grid's own intersections)
points = getIntPoints(points, vertices, max_diff,
max_i_point, max_j_point, debug);
// Some debug info about our points
if (debug) {
for (unsigned int pointNum = 0; pointNum < points.size(); pointNum++) {
printf("Point %u at i = %d, j = %d: %4.4f:%4.4f, type = %d\n",
pointNum, i, j,
points.at(pointNum).x, points.at(pointNum).y,
points.at(pointNum).type);
}
}
// We'll now make a vector of all cells where our polygon is
cells = makeCells(vertices_ij, max_i_point, max_j_point, debug);
// Debug for making a good text ;)
if (debug)
printf("\nNow will arrange points in those cells\n");
// Main loop where each cell's weight is calculated
double totalWeight = 0;
for (unsigned int idx = 0; idx < cells.size(); idx++) {
// We'll use center of each of those cells to determine how much points we have in each cell
std::vector <TPoint2D> pointsInCell = getPointsInCell(idx,
points, cells, debug);
if (pointsInCell.size() < 3)
continue;
// Reorder IDs
pointsInCell = fixPointOrder(pointsInCell, debug);
if (debug) {
printf("test points in order: \n");
for (unsigned int testIdx = 0; testIdx < pointsInCell.size(); testIdx++) {
printf("%10.10f:%10.10f\n",pointsInCell.at(testIdx).x,
pointsInCell.at(testIdx).y);
}
getchar();
}
// Triangulate
Vector2dVector triangles = triangulateCell(pointsInCell, debug);
int tcount = triangles.size()/3;
// Now we'll use the result in polygonArea function
double area = 0;
for (int i=0; i<tcount; i++)
{
const Vector2d &p1 = triangles[i*3+0];
const Vector2d &p2 = triangles[i*3+1];
const Vector2d &p3 = triangles[i*3+2];
if (debug)
printf("Triangle %d => (%6.6f,%6.6f) (%6.6f,%6.6f) (%6.6f,%6.6f)\n",
i+1,p1.GetX(),p1.GetY(),p2.GetX(),p2.GetY(),p3.GetX(),p3.GetY());
area += fabs(triangleArea(p1.GetX(), p1.GetY(), p2.GetX(), p2.GetY(),
p3.GetX(), p3.GetY()));
}
if (debug) printf("Polygon area: %8.8f\n", area);
// Populating weightPart and pushing it to the cell's weightVector
WeightPart weightPart;
weightPart.weight = area / origArea;
weightPart.i = cells.at(idx).i;
weightPart.j = cells.at(idx).j;
if (debug)
printf("Weight of this cell: %4.4f\n\n\n",weightPart.weight);
if (weightCell == 0) {
result.x.push_back(weightPart);
} else if (weightCell == 1) {
result.y.push_back(weightPart);
} else if (weightCell == 2) {
result.xy.push_back(weightPart);
}
totalWeight += weightPart.weight;
}
// Scaling to 1
double scale = 1.0/totalWeight;
if (weightCell == 0) {
for (unsigned int idx = 0; idx < result.x.size(); idx++) {
result.x.at(idx).weight *= scale;
}
} else if (weightCell == 1) {
for (unsigned int idx = 0; idx < result.y.size(); idx++) {
result.y.at(idx).weight *= scale;
}
} else if (weightCell == 2) {
for (unsigned int idx = 0; idx < result.xy.size(); idx++) {