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#include "levelset_util.h"
//Given two signed distance values (line endpoints), determine what fraction of a connecting segment is "inside"
float fraction_inside(float phi_left, float phi_right) {
if(phi_left < 0 && phi_right < 0)
return 1;
if (phi_left < 0 && phi_right >= 0)
return phi_left / (phi_left - phi_right);
if(phi_left >= 0 && phi_right < 0)
return phi_right / (phi_right - phi_left);
else
return 0;
}
static void cycle_array(float* arr, int size) {
float t = arr[0];
for(int i = 0; i < size-1; ++i)
arr[i] = arr[i+1];
arr[size-1] = t;
}
//Given four signed distance values (square corners), determine what fraction of the square is "inside"
float fraction_inside(float phi_bl, float phi_br, float phi_tl, float phi_tr) {
int inside_count = (phi_bl<0?1:0) + (phi_tl<0?1:0) + (phi_br<0?1:0) + (phi_tr<0?1:0);
float list[] = { phi_bl, phi_br, phi_tr, phi_tl };
if(inside_count == 4)
return 1;
else if (inside_count == 3) {
//rotate until the positive value is in the first position
while(list[0] < 0) {
cycle_array(list,4);
}
//Work out the area of the exterior triangle
float side0 = 1-fraction_inside(list[0], list[3]);
float side1 = 1-fraction_inside(list[0], list[1]);
return 1 - 0.5f*side0*side1;
}
else if(inside_count == 2) {
//rotate until a negative value is in the first position, and the next negative is in either slot 1 or 2.
while(list[0] >= 0 || !(list[1] < 0 || list[2] < 0)) {
cycle_array(list,4);
}
if(list[1] < 0) { //the matching signs are adjacent
float side_left = fraction_inside(list[0], list[3]);
float side_right = fraction_inside(list[1], list[2]);
return 0.5f*(side_left + side_right);
}
else { //matching signs are diagonally opposite
//determine the centre point's sign to disambiguate this case
float middle_point = 0.25f*(list[0] + list[1] + list[2] + list[3]);
if(middle_point < 0) {
float area = 0;
//first triangle (top left)
float side1 = 1-fraction_inside(list[0], list[3]);
float side3 = 1-fraction_inside(list[2], list[3]);
area += 0.5f*side1*side3;
//second triangle (top right)
float side2 = 1-fraction_inside(list[2], list[1]);
float side0 = 1-fraction_inside(list[0], list[1]);
area += 0.5f*side0*side2;
return 1-area;
}
else {
float area = 0;
//first triangle (bottom left)
float side0 = fraction_inside(list[0], list[1]);
float side1 = fraction_inside(list[0], list[3]);
area += 0.5f*side0*side1;
//second triangle (top right)
float side2 = fraction_inside(list[2], list[1]);
float side3 = fraction_inside(list[2], list[3]);
area += 0.5f*side2*side3;
return area;
}
}
}
else if(inside_count == 1) {
//rotate until the negative value is in the first position
while(list[0] >= 0) {
cycle_array(list,4);
}
//Work out the area of the interior triangle, and subtract from 1.
float side0 = fraction_inside(list[0], list[3]);
float side1 = fraction_inside(list[0], list[1]);
return 0.5f*side0*side1;
}
else
return 0;
}
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