Rectangle Intersection. print message for empty intersection - c++

Question

I have four coordinates: x,y,width=w,height=h and I have two rectangles with the following coordinates:
r1.x=2,r1.y=3,r1.w=5,r1.h=6;
r2.x=0, r2.y=7,r2.w=-4,r4.h=2
How you can observe this intersection is empty.
what I did until now it was:
rectangle intersection (rectangle r1, rectangle r2){
r1.x=max(r1.x,r2.x);
r1.y=max(r1.y,r2.y);
r1.w=min(r1.w,r2.w);
r1.h=min(r1.h,r2.h);
return r1;
}
I think the above code it is used when there is an intersection, but when the intersection is empty I do not know. Also, I would like to print a message "empty" when there is no intersection.
thanks!

Answer 1

The method you are using for rectangle intersection does NOT work when rectangles are represented with their width and height.
It could work if you store the rectangles' two opposite corners (instead of one corner and the dimensions) and make sure that the first corner's coordinates are always less than or equal to the second corner, effectively storing min_x, min_y, max_x, and max_y for your rectangles.
I would suggest that you adopt the convention of making sure the rectangles always include their min coordinates and always exclude their max coords.

Answer 2

Assuming you have something not very different from:
struct rectangle {
int x;
int y;
int w;
int h;
};
(or the same using float or double instead of int)
I will assume here that w and h are always positive, if they may be negative, you should first normalize the input rectangle to ensure that they are.
You find the intersection by finding its opposite corners, and ensuring that lower left come before upper right:
rectangle intersection(const rectangle& r1, const rectangle& r2) {
// optionaly control arguments:
if (r1.w < 0 || r1.h < 0 || r2.w < 0 || r2.h < 0) {
throw std::domain_error("Unnormalized rectangles on input");
}
int lowx = max(r1.x, r2.x); // Ok, x coordinate of lower left corner
int lowy = max(r1.y, r2.y); // same for y coordinate
int upx = min(r1.x + r1.w, r2.x + r2.w) // x for upper right corner
int upy = min(r1.y + r1.h, r2.y + r2.h) // y for upper right corner
if (upx < lowx || upy < lowy) { // empty intersection
throw std::domain_error("Empty intersection");
}
return rectangle(lowx, lowy, upx - lowx, upy - lowy);
}
You can normalize a rectangle by forcing positive values for width and height:
rectangle& normalize(rectangle& r) {
if (r.w < 0) {
r.x += r.w;
r.w = - r.w;
}
if (r.h < 0) {
r.y += r.h;
r.h = -r.h;
}
return r;
}
You can then use that in a second function to display the intersection result:
void display_intersection(std::outstream out, rectangle r1, rectangle r2) {
try {
rectangle inter = intersection(normalize(r1), normalize(r2));
out << "(" << inter.x << ", " << inter.y << ") to (";
out << inter.x + inter.w << ", " << inter.y + inter.h << ")" << std::endl;
}
except (std::domain_error& e) {
out << "empty" << std::endl;
}
}