How to check is two lines intersect/overlap on a grid? - objective-c

Question

This is a rather trivial algorithmic problem but my implementation leaves speed and simplicity to be desired. I've got two Line objects which each hold two Coordinate structs in the form of {unsigned int x, unsigned int y}. This first Coordinate holds the position of the beginning of the line and the second Coordinate, the end of it. Assuming that Lines can only be vertical or horizontal on the grid, how can I check when two lines overlap parallelly or intersect perpendicularly. Preferably this is implemented as a method in Line:
- (BOOL)intersectsLine:(Line)otherLine;
THANKS!

Answer 1

Since we're talking only about horizontal or vertical lines, the first step I'd take it checking whether or not the lines have the same orientation.
typedef (NSUInteger, LineOrientation) {
HorizontalLine = 0,
VerticalLine = 1
};
So, given a line with two points...
LineOrientation line1orientation;
LineOrientation line2orientation;
if (a.x1 == a.x2) {
line1orientation = HorizontalLine;
} else {
line1orientation = VerticalLine;
}
if (b.x1 == b.x2) {
line2orientation = VerticalLine;
} else {
line2orientation = Horizontal;
}
Now we need to check whether they're both horizontal, both vertical, or one of each, and then test particular values:
if (line1orientation == line2orientation) {
if (line1orientation == VerticalLine) {
if (a.x1 != b.x1) {
return false;
} else {
if (a.y1 < a.y2) {
return ((b.y1 > a.y1 && b.y1 < a.y2) ||
(b.y2 > a.y1 && b.y2 < a.y2));
} else {
return ((b.y1 > a.y2 && b.y1 < a.y1) ||
(b.y2 > a.y2 && b.y2 < a.y1));
}
}
} else {
if (a.y1 != b.y1) {
return false;
} else {
if (a.x1 < a.x2) {
return ((b.x1 > a.x1 && b.x1 < a.x2) ||
(b.x2 > a.x1 && b.x2 < a.x2));
} else {
return ((b.x1 > a.x2 && b.x1 < a.x1) ||
(b.x2 > a.x2 && b.x2 < a.x1));
}
}
}
} else {
if (line1orientation == VerticalLine) {
if (a.y1 < a.y2) {
return (((b.y1 > a.y1) && (b.y1 < a.y2)) && ((b.x1 > a.x1 && b.x2
< a.x1) || (b.x2 > a.x1 && b.x1 < a.x1)));
} else {
return (((b.y1 > a.y2) && (b.y1 < a.y1)) && ((b.x1 > a.x1 && b.x2
< a.x1) || (b.x2 > a.x1 && b.x1 < a.x1)))
}
} else {
if (a.x1 < a.x2) {
return (((b.x1 > a.x1) && (b.x1 < a.x2)) && ((b.y1 > a.y1 && b.y2
< a.y2) || (b.y2 > a.y1 && b.y1 < a.y1)));
} else {
return (((b.x1 > a.x2) && (b.x1 < a.x1)) && ((b.y1 > a.y1 && b.y2
< a.y2) || (b.y2 > a.y1 && b.y1 < a.y1)));
}
}
This could be more efficient if you start with a check to make sure the lines aren't the same line.