Rectangles Intersection (Vertical line)

Question

For a given rectangle R1 I am trying to find out which are the other rectangles that could intersect with it IF I draw a vectical line segment.

The rectangles that intersect with R1 are marked in Red.

Every rectangle is characterized by its (top, left) and (bottom, right) coordinates.

R1 = [top, left, bottom, right],...,Rn = [top, left, bottom, right]

By using the coordinates and the vertical line. I want to find the rectangles that intersects with R1

Solution

I found the following library which does the same work as the icl boost library but must simpler: download site: [ https://github.com/ekg/intervaltree][2]

#include <iostream>
#include <fstream>
#include "IntervalTree.h"

using namespace std;

struct Position
{
    int x;
    int y;
    string id;
};

int main()
{
    vector<Interval<Position>> intervals;
    intervals.push_back(Interval<Position>(4,10,{1,2,"r1"}));
    intervals.push_back(Interval<Position>(6,10,{-6,-3,"r2"}));
    intervals.push_back(Interval<Position>(8,10,{5,6,"r3"}));

    vector<Interval<Position> > results;
    vector<string> value;
    int start = 4;
    int stop = 10;

    IntervalTree<Position> tree(intervals);
   // tree.findContained(start, stop, results);
    tree.findOverlapping(start, stop, results);
    cout << "found " << results.size() << " overlapping intervals" << endl;
}

---

Example

• LEFT = 4;
• RIGHT = 10;
• structure {1,2,"rc1"};

intervals.push_back(Interval(4,10,{1,2,"r1"}));

Answer 1

Your need a collision detection algorithm. In C++ there's boost.geometry for doing such things among many others.

Answer 2

You don't care where the rectangles are vertically. You can project everything onto the x-axis and then solve the corresponding 1-dimensional problem: you have a set of intervals and you want to know which overlap with a given interval. This is exactly what an interval tree is does:

https://en.wikipedia.org/wiki/Interval_tree

Answer 3

Where:

• Rect is a collection of all rectangles.
• R is the rectangle to test
• x1 is one x-coordinate
• x2 is other x-coordinate

Pseudo Code

// make sure x1 is on the left of x2
if (R.x1 > R.x2)
    tmp = R.x2
    R.x2 = R.x1
    R.x1 = tmp
end if

for each Rect as r
    // don't test itself
    if (R != r)
        // make sure x1 is on the left of x2
        if (r.x1 > r.x2)
            tmp = r.x2
            r.x2 = r.x1
            r.x1 = tmp
        end if

        if ((r.x2 < R.x1) // if r rect to left of R rect
                || (r.x1 > R.x2)) // if r rect to right of R rect
            // r rect does not intersect R rect
        else
            // r rect does intersect R rect
        end if
    end if
end for