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Asked: 2026-06-03T09:07:04+00:00

I have: axis-aligned rectangle R ; non-vertical line A (specified by two points); vertical

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I have:

  1. axis-aligned rectangle R;
  2. non-vertical line A (specified by two points);
  3. vertical line B (specified by x-coordinate).

All objects above is specified by integer coordinates.

I need to check, if result of crossing A and B is in the R. But I can’t just calculate result of crossing A and B because it may be unpresentable in integer coordinates. Also I can’t convert it to doubles because I need to get absolutely accurate result without any inaccuracy.

So, how can I check it?

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1 Answer

  1. Editorial Team

    If lines are specified by integer coordinates, then their crossing point has rational coordinates, which may be compared with absolutely precision.

    Let’s A goes through points (ax0, ay0) and (ax1, ay1), and B is at X0 coordinate.
    Then crossing point Y-coordinate is (ay0*(ax1-ax0)+(X0-ax0)*(ay1-ay0))/(ax1-ax0) = p/q, where p and q are integer, and q is positive (negate nominator if needed).

    Then p may be compared with R.Top*q and R.Bottom*q

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