Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Categories

Welcome to the new platform of Programmer's Heaven! We apologize for the inconvenience caused, if you visited us from a broken link of the previous version. The main reason to move to a new platform is to provide more effective and collaborative experience to you all. Please feel free to experience the new platform and use its exciting features. Contact us for any issue that you need to get clarified. We are more than happy to help you.

Function to see whether two lines intersect

zeolitezeolite Posts: 78Member
Suppose I have an array of size n, storing information about lines on a grid by storing the (left,top) and (right,bottom) co-ordinates using a RECT structure. How could a function determine whether a line specified by the user intersects any of the lines stored in this array?

The code would look something like the following:
[CODE]RECT rect_array[n];
...
bool DoesLineIntersectAny(RECT line)
{
for(int i = 0; i < n; i++)
if(LineIntersects(rect_array[i], line)
return true;

return false;
}
[/CODE]Unfortunately I cannot find a function such as "LineIntersects" in any standard libraries or API's. Any help would be greatly appreciated.

Comments

  • FazFaz Posts: 75Member
    You can use a bit of algebra to determine whether 2 lines cross.

    First, determine an equation for each line. You can do this easily by working out the gradient of the line (increase in y / increase in x) and the find the constant of the equation, which will be the value of y when x = 0.

    So say you have a line made up of 2 points with co-ordinates (10, 10) and (15, 20). The increase in y is 10 and the increase in x is 5, so the gradient is 10 / 5 = 2. When x = 0, y will be 5, so the constant in the equation is 5. This will give equation of the line as
    y = 2x + 5

    Now do the same for the second line. Assume the gradient is 4 and the constant is 13. This makes the second equation
    y = 4x + 13

    To find the point of intersection, you just need to find where the 2 equations are equal. Do this by combining the equations like this:

    2x + 5
    4x + 13

    2x + 5 = 4x + 13

    Rearrange this to make x on it's own on the left hand side:

    2x + 5 = 4x + 13
    -2x + 5 = 0x + 13
    -2x + 0 = 0x + 8
    -2x = 8
    x = -4

    This result means the 2 lines intersect when x is at -4
    You can then substitute this value of x into any of the 2 equations to retrieve the y co-ordinate.

    Actually the thing with straight lines is, there will ALWAYS be a point of intersection! The only exception of course is if the 2 lines are parallel, or they have the same gradient. To do a simple check of whether 2 lines will ever cross, check to see if their gradients are equal. I'm just assuming you wanted to know where they intersect.

    Hope that solves your problem.
  • zeolitezeolite Posts: 78Member
    That's a great help! Thank you very much :-)
  • tsagldtsagld Posts: 621Member
    : You can use a bit of algebra to determine whether 2 lines cross.
    :
    : First, determine an equation for each line. You can do this easily by working out the gradient of the line (increase in y / increase in x) and the find the constant of the equation, which will be the value of y when x = 0.
    :
    : So say you have a line made up of 2 points with co-ordinates (10, 10) and (15, 20). The increase in y is 10 and the increase in x is 5, so the gradient is 10 / 5 = 2. When x = 0, y will be 5, so the constant in the equation is 5. This will give equation of the line as
    : y = 2x + 5
    :
    : Now do the same for the second line. Assume the gradient is 4 and the constant is 13. This makes the second equation
    : y = 4x + 13
    :
    : To find the point of intersection, you just need to find where the 2 equations are equal. Do this by combining the equations like this:
    :
    : 2x + 5
    : 4x + 13
    :
    : 2x + 5 = 4x + 13
    :
    : Rearrange this to make x on it's own on the left hand side:
    :
    : 2x + 5 = 4x + 13
    : -2x + 5 = 0x + 13
    : -2x + 0 = 0x + 8
    : -2x = 8
    : x = -4
    :
    : This result means the 2 lines intersect when x is at -4
    : You can then substitute this value of x into any of the 2 equations to retrieve the y co-ordinate.
    :
    : Actually the thing with straight lines is, there will ALWAYS be a point of intersection! The only exception of course is if the 2 lines are parallel, or they have the same gradient. To do a simple check of whether 2 lines will ever cross, check to see if their gradients are equal. I'm just assuming you wanted to know where they intersect.
    :
    : Hope that solves your problem.

    The lines mentioned do not always intersect. They have a start and end point and therefore have a length.
    If you find the X for which two lines intersect, you'll have to check if that value does not fall outside of both lines' starting and ending X-values.


    Greets,
    Eric Goldstein
    http://www.gvh-maatwerk.nl


  • shaolin007shaolin007 Posts: 1,018Member
    : : You can use a bit of algebra to determine whether 2 lines cross.
    : :
    : : First, determine an equation for each line. You can do this easily by working out the gradient of the line (increase in y / increase in x) and the find the constant of the equation, which will be the value of y when x = 0.
    : :
    : : So say you have a line made up of 2 points with co-ordinates (10, 10) and (15, 20). The increase in y is 10 and the increase in x is 5, so the gradient is 10 / 5 = 2. When x = 0, y will be 5, so the constant in the equation is 5. This will give equation of the line as
    : : y = 2x + 5
    : :
    : : Now do the same for the second line. Assume the gradient is 4 and the constant is 13. This makes the second equation
    : : y = 4x + 13
    : :
    : : To find the point of intersection, you just need to find where the 2 equations are equal. Do this by combining the equations like this:
    : :
    : : 2x + 5
    : : 4x + 13
    : :
    : : 2x + 5 = 4x + 13
    : :
    : : Rearrange this to make x on it's own on the left hand side:
    : :
    : : 2x + 5 = 4x + 13
    : : -2x + 5 = 0x + 13
    : : -2x + 0 = 0x + 8
    : : -2x = 8
    : : x = -4
    : :
    : : This result means the 2 lines intersect when x is at -4
    : : You can then substitute this value of x into any of the 2 equations to retrieve the y co-ordinate.
    : :
    : : Actually the thing with straight lines is, there will ALWAYS be a point of intersection! The only exception of course is if the 2 lines are parallel, or they have the same gradient. To do a simple check of whether 2 lines will ever cross, check to see if their gradients are equal. I'm just assuming you wanted to know where they intersect.
    : :
    : : Hope that solves your problem.
    :
    : The lines mentioned do not always intersect. They have a start and end point and therefore have a length.
    : If you find the X for which two lines intersect, you'll have to check if that value does not fall outside of both lines' starting and ending X-values.
    :
    :
    : Greets,
    : Eric Goldstein
    : http://www.gvh-maatwerk.nl
    :
    :
    :
    [green]
    The domain of line y=mx+b is the set of reals. It's range is the set of all reals, so it could go on to -infinity to +infinity. What you are describing is the distance between two points which is only part of a line or also called a line segment.
    [/green]

Sign In or Register to comment.