Mixing
Determine if a Rectangle is Inside, Overlaps, Doesn't Overlaps Another Rectangle
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Using the center's x- and y-coordinates, width and length of each rectangle, determine if the second rectangle is inside, overlaps or doesn't overlap the first rectangle.
I know that if I divide the width or height by 2, I will get the reach of both sides of rectangle, horizontally and vertically. I can't seem to come up with a formula to solve for each condition.
Here's the list of variables I'm using:
Rectangle 1: x1, y1, width1, height1
Rectangle 2: x2, y2, width2, height2
Here's the formulas I'm coming up with:
The absolute value of the horizontal distance = x1 - x2
The absolute value of the vertical distance = y1 - y2
Or is it better to subtract the smaller number from the larger one?
Any ideas? Thank you
geometry rectangles
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
$endgroup$
add a comment |
$begingroup$
Using the center's x- and y-coordinates, width and length of each rectangle, determine if the second rectangle is inside, overlaps or doesn't overlap the first rectangle.
I know that if I divide the width or height by 2, I will get the reach of both sides of rectangle, horizontally and vertically. I can't seem to come up with a formula to solve for each condition.
Here's the list of variables I'm using:
Rectangle 1: x1, y1, width1, height1
Rectangle 2: x2, y2, width2, height2
Here's the formulas I'm coming up with:
The absolute value of the horizontal distance = x1 - x2
The absolute value of the vertical distance = y1 - y2
Or is it better to subtract the smaller number from the larger one?
Any ideas? Thank you
geometry rectangles
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
$endgroup$
$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33
add a comment |
$begingroup$
Using the center's x- and y-coordinates, width and length of each rectangle, determine if the second rectangle is inside, overlaps or doesn't overlap the first rectangle.
I know that if I divide the width or height by 2, I will get the reach of both sides of rectangle, horizontally and vertically. I can't seem to come up with a formula to solve for each condition.
Here's the list of variables I'm using:
Rectangle 1: x1, y1, width1, height1
Rectangle 2: x2, y2, width2, height2
Here's the formulas I'm coming up with:
The absolute value of the horizontal distance = x1 - x2
The absolute value of the vertical distance = y1 - y2
Or is it better to subtract the smaller number from the larger one?
Any ideas? Thank you
geometry rectangles
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
$endgroup$
Using the center's x- and y-coordinates, width and length of each rectangle, determine if the second rectangle is inside, overlaps or doesn't overlap the first rectangle.
I know that if I divide the width or height by 2, I will get the reach of both sides of rectangle, horizontally and vertically. I can't seem to come up with a formula to solve for each condition.
Here's the list of variables I'm using:
Rectangle 1: x1, y1, width1, height1
Rectangle 2: x2, y2, width2, height2
Here's the formulas I'm coming up with:
The absolute value of the horizontal distance = x1 - x2
The absolute value of the vertical distance = y1 - y2
Or is it better to subtract the smaller number from the larger one?
Any ideas? Thank you
geometry rectangles
geometry rectangles
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
asked Jan 25 at 1:18
donfontaine12donfontaine12
82
82
$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33
add a comment |
$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33
$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If any of the following are true, the rectangles don't intersect, otherwise they do:
$$x_1+frac{w_1}{2} < x_2-frac{w_2}{2}$$
$$x_1-frac{w_1}{2} > x_2+frac{w_2}{2}$$
$$y_1+frac{h_1}{2} < y_2-frac{h_2}{2}$$
$$y_1-frac{h_1}{2} > y_2+frac{h_2}{2}$$
Edit
For the second rectangle to be inside the first, all of the following must be true:
$$x_2+frac{w_2}{2} le x_1+frac{w_1}{2}$$
$$x_2-frac{w_2}{2} ge x_1-frac{w_1}{2}$$
$$y_2+frac{h_2}{2} le y_1+frac{h_1}{2}$$
$$y_2-frac{h_2}{2} ge y_1-frac{h_1}{2}$$
answered Jan 25 at 2:20
JensJens
3,94521031
$endgroup$
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If any of the following are true, the rectangles don't intersect, otherwise they do:
$$x_1+frac{w_1}{2} < x_2-frac{w_2}{2}$$
$$x_1-frac{w_1}{2} > x_2+frac{w_2}{2}$$
$$y_1+frac{h_1}{2} < y_2-frac{h_2}{2}$$
$$y_1-frac{h_1}{2} > y_2+frac{h_2}{2}$$
Edit
For the second rectangle to be inside the first, all of the following must be true:
$$x_2+frac{w_2}{2} le x_1+frac{w_1}{2}$$
$$x_2-frac{w_2}{2} ge x_1-frac{w_1}{2}$$
$$y_2+frac{h_2}{2} le y_1+frac{h_1}{2}$$
$$y_2-frac{h_2}{2} ge y_1-frac{h_1}{2}$$
answered Jan 25 at 2:20
JensJens
3,94521031
$endgroup$
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
add a comment |
$begingroup$
If any of the following are true, the rectangles don't intersect, otherwise they do:
$$x_1+frac{w_1}{2} < x_2-frac{w_2}{2}$$
$$x_1-frac{w_1}{2} > x_2+frac{w_2}{2}$$
$$y_1+frac{h_1}{2} < y_2-frac{h_2}{2}$$
$$y_1-frac{h_1}{2} > y_2+frac{h_2}{2}$$
Edit
For the second rectangle to be inside the first, all of the following must be true:
$$x_2+frac{w_2}{2} le x_1+frac{w_1}{2}$$
$$x_2-frac{w_2}{2} ge x_1-frac{w_1}{2}$$
$$y_2+frac{h_2}{2} le y_1+frac{h_1}{2}$$
$$y_2-frac{h_2}{2} ge y_1-frac{h_1}{2}$$
answered Jan 25 at 2:20
JensJens
3,94521031
$endgroup$
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
add a comment |
$begingroup$
If any of the following are true, the rectangles don't intersect, otherwise they do:
$$x_1+frac{w_1}{2} < x_2-frac{w_2}{2}$$
$$x_1-frac{w_1}{2} > x_2+frac{w_2}{2}$$
$$y_1+frac{h_1}{2} < y_2-frac{h_2}{2}$$
$$y_1-frac{h_1}{2} > y_2+frac{h_2}{2}$$
Edit
For the second rectangle to be inside the first, all of the following must be true:
$$x_2+frac{w_2}{2} le x_1+frac{w_1}{2}$$
$$x_2-frac{w_2}{2} ge x_1-frac{w_1}{2}$$
$$y_2+frac{h_2}{2} le y_1+frac{h_1}{2}$$
$$y_2-frac{h_2}{2} ge y_1-frac{h_1}{2}$$
answered Jan 25 at 2:20
JensJens
3,94521031
$endgroup$
If any of the following are true, the rectangles don't intersect, otherwise they do:
$$x_1+frac{w_1}{2} < x_2-frac{w_2}{2}$$
$$x_1-frac{w_1}{2} > x_2+frac{w_2}{2}$$
$$y_1+frac{h_1}{2} < y_2-frac{h_2}{2}$$
$$y_1-frac{h_1}{2} > y_2+frac{h_2}{2}$$
Edit
For the second rectangle to be inside the first, all of the following must be true:
$$x_2+frac{w_2}{2} le x_1+frac{w_1}{2}$$
$$x_2-frac{w_2}{2} ge x_1-frac{w_1}{2}$$
$$y_2+frac{h_2}{2} le y_1+frac{h_1}{2}$$
$$y_2-frac{h_2}{2} ge y_1-frac{h_1}{2}$$
answered Jan 25 at 2:20
JensJens
3,94521031
edited Jan 25 at 16:37
answered Jan 25 at 2:20
JensJens
3,94521031
answered Jan 25 at 2:20
JensJens
3,94521031
answered Jan 25 at 2:20
JensJens
3,94521031
3,94521031
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
add a comment |
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
What conditions will occur when the rectangle is completely inside?
$endgroup$
– donfontaine12
Jan 25 at 10:53
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
$begingroup$
It works for each condition now. Thank you.
$endgroup$
– donfontaine12
Jan 25 at 18:30
add a comment |
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$begingroup$
You may possibly need more variables , as in your case , the rectangles can be rotated , which can consequently yield more than $1$ answer . Or are you assuming that the sides are parallel to the axes ?
$endgroup$
– Sinπ
Jan 25 at 1:23
$begingroup$
Yes, the sides will be parallel to the axis. Rotation won't be necessary.
$endgroup$
– donfontaine12
Jan 25 at 1:33