Rectangle size calculation
$begingroup$
I am trying to calculate rectangle size. I have the rectangle width and height and the ratio between the width and height that has to be met. Resulting width and height of the rectangle have to be an integer(whole number).
ratio is a constant number
width, height are the given numbers
width_r, height_r are the result
width_0, height_0 are the numbers subtracted from the original width and height
Formulas:
width_r/height_r = ratio
width = width_r - width_0
height = height_r - height_0
width > width_r
height > height_r
Ex:
width = 1829
height = 3856
ratio = 16/9
9*width_r = 16*height_r
9(width - width_0) = 16(height - height_0)
I can calculate that the result is width_r = 1824, height_r = 1026. width_0 + height_0 should be the lowest possible while being whole numbers. I can calculate it but i need to create a function that a program can execute.
algebra-precalculus geometry
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
$endgroup$
add a comment |
$begingroup$
I am trying to calculate rectangle size. I have the rectangle width and height and the ratio between the width and height that has to be met. Resulting width and height of the rectangle have to be an integer(whole number).
ratio is a constant number
width, height are the given numbers
width_r, height_r are the result
width_0, height_0 are the numbers subtracted from the original width and height
Formulas:
width_r/height_r = ratio
width = width_r - width_0
height = height_r - height_0
width > width_r
height > height_r
Ex:
width = 1829
height = 3856
ratio = 16/9
9*width_r = 16*height_r
9(width - width_0) = 16(height - height_0)
I can calculate that the result is width_r = 1824, height_r = 1026. width_0 + height_0 should be the lowest possible while being whole numbers. I can calculate it but i need to create a function that a program can execute.
algebra-precalculus geometry
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
$endgroup$
$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35
add a comment |
$begingroup$
I am trying to calculate rectangle size. I have the rectangle width and height and the ratio between the width and height that has to be met. Resulting width and height of the rectangle have to be an integer(whole number).
ratio is a constant number
width, height are the given numbers
width_r, height_r are the result
width_0, height_0 are the numbers subtracted from the original width and height
Formulas:
width_r/height_r = ratio
width = width_r - width_0
height = height_r - height_0
width > width_r
height > height_r
Ex:
width = 1829
height = 3856
ratio = 16/9
9*width_r = 16*height_r
9(width - width_0) = 16(height - height_0)
I can calculate that the result is width_r = 1824, height_r = 1026. width_0 + height_0 should be the lowest possible while being whole numbers. I can calculate it but i need to create a function that a program can execute.
algebra-precalculus geometry
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
$endgroup$
I am trying to calculate rectangle size. I have the rectangle width and height and the ratio between the width and height that has to be met. Resulting width and height of the rectangle have to be an integer(whole number).
ratio is a constant number
width, height are the given numbers
width_r, height_r are the result
width_0, height_0 are the numbers subtracted from the original width and height
Formulas:
width_r/height_r = ratio
width = width_r - width_0
height = height_r - height_0
width > width_r
height > height_r
Ex:
width = 1829
height = 3856
ratio = 16/9
9*width_r = 16*height_r
9(width - width_0) = 16(height - height_0)
I can calculate that the result is width_r = 1824, height_r = 1026. width_0 + height_0 should be the lowest possible while being whole numbers. I can calculate it but i need to create a function that a program can execute.
algebra-precalculus geometry
algebra-precalculus geometry
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
edited Jan 26 at 0:02
J. W. Tanner
2,9541218
2,9541218
asked Jan 24 at 20:56
OrionOrion
12
asked Jan 24 at 20:56
OrionOrion
12
asked Jan 24 at 20:56
OrionOrion
12
12
$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35
add a comment |
$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35
$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I think you just want this: one option is (width,width/ratio), and the other is (height*ratio,height), both rounded down to the nearest integer. Then take the smaller one. This way, it fits to the window along at least one dimension (this is "fit to window" function in image viewers, for instance).
This assumes that any rounded pair of integers is acceptable. However, if you want to put restrictions on how much deviation in ratio=width/height from the desired ratio is acceptable, you need more information. You need a trade-off condition between how much you shrink and how wrong the ratio is. Do you allow shrinking by at most $n$ pixels and pick the best result? Do you impose a minimum acceptable error in aspect ratio and pick the first acceptable choice? Do you construct a trade-off as a weighted sum of the shrinkage and ratio error, and find the minimum? You need to make a choice, there is no "best" selection.
As this is probably about image resizing, I'd say the nearest integer rounded result is what you want, all the rest is just splitting hairs.
answered Jan 24 at 21:23
orionorion
13.7k11837
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add a comment |
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1 Answer
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$begingroup$
I think you just want this: one option is (width,width/ratio), and the other is (height*ratio,height), both rounded down to the nearest integer. Then take the smaller one. This way, it fits to the window along at least one dimension (this is "fit to window" function in image viewers, for instance).
This assumes that any rounded pair of integers is acceptable. However, if you want to put restrictions on how much deviation in ratio=width/height from the desired ratio is acceptable, you need more information. You need a trade-off condition between how much you shrink and how wrong the ratio is. Do you allow shrinking by at most $n$ pixels and pick the best result? Do you impose a minimum acceptable error in aspect ratio and pick the first acceptable choice? Do you construct a trade-off as a weighted sum of the shrinkage and ratio error, and find the minimum? You need to make a choice, there is no "best" selection.
As this is probably about image resizing, I'd say the nearest integer rounded result is what you want, all the rest is just splitting hairs.
answered Jan 24 at 21:23
orionorion
13.7k11837
$endgroup$
add a comment |
$begingroup$
I think you just want this: one option is (width,width/ratio), and the other is (height*ratio,height), both rounded down to the nearest integer. Then take the smaller one. This way, it fits to the window along at least one dimension (this is "fit to window" function in image viewers, for instance).
This assumes that any rounded pair of integers is acceptable. However, if you want to put restrictions on how much deviation in ratio=width/height from the desired ratio is acceptable, you need more information. You need a trade-off condition between how much you shrink and how wrong the ratio is. Do you allow shrinking by at most $n$ pixels and pick the best result? Do you impose a minimum acceptable error in aspect ratio and pick the first acceptable choice? Do you construct a trade-off as a weighted sum of the shrinkage and ratio error, and find the minimum? You need to make a choice, there is no "best" selection.
As this is probably about image resizing, I'd say the nearest integer rounded result is what you want, all the rest is just splitting hairs.
answered Jan 24 at 21:23
orionorion
13.7k11837
$endgroup$
add a comment |
$begingroup$
I think you just want this: one option is (width,width/ratio), and the other is (height*ratio,height), both rounded down to the nearest integer. Then take the smaller one. This way, it fits to the window along at least one dimension (this is "fit to window" function in image viewers, for instance).
This assumes that any rounded pair of integers is acceptable. However, if you want to put restrictions on how much deviation in ratio=width/height from the desired ratio is acceptable, you need more information. You need a trade-off condition between how much you shrink and how wrong the ratio is. Do you allow shrinking by at most $n$ pixels and pick the best result? Do you impose a minimum acceptable error in aspect ratio and pick the first acceptable choice? Do you construct a trade-off as a weighted sum of the shrinkage and ratio error, and find the minimum? You need to make a choice, there is no "best" selection.
As this is probably about image resizing, I'd say the nearest integer rounded result is what you want, all the rest is just splitting hairs.
answered Jan 24 at 21:23
orionorion
13.7k11837
$endgroup$
I think you just want this: one option is (width,width/ratio), and the other is (height*ratio,height), both rounded down to the nearest integer. Then take the smaller one. This way, it fits to the window along at least one dimension (this is "fit to window" function in image viewers, for instance).
This assumes that any rounded pair of integers is acceptable. However, if you want to put restrictions on how much deviation in ratio=width/height from the desired ratio is acceptable, you need more information. You need a trade-off condition between how much you shrink and how wrong the ratio is. Do you allow shrinking by at most $n$ pixels and pick the best result? Do you impose a minimum acceptable error in aspect ratio and pick the first acceptable choice? Do you construct a trade-off as a weighted sum of the shrinkage and ratio error, and find the minimum? You need to make a choice, there is no "best" selection.
As this is probably about image resizing, I'd say the nearest integer rounded result is what you want, all the rest is just splitting hairs.
answered Jan 24 at 21:23
orionorion
13.7k11837
answered Jan 24 at 21:23
orionorion
13.7k11837
answered Jan 24 at 21:23
orionorion
13.7k11837
answered Jan 24 at 21:23
orionorion
13.7k11837
13.7k11837
add a comment |
add a comment |
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$begingroup$
Closest according to which criteria ? Perimeter, area, min max differences ?
$endgroup$
– Damien
Jan 24 at 21:11
$begingroup$
width_0 + height_0 has to be the smallest possible while being an integer.
$endgroup$
– Orion
Jan 24 at 21:15
$begingroup$
You need more information. Are you enlarging or shrinking? Should the result stay inside the same box or can it grow? To what end do you need it to be "close"? Is any rounding up to the closest pixel ok, or do you need special good approximations (which will strongly depend on the prime factors of both dimensions).
$endgroup$
– orion
Jan 24 at 21:17
$begingroup$
It cannot grow beyond the given width and height, it is shrinking. There should be no decimal numbers. I calculated it by taking the lower number between width and height and then subtracting it one by one until it fit the criteria.
$endgroup$
– Orion
Jan 24 at 21:23
$begingroup$
With Bézout coefficients, you can generate all possible values that satisfy the ratio. It can help finding the minimum
$endgroup$
– Damien
Jan 24 at 21:35