How to re-scale a rectangle to a smaller area?
$begingroup$
I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about doing that?
X*Y = Z
if(Z > AREA_MAX){
Z = AREA_MAX
X = ?
Y = ?
}
Thank you
geometry rectangles
asked Jan 16 at 12:33
Katya SKatya S
1082
$endgroup$
add a comment |
$begingroup$
I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about doing that?
X*Y = Z
if(Z > AREA_MAX){
Z = AREA_MAX
X = ?
Y = ?
}
Thank you
geometry rectangles
asked Jan 16 at 12:33
Katya SKatya S
1082
$endgroup$
add a comment |
$begingroup$
I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about doing that?
X*Y = Z
if(Z > AREA_MAX){
Z = AREA_MAX
X = ?
Y = ?
}
Thank you
geometry rectangles
asked Jan 16 at 12:33
Katya SKatya S
1082
$endgroup$
I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about doing that?
X*Y = Z
if(Z > AREA_MAX){
Z = AREA_MAX
X = ?
Y = ?
}
Thank you
geometry rectangles
geometry rectangles
asked Jan 16 at 12:33
Katya SKatya S
1082
asked Jan 16 at 12:33
Katya SKatya S
1082
asked Jan 16 at 12:33
Katya SKatya S
1082
asked Jan 16 at 12:33
Katya SKatya S
1082
asked Jan 16 at 12:33
Katya SKatya S
1082
1082
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Well, you have
$$
XY = Z qquad Rightarrow qquad frac{Z_{text{max}}}{Z} XY =
frac{Z_{text{max}}}{Z} Z = Z_{text{max}}
$$
And if you want to scale both $X$ and $Y$ equally, you can put
$$
sqrt{frac{Z_{text{max}}}{Z}} X times sqrt{frac{Z_{text{max}}}{Z}} Y = Z_{text{max}}
$$
Therefore, you can scale both $X$ and $Y$ by $sqrt{frac{Z_{text{max}}}{Z}} $, where $Z=XY$.
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Well, you have
$$
XY = Z qquad Rightarrow qquad frac{Z_{text{max}}}{Z} XY =
frac{Z_{text{max}}}{Z} Z = Z_{text{max}}
$$
And if you want to scale both $X$ and $Y$ equally, you can put
$$
sqrt{frac{Z_{text{max}}}{Z}} X times sqrt{frac{Z_{text{max}}}{Z}} Y = Z_{text{max}}
$$
Therefore, you can scale both $X$ and $Y$ by $sqrt{frac{Z_{text{max}}}{Z}} $, where $Z=XY$.
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
add a comment |
$begingroup$
Well, you have
$$
XY = Z qquad Rightarrow qquad frac{Z_{text{max}}}{Z} XY =
frac{Z_{text{max}}}{Z} Z = Z_{text{max}}
$$
And if you want to scale both $X$ and $Y$ equally, you can put
$$
sqrt{frac{Z_{text{max}}}{Z}} X times sqrt{frac{Z_{text{max}}}{Z}} Y = Z_{text{max}}
$$
Therefore, you can scale both $X$ and $Y$ by $sqrt{frac{Z_{text{max}}}{Z}} $, where $Z=XY$.
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
add a comment |
$begingroup$
Well, you have
$$
XY = Z qquad Rightarrow qquad frac{Z_{text{max}}}{Z} XY =
frac{Z_{text{max}}}{Z} Z = Z_{text{max}}
$$
And if you want to scale both $X$ and $Y$ equally, you can put
$$
sqrt{frac{Z_{text{max}}}{Z}} X times sqrt{frac{Z_{text{max}}}{Z}} Y = Z_{text{max}}
$$
Therefore, you can scale both $X$ and $Y$ by $sqrt{frac{Z_{text{max}}}{Z}} $, where $Z=XY$.
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
$endgroup$
Well, you have
$$
XY = Z qquad Rightarrow qquad frac{Z_{text{max}}}{Z} XY =
frac{Z_{text{max}}}{Z} Z = Z_{text{max}}
$$
And if you want to scale both $X$ and $Y$ equally, you can put
$$
sqrt{frac{Z_{text{max}}}{Z}} X times sqrt{frac{Z_{text{max}}}{Z}} Y = Z_{text{max}}
$$
Therefore, you can scale both $X$ and $Y$ by $sqrt{frac{Z_{text{max}}}{Z}} $, where $Z=XY$.
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
answered Jan 16 at 12:41
Matti P.Matti P.
2,2811514
2,2811514
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
add a comment |
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
$begingroup$
Thank you very muich for a a seedy response! :)
$endgroup$
– Katya S
Jan 16 at 12:45
add a comment |
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