Maximized dimensions of bounding box around rotated rectangle [closed]
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Given an orthogonal rectangle with sides a and b, what rotations $theta$ result in a bounding box with maximum height c.q. width?
I hope this is formulated correctly. By bounding box, I mean the smallest orthogonal rectangle that contains each of the 4 corners of the inner rectangle after rotating this inner rectangle. I'm interested in the largest individual sides, not their area.
I believe this comes down to deriving the width and height of the resulting rectangle as a function of the given variables and maximizing those.
Taking an example:
The sides of the resulting bounding box are given by $h = h_1 + h_2 = a sin theta + b cos theta$.
I'm unsure if there is a distinction between situation $a<b$ or not but I believe the result will be obtained in analogous manner regardless.
How would I in this example with $a<b$ maximize $h$?
trigonometry rectangles
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
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closed as off-topic by Cesareo, Leucippus, KReiser, José Carlos Santos, metamorphy Dec 29 '18 at 8:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Cesareo, Leucippus, José Carlos Santos, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Given an orthogonal rectangle with sides a and b, what rotations $theta$ result in a bounding box with maximum height c.q. width?
I hope this is formulated correctly. By bounding box, I mean the smallest orthogonal rectangle that contains each of the 4 corners of the inner rectangle after rotating this inner rectangle. I'm interested in the largest individual sides, not their area.
I believe this comes down to deriving the width and height of the resulting rectangle as a function of the given variables and maximizing those.
Taking an example:
The sides of the resulting bounding box are given by $h = h_1 + h_2 = a sin theta + b cos theta$.
I'm unsure if there is a distinction between situation $a<b$ or not but I believe the result will be obtained in analogous manner regardless.
How would I in this example with $a<b$ maximize $h$?
trigonometry rectangles
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
$endgroup$
closed as off-topic by Cesareo, Leucippus, KReiser, José Carlos Santos, metamorphy Dec 29 '18 at 8:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Cesareo, Leucippus, José Carlos Santos, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59
add a comment |
$begingroup$
Given an orthogonal rectangle with sides a and b, what rotations $theta$ result in a bounding box with maximum height c.q. width?
I hope this is formulated correctly. By bounding box, I mean the smallest orthogonal rectangle that contains each of the 4 corners of the inner rectangle after rotating this inner rectangle. I'm interested in the largest individual sides, not their area.
I believe this comes down to deriving the width and height of the resulting rectangle as a function of the given variables and maximizing those.
Taking an example:
The sides of the resulting bounding box are given by $h = h_1 + h_2 = a sin theta + b cos theta$.
I'm unsure if there is a distinction between situation $a<b$ or not but I believe the result will be obtained in analogous manner regardless.
How would I in this example with $a<b$ maximize $h$?
trigonometry rectangles
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
$endgroup$
Given an orthogonal rectangle with sides a and b, what rotations $theta$ result in a bounding box with maximum height c.q. width?
I hope this is formulated correctly. By bounding box, I mean the smallest orthogonal rectangle that contains each of the 4 corners of the inner rectangle after rotating this inner rectangle. I'm interested in the largest individual sides, not their area.
I believe this comes down to deriving the width and height of the resulting rectangle as a function of the given variables and maximizing those.
Taking an example:
The sides of the resulting bounding box are given by $h = h_1 + h_2 = a sin theta + b cos theta$.
I'm unsure if there is a distinction between situation $a<b$ or not but I believe the result will be obtained in analogous manner regardless.
How would I in this example with $a<b$ maximize $h$?
trigonometry rectangles
trigonometry rectangles
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
asked Dec 28 '18 at 16:35
Frank RazenbergFrank Razenberg
1032
1032
closed as off-topic by Cesareo, Leucippus, KReiser, José Carlos Santos, metamorphy Dec 29 '18 at 8:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Cesareo, Leucippus, José Carlos Santos, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Cesareo, Leucippus, KReiser, José Carlos Santos, metamorphy Dec 29 '18 at 8:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Cesareo, Leucippus, José Carlos Santos, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59
add a comment |
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59
add a comment |
1 Answer
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The maximum height possible is the length of the diagonal. This occurs when the diagonal is verticle. $$h_{max}=sqrt{a^2+b^2}$$
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The maximum height possible is the length of the diagonal. This occurs when the diagonal is verticle. $$h_{max}=sqrt{a^2+b^2}$$
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
$endgroup$
add a comment |
$begingroup$
The maximum height possible is the length of the diagonal. This occurs when the diagonal is verticle. $$h_{max}=sqrt{a^2+b^2}$$
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
$endgroup$
add a comment |
$begingroup$
The maximum height possible is the length of the diagonal. This occurs when the diagonal is verticle. $$h_{max}=sqrt{a^2+b^2}$$
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
$endgroup$
The maximum height possible is the length of the diagonal. This occurs when the diagonal is verticle. $$h_{max}=sqrt{a^2+b^2}$$
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
answered Dec 28 '18 at 16:51
Daniel MathiasDaniel Mathias
1,36018
1,36018
add a comment |
add a comment |
$begingroup$
rotation around the center of the rectangle?
$endgroup$
– T. Fo
Dec 28 '18 at 16:59