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Given area of circle, find the radius of each circle that can fit the area
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I have the following given values:
- area of the big circle
- values ranging from 1 to 100 (it can be more or less)
I need to create a circle for each value, where its size is proportional to its value. For example, a value of 5 will become a circle that is smaller, while a value of 20 will become a larger circle.
Then, all these circles should fit inside the big circle.
My goal is to find the radius of each circle.
algorithms circle
asked Jul 30 at 14:38
iPhoneJavaDev
1011
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up vote
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down vote
favorite
I have the following given values:
- area of the big circle
- values ranging from 1 to 100 (it can be more or less)
I need to create a circle for each value, where its size is proportional to its value. For example, a value of 5 will become a circle that is smaller, while a value of 20 will become a larger circle.
Then, all these circles should fit inside the big circle.
My goal is to find the radius of each circle.
algorithms circle
asked Jul 30 at 14:38
iPhoneJavaDev
1011
Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have the following given values:
- area of the big circle
- values ranging from 1 to 100 (it can be more or less)
I need to create a circle for each value, where its size is proportional to its value. For example, a value of 5 will become a circle that is smaller, while a value of 20 will become a larger circle.
Then, all these circles should fit inside the big circle.
My goal is to find the radius of each circle.
algorithms circle
asked Jul 30 at 14:38
iPhoneJavaDev
1011
I have the following given values:
- area of the big circle
- values ranging from 1 to 100 (it can be more or less)
I need to create a circle for each value, where its size is proportional to its value. For example, a value of 5 will become a circle that is smaller, while a value of 20 will become a larger circle.
Then, all these circles should fit inside the big circle.
My goal is to find the radius of each circle.
algorithms circle
asked Jul 30 at 14:38
iPhoneJavaDev
1011
asked Jul 30 at 14:38
iPhoneJavaDev
1011
asked Jul 30 at 14:38
iPhoneJavaDev
1011
asked Jul 30 at 14:38
iPhoneJavaDev
1011
1011
Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20
add a comment |Â
Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20
Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20
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Not clear to me, but if the values are $A_1,A_2,A_3,ldots$, and each one is to be interpreted as the area $A_i = pi r_i^2$ of the $i$-th circle, then $$r_i = sqrtfracA_ipi$$ Is that helpful? EDIT: Or is this instead a packing problem where you try to pack a bunch of circular discs of different sizes into one big circle? In that case, it is hard to find an optimal packing!
– Jeppe Stig Nielsen
Jul 30 at 14:47
I think it's straightforward to get the radius of each circle whose area is Ai. However, I still need to know the area of each circle, which is the Ai of each circle. This is provided that all these circles will be packed inside a big circle having an area of, say, Abig. Meaning Abig > A1 + A2 +.... An.
– iPhoneJavaDev
Jul 30 at 14:53
@iPhoneJavaDev What are you doing this for? Do you need a visualization for $100 = 50 + 25 + 10 + 7 + 5 + 3$ that involves pouring little circles into a big one in a way that visually fills up the big circle? Like Jeppe mentioned, this is a fairly intensive problem and I might suggest not using circles. Maybe stuff flexible bubbles in there? ...
– John
Jul 30 at 15:11
Yes, I need to display the data into bubble chart. However, I need them to be circles that merge in the center forming a big circle. The reason that Abig > A1 + A2 + ... An is that if I pack those circles together, there will be gaps among them to avoid overlapping of circles. I try to scale the radius of each circle based on their value, however, for some case, they perfectly fit the big area Abig. For some combinations of data, they overflow. And for some case, they form into a circle much smaller than Abig. I need to scale the circles based on their value to somehow fit Abig properly.
– iPhoneJavaDev
Jul 30 at 15:20