Finding Total Area of Intersecting Planes

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In summary, the conversation discusses different methods for calculating the total area or volume of intersecting planes or polygons. The main concern is finding a method that is easily programmable and does not require long computations. The specific example mentioned is finding the volume of intersecting cubes, but the question is more generally about finding the total volume or area of overlapping polygons or polyhedrons.
  • #1
nash_81
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hello grp...

is there any algorithm of findin the total area of an intersecting plane. i have tried with set theory if a n b r two planes,
area(a)+Area(b)-Area(a intersection b)

but it takes such a long computation when u go on adding planes to the existing ones. I want to have something which cud b easily programmable...without takin much longer 4 computations(by the processor)...

So is there any new method...

thnx in advance
 
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  • #2
what do, you mean by a plane? To me a euclidean plane has infinite euclidean area.

and the intersection of two general planes in three space is a line, which has zero area, although it has infinite length.
 
  • #3
hi mathwonk,

sorry 4 not makin it clear...i want to calculate the volume in principle of two intersecting cubes and mainly the volume of two intersecting regions which may have its intersection point anywhere...jus like stemnitz solid r an intersecting cylinder..hope that makes it clear...but its not result of jus two intersecting cubes but a lot more cud b added r deleted and it may jus be anywhere...
 
  • #4
i'm still pretty much in the dark as to what you want.
 
  • #5
nash_81, let me see if I understand your question.

Given polygons A and B, calculate the total area of the union of those (possibly overlapping) polygons.

More generally, given polyhedrons A and B, calculate the total volume of the union of those (possibly overlapping) polyhedrons.

Are these your questions?
 
  • #6
exactly robphy

dats wat i wan xactly
 

1. How do you find the total area of intersecting planes?

To find the total area of intersecting planes, you will need to first determine the individual areas of each plane. Then, you can use the formula A = L * W to calculate the area of each plane. Finally, add up all the individual areas to get the total area of the intersecting planes.

2. What are the key considerations when finding the total area of intersecting planes?

Some key considerations when finding the total area of intersecting planes include making sure that the planes intersect at right angles, accurately measuring the dimensions of each plane, and correctly using the formula for area calculation.

3. Can you find the total area of intersecting planes if they are not perpendicular?

Yes, you can find the total area of intersecting planes even if they are not perpendicular. However, the calculation will be more complex and may require the use of trigonometric functions.

4. How does finding the total area of intersecting planes relate to real-world applications?

Finding the total area of intersecting planes is a common task in various fields such as architecture, engineering, and construction. It is used to determine the total area of surfaces that intersect, which is important for designing structures, calculating material needs, and estimating costs.

5. Are there any tools or software that can assist with finding the total area of intersecting planes?

Yes, there are various tools and software available that can assist with finding the total area of intersecting planes. These include calculators with area calculation functions, as well as more advanced CAD (computer-aided design) software that can accurately calculate and visualize the intersecting planes.

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