Finding Total Area of Intersecting Planes

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Discussion Overview

The discussion revolves around finding an efficient method to calculate the total area or volume of intersecting planes or polyhedrons, particularly focusing on the computational aspects and potential algorithms for handling multiple intersecting shapes.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about algorithms for calculating the total area of intersecting planes, expressing concerns about the computational complexity of existing methods using set theory.
  • Another participant questions the definition of a plane, noting that a Euclidean plane has infinite area and that the intersection of two planes in three-dimensional space results in a line with zero area.
  • A participant clarifies that they are interested in calculating the volume of intersecting regions, specifically mentioning examples like intersecting cubes and cylinders, and the potential for adding or removing shapes.
  • One participant seeks to confirm their understanding of the original question, restating it in terms of calculating the total area of overlapping polygons or the total volume of overlapping polyhedrons.
  • A later reply confirms that the restatement accurately captures the original inquiry.

Areas of Agreement / Disagreement

Participants express differing views on the definition of planes and the nature of intersections, leading to some confusion. There is no consensus on the best method for calculating areas or volumes, and the discussion remains unresolved regarding the most efficient computational approach.

Contextual Notes

There are limitations in the definitions used by participants, particularly regarding the nature of planes and intersections. The discussion also highlights the complexity involved in calculating areas and volumes of multiple intersecting shapes.

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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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.
 
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...
 
i'm still pretty much in the dark as to what you want.
 
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?
 
exactly robphy

dats wat i wan xactly
 

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