Finding Overlap of polygons in 3D space The Next CEO of Stack OverflowAlgorithm for joining two polygons based on set of 2D pointsDetermine direction of minimum overlap of convex polygonsAlgorithms for covering a rectilinear polygon using rectangles of the same sizesample variance of regular polygon upon superimposition of verticesDerivation/equation for solid angle factor correctionEvaluating percentage area matched of two polygons (trapezoids)Which polygons are “mediogons” of simple polygons?The most effective windshield-wiper setup. (Packing a square with sectors)Detecting topology in 3d space for polygonsChoosing the optimal nonempty intersection from a list of pairs of shapes
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Finding Overlap of polygons in 3D space
The Next CEO of Stack OverflowAlgorithm for joining two polygons based on set of 2D pointsDetermine direction of minimum overlap of convex polygonsAlgorithms for covering a rectilinear polygon using rectangles of the same sizesample variance of regular polygon upon superimposition of verticesDerivation/equation for solid angle factor correctionEvaluating percentage area matched of two polygons (trapezoids)Which polygons are “mediogons” of simple polygons?The most effective windshield-wiper setup. (Packing a square with sectors)Detecting topology in 3d space for polygonsChoosing the optimal nonempty intersection from a list of pairs of shapes
$begingroup$
I'm trying to find the amount of "overlap" between two (or more) polygons in a 3D space.
The planes all have vector normals pointing in the same direction, so they are guaranteed to be parallel to each other.
The concrete example I can think of is as following:
if arranging playing cards perpendicular to a light source such as the sun, where some may overlap, "What is the total area of the shadow they cast?"
Visual example is given below with two "overlapping" polygons:
overlapping polygons
For instance, if the z-axis is shown vertically, the planes might be stacked something like this:
____________________
|
|
|
_________
|
|
_____________
Or viewing the X-Y plane, where - represents areas of overlap which should be counted only once in a final area measurement:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
Is there an algorithm that can determine the total area "shadow cast" of these polygons? They may not be rectangles, so the data I have to work with will be simply the points of each polygon (and which polygon it belongs to), represented as (x,y,z) digits.
geometry euclidean-geometry 3d
asked Mar 19 at 10:08
partytrainpartytrain
11
$endgroup$
add a comment |
$begingroup$
I'm trying to find the amount of "overlap" between two (or more) polygons in a 3D space.
The planes all have vector normals pointing in the same direction, so they are guaranteed to be parallel to each other.
The concrete example I can think of is as following:
if arranging playing cards perpendicular to a light source such as the sun, where some may overlap, "What is the total area of the shadow they cast?"
Visual example is given below with two "overlapping" polygons:
overlapping polygons
For instance, if the z-axis is shown vertically, the planes might be stacked something like this:
____________________
|
|
|
_________
|
|
_____________
Or viewing the X-Y plane, where - represents areas of overlap which should be counted only once in a final area measurement:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
Is there an algorithm that can determine the total area "shadow cast" of these polygons? They may not be rectangles, so the data I have to work with will be simply the points of each polygon (and which polygon it belongs to), represented as (x,y,z) digits.
geometry euclidean-geometry 3d
asked Mar 19 at 10:08
partytrainpartytrain
11
$endgroup$
add a comment |
$begingroup$
I'm trying to find the amount of "overlap" between two (or more) polygons in a 3D space.
The planes all have vector normals pointing in the same direction, so they are guaranteed to be parallel to each other.
The concrete example I can think of is as following:
if arranging playing cards perpendicular to a light source such as the sun, where some may overlap, "What is the total area of the shadow they cast?"
Visual example is given below with two "overlapping" polygons:
overlapping polygons
For instance, if the z-axis is shown vertically, the planes might be stacked something like this:
____________________
|
|
|
_________
|
|
_____________
Or viewing the X-Y plane, where - represents areas of overlap which should be counted only once in a final area measurement:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
Is there an algorithm that can determine the total area "shadow cast" of these polygons? They may not be rectangles, so the data I have to work with will be simply the points of each polygon (and which polygon it belongs to), represented as (x,y,z) digits.
geometry euclidean-geometry 3d
asked Mar 19 at 10:08
partytrainpartytrain
11
$endgroup$
I'm trying to find the amount of "overlap" between two (or more) polygons in a 3D space.
The planes all have vector normals pointing in the same direction, so they are guaranteed to be parallel to each other.
The concrete example I can think of is as following:
if arranging playing cards perpendicular to a light source such as the sun, where some may overlap, "What is the total area of the shadow they cast?"
Visual example is given below with two "overlapping" polygons:
overlapping polygons
For instance, if the z-axis is shown vertically, the planes might be stacked something like this:
____________________
|
|
|
_________
|
|
_____________
Or viewing the X-Y plane, where - represents areas of overlap which should be counted only once in a final area measurement:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
AAAAAAAAAAAAAAAA--------------BBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBB
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
BBBBBB-----------CCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCC
Is there an algorithm that can determine the total area "shadow cast" of these polygons? They may not be rectangles, so the data I have to work with will be simply the points of each polygon (and which polygon it belongs to), represented as (x,y,z) digits.
geometry euclidean-geometry 3d
geometry euclidean-geometry 3d
asked Mar 19 at 10:08
partytrainpartytrain
11
asked Mar 19 at 10:08
partytrainpartytrain
11
edited Mar 19 at 10:23
partytrain
asked Mar 19 at 10:08
partytrainpartytrain
11
asked Mar 19 at 10:08
partytrainpartytrain
11
asked Mar 19 at 10:08
partytrainpartytrain
11
11
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You can use a "scanline" approach. Consider drawing an horizontal line by every vertex. Two successive lines cut trapeziums (trapezia ?) or triangles out of the polygons. If the input polygons are convex, there is never more than one trapezium per slab.
It is a relatively easier matter to check if two trapeziums overlap or not, and if they overlap, what is their union (in the worst case, there are four side/side intersections to be considered).
Depending on your application, you can just compute the areas of the unions, or reconstruct the global polygon. There are classical algorithms to achieve this, but they are difficult. https://en.wikipedia.org/wiki/Vatti_clipping_algorithm
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
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$begingroup$
You can use a "scanline" approach. Consider drawing an horizontal line by every vertex. Two successive lines cut trapeziums (trapezia ?) or triangles out of the polygons. If the input polygons are convex, there is never more than one trapezium per slab.
It is a relatively easier matter to check if two trapeziums overlap or not, and if they overlap, what is their union (in the worst case, there are four side/side intersections to be considered).
Depending on your application, you can just compute the areas of the unions, or reconstruct the global polygon. There are classical algorithms to achieve this, but they are difficult. https://en.wikipedia.org/wiki/Vatti_clipping_algorithm
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
You can use a "scanline" approach. Consider drawing an horizontal line by every vertex. Two successive lines cut trapeziums (trapezia ?) or triangles out of the polygons. If the input polygons are convex, there is never more than one trapezium per slab.
It is a relatively easier matter to check if two trapeziums overlap or not, and if they overlap, what is their union (in the worst case, there are four side/side intersections to be considered).
Depending on your application, you can just compute the areas of the unions, or reconstruct the global polygon. There are classical algorithms to achieve this, but they are difficult. https://en.wikipedia.org/wiki/Vatti_clipping_algorithm
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
You can use a "scanline" approach. Consider drawing an horizontal line by every vertex. Two successive lines cut trapeziums (trapezia ?) or triangles out of the polygons. If the input polygons are convex, there is never more than one trapezium per slab.
It is a relatively easier matter to check if two trapeziums overlap or not, and if they overlap, what is their union (in the worst case, there are four side/side intersections to be considered).
Depending on your application, you can just compute the areas of the unions, or reconstruct the global polygon. There are classical algorithms to achieve this, but they are difficult. https://en.wikipedia.org/wiki/Vatti_clipping_algorithm
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
$endgroup$
You can use a "scanline" approach. Consider drawing an horizontal line by every vertex. Two successive lines cut trapeziums (trapezia ?) or triangles out of the polygons. If the input polygons are convex, there is never more than one trapezium per slab.
It is a relatively easier matter to check if two trapeziums overlap or not, and if they overlap, what is their union (in the worst case, there are four side/side intersections to be considered).
Depending on your application, you can just compute the areas of the unions, or reconstruct the global polygon. There are classical algorithms to achieve this, but they are difficult. https://en.wikipedia.org/wiki/Vatti_clipping_algorithm
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
answered Mar 19 at 10:47
Yves DaoustYves Daoust
131k676229
131k676229
add a comment |
add a comment |
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