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Get Intersection line between two rectangles in 3D
I am trying to find a way to get the line (two points in 3D space) of the intersection between two rectangles.
I ran into this question: Intersection between two rectangles in 3D
But this is not my issue. In that question, the rectangle is treated as only the bounds (the perimeter), while I am looking for the rectangle as a whole (think about a picture frame vs the picture itself).
I've figured out that, in every case, there will either be an intersection line (two points), or no intersection at all. If the intersection was just on the borders, therefore just a point, it can be treated as no intersection in my case.
My scenario is that one of these rectangle represents a "static" surface, which cannot move or change. The other one represents a "dynamic" surface, which I have to adapt to avoid crossing
Example:
Once I obtain p1 and p2, which are points in the 3D space, my goal is to modify the Dynamic rectangle into a 3d polygon, which will no longer cross the static rectangle, like this:
So you can see why "edge intersections" are irrelevant to my situation. I am turning "real" intersections into edge intersections, so any edge intersection doesn't require me to do anything with it.
I am only looking for a formula, starting with two sets of 4 points (the rectangles), that would give me the two points of the line of their intersection, or would tell me that there is no (relevant) intersection.
Every formula I've found on this site or others doesn't fit my needs, or doesn't let me input arbitrary rectangles (for example, I can't fix my problem with a formula that uses planes or that treats a rectangle as simply 4 lines)
I am, of course, trying to code it (in C#), therefore any code answer is a great help, but I am confident that even a math-only answer would suffice for me to produce the code from it, therefore I will accept an answer that is only composed of pseudo-code or straight up mathematical formulas, provided they are either simple enough or explained well enough for me to understand what is happening.
c# math 3d intersection rectangles
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
add a comment |
I am trying to find a way to get the line (two points in 3D space) of the intersection between two rectangles.
I ran into this question: Intersection between two rectangles in 3D
But this is not my issue. In that question, the rectangle is treated as only the bounds (the perimeter), while I am looking for the rectangle as a whole (think about a picture frame vs the picture itself).
I've figured out that, in every case, there will either be an intersection line (two points), or no intersection at all. If the intersection was just on the borders, therefore just a point, it can be treated as no intersection in my case.
My scenario is that one of these rectangle represents a "static" surface, which cannot move or change. The other one represents a "dynamic" surface, which I have to adapt to avoid crossing
Example:
Once I obtain p1 and p2, which are points in the 3D space, my goal is to modify the Dynamic rectangle into a 3d polygon, which will no longer cross the static rectangle, like this:
So you can see why "edge intersections" are irrelevant to my situation. I am turning "real" intersections into edge intersections, so any edge intersection doesn't require me to do anything with it.
I am only looking for a formula, starting with two sets of 4 points (the rectangles), that would give me the two points of the line of their intersection, or would tell me that there is no (relevant) intersection.
Every formula I've found on this site or others doesn't fit my needs, or doesn't let me input arbitrary rectangles (for example, I can't fix my problem with a formula that uses planes or that treats a rectangle as simply 4 lines)
I am, of course, trying to code it (in C#), therefore any code answer is a great help, but I am confident that even a math-only answer would suffice for me to produce the code from it, therefore I will accept an answer that is only composed of pseudo-code or straight up mathematical formulas, provided they are either simple enough or explained well enough for me to understand what is happening.
c# math 3d intersection rectangles
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20
add a comment |
I am trying to find a way to get the line (two points in 3D space) of the intersection between two rectangles.
I ran into this question: Intersection between two rectangles in 3D
But this is not my issue. In that question, the rectangle is treated as only the bounds (the perimeter), while I am looking for the rectangle as a whole (think about a picture frame vs the picture itself).
I've figured out that, in every case, there will either be an intersection line (two points), or no intersection at all. If the intersection was just on the borders, therefore just a point, it can be treated as no intersection in my case.
My scenario is that one of these rectangle represents a "static" surface, which cannot move or change. The other one represents a "dynamic" surface, which I have to adapt to avoid crossing
Example:
Once I obtain p1 and p2, which are points in the 3D space, my goal is to modify the Dynamic rectangle into a 3d polygon, which will no longer cross the static rectangle, like this:
So you can see why "edge intersections" are irrelevant to my situation. I am turning "real" intersections into edge intersections, so any edge intersection doesn't require me to do anything with it.
I am only looking for a formula, starting with two sets of 4 points (the rectangles), that would give me the two points of the line of their intersection, or would tell me that there is no (relevant) intersection.
Every formula I've found on this site or others doesn't fit my needs, or doesn't let me input arbitrary rectangles (for example, I can't fix my problem with a formula that uses planes or that treats a rectangle as simply 4 lines)
I am, of course, trying to code it (in C#), therefore any code answer is a great help, but I am confident that even a math-only answer would suffice for me to produce the code from it, therefore I will accept an answer that is only composed of pseudo-code or straight up mathematical formulas, provided they are either simple enough or explained well enough for me to understand what is happening.
c# math 3d intersection rectangles
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
I am trying to find a way to get the line (two points in 3D space) of the intersection between two rectangles.
I ran into this question: Intersection between two rectangles in 3D
But this is not my issue. In that question, the rectangle is treated as only the bounds (the perimeter), while I am looking for the rectangle as a whole (think about a picture frame vs the picture itself).
I've figured out that, in every case, there will either be an intersection line (two points), or no intersection at all. If the intersection was just on the borders, therefore just a point, it can be treated as no intersection in my case.
My scenario is that one of these rectangle represents a "static" surface, which cannot move or change. The other one represents a "dynamic" surface, which I have to adapt to avoid crossing
Example:
Once I obtain p1 and p2, which are points in the 3D space, my goal is to modify the Dynamic rectangle into a 3d polygon, which will no longer cross the static rectangle, like this:
So you can see why "edge intersections" are irrelevant to my situation. I am turning "real" intersections into edge intersections, so any edge intersection doesn't require me to do anything with it.
I am only looking for a formula, starting with two sets of 4 points (the rectangles), that would give me the two points of the line of their intersection, or would tell me that there is no (relevant) intersection.
Every formula I've found on this site or others doesn't fit my needs, or doesn't let me input arbitrary rectangles (for example, I can't fix my problem with a formula that uses planes or that treats a rectangle as simply 4 lines)
I am, of course, trying to code it (in C#), therefore any code answer is a great help, but I am confident that even a math-only answer would suffice for me to produce the code from it, therefore I will accept an answer that is only composed of pseudo-code or straight up mathematical formulas, provided they are either simple enough or explained well enough for me to understand what is happening.
c# math 3d intersection rectangles
c# math 3d intersection rectangles
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
edited Jan 3 at 18:54
Kaito Kid
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
asked Jan 2 at 20:40
Kaito KidKaito Kid
2031621
2031621
Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20
add a comment |
Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20
Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20
add a comment |
1 Answer
1
active
oldest
votes
If you are OK with just algorithm rather than full code here is a sketch:
- Build 2 planes from the rectangles (any 3 points will do as in this answer)
- Find the intersection line
Iof those 2 planes as in this answer or find out that the planes are parallel so there is no intersection - Find the intersections of the
Iline with the lines containing all sides of the rectangles as in this answer
- Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the
Iline with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles. - Assuming at the previous step you found 2 segments (one in each rectangle) on the line
I, you just need to find their intersection and it will be your answer (again, empty means no intersection).
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
If you are OK with just algorithm rather than full code here is a sketch:
- Build 2 planes from the rectangles (any 3 points will do as in this answer)
- Find the intersection line
Iof those 2 planes as in this answer or find out that the planes are parallel so there is no intersection - Find the intersections of the
Iline with the lines containing all sides of the rectangles as in this answer
- Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the
Iline with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles. - Assuming at the previous step you found 2 segments (one in each rectangle) on the line
I, you just need to find their intersection and it will be your answer (again, empty means no intersection).
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
add a comment |
If you are OK with just algorithm rather than full code here is a sketch:
- Build 2 planes from the rectangles (any 3 points will do as in this answer)
- Find the intersection line
Iof those 2 planes as in this answer or find out that the planes are parallel so there is no intersection - Find the intersections of the
Iline with the lines containing all sides of the rectangles as in this answer
- Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the
Iline with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles. - Assuming at the previous step you found 2 segments (one in each rectangle) on the line
I, you just need to find their intersection and it will be your answer (again, empty means no intersection).
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
add a comment |
If you are OK with just algorithm rather than full code here is a sketch:
- Build 2 planes from the rectangles (any 3 points will do as in this answer)
- Find the intersection line
Iof those 2 planes as in this answer or find out that the planes are parallel so there is no intersection - Find the intersections of the
Iline with the lines containing all sides of the rectangles as in this answer
- Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the
Iline with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles. - Assuming at the previous step you found 2 segments (one in each rectangle) on the line
I, you just need to find their intersection and it will be your answer (again, empty means no intersection).
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
If you are OK with just algorithm rather than full code here is a sketch:
- Build 2 planes from the rectangles (any 3 points will do as in this answer)
- Find the intersection line
Iof those 2 planes as in this answer or find out that the planes are parallel so there is no intersection - Find the intersections of the
Iline with the lines containing all sides of the rectangles as in this answer
- Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the
Iline with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles. - Assuming at the previous step you found 2 segments (one in each rectangle) on the line
I, you just need to find their intersection and it will be your answer (again, empty means no intersection).
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
answered Jan 3 at 2:11
SergGrSergGr
21.4k22243
21.4k22243
add a comment |
add a comment |
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Tough problem with a lot of edge cases. Not simple. CAD tools do this well. Why would you not be able to use a tool?
– duffymo
Jan 2 at 21:25
I did not give out the whole picture here, but the rectangles are actually a big simplification of what I have, so having our own solution instead of using a tool is more flexible
– Kaito Kid
Jan 3 at 13:20