Finding the faces of a shape from coordinates
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I have shapes, both regular and irregular that are defined by a set of 3D xyz coordinates i.e. 100 coordinates that define a cube. Some of there coordinates make up the faces of the cube and some of the coordinates are within the cube.
I want to know whether there is some form of algorithm or formula that can analyse the coordinates and determine which of the coordinates make up the faces of the cube?
Thanks for the help in advance.
geometry coordinate-systems
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up vote
0
down vote
favorite
I have shapes, both regular and irregular that are defined by a set of 3D xyz coordinates i.e. 100 coordinates that define a cube. Some of there coordinates make up the faces of the cube and some of the coordinates are within the cube.
I want to know whether there is some form of algorithm or formula that can analyse the coordinates and determine which of the coordinates make up the faces of the cube?
Thanks for the help in advance.
geometry coordinate-systems
A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have shapes, both regular and irregular that are defined by a set of 3D xyz coordinates i.e. 100 coordinates that define a cube. Some of there coordinates make up the faces of the cube and some of the coordinates are within the cube.
I want to know whether there is some form of algorithm or formula that can analyse the coordinates and determine which of the coordinates make up the faces of the cube?
Thanks for the help in advance.
geometry coordinate-systems
I have shapes, both regular and irregular that are defined by a set of 3D xyz coordinates i.e. 100 coordinates that define a cube. Some of there coordinates make up the faces of the cube and some of the coordinates are within the cube.
I want to know whether there is some form of algorithm or formula that can analyse the coordinates and determine which of the coordinates make up the faces of the cube?
Thanks for the help in advance.
geometry coordinate-systems
edited Aug 16 at 9:52
asked Aug 16 at 9:18
user584683
A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30
add a comment |Â
A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30
A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30
add a comment |Â
1 Answer
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It is very important to know, whether the set of coordinates (let's call it $C$) really contains corner-vertices. If not, the cube won't be unique (but you could search for a cube with minimal volume or something like that). See those 2D-pictures:
We see two possible "cubes" that realise the coordinates, though the middle picture really realises some coordinates as corners.
If you know that the $C$ contains all corners of the cube you search, then the cube is the convex hull of $C$. There is a well etablished set of algorithms which calculate the convex hull, as Jaap Scherphuis already pointed out.
answered Aug 16 at 9:43
Babelfish
647115
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
It is very important to know, whether the set of coordinates (let's call it $C$) really contains corner-vertices. If not, the cube won't be unique (but you could search for a cube with minimal volume or something like that). See those 2D-pictures:
We see two possible "cubes" that realise the coordinates, though the middle picture really realises some coordinates as corners.
If you know that the $C$ contains all corners of the cube you search, then the cube is the convex hull of $C$. There is a well etablished set of algorithms which calculate the convex hull, as Jaap Scherphuis already pointed out.
answered Aug 16 at 9:43
Babelfish
647115
add a comment |Â
up vote
1
down vote
It is very important to know, whether the set of coordinates (let's call it $C$) really contains corner-vertices. If not, the cube won't be unique (but you could search for a cube with minimal volume or something like that). See those 2D-pictures:
We see two possible "cubes" that realise the coordinates, though the middle picture really realises some coordinates as corners.
If you know that the $C$ contains all corners of the cube you search, then the cube is the convex hull of $C$. There is a well etablished set of algorithms which calculate the convex hull, as Jaap Scherphuis already pointed out.
answered Aug 16 at 9:43
Babelfish
647115
add a comment |Â
up vote
1
down vote
up vote
1
down vote
It is very important to know, whether the set of coordinates (let's call it $C$) really contains corner-vertices. If not, the cube won't be unique (but you could search for a cube with minimal volume or something like that). See those 2D-pictures:
We see two possible "cubes" that realise the coordinates, though the middle picture really realises some coordinates as corners.
If you know that the $C$ contains all corners of the cube you search, then the cube is the convex hull of $C$. There is a well etablished set of algorithms which calculate the convex hull, as Jaap Scherphuis already pointed out.
answered Aug 16 at 9:43
Babelfish
647115
It is very important to know, whether the set of coordinates (let's call it $C$) really contains corner-vertices. If not, the cube won't be unique (but you could search for a cube with minimal volume or something like that). See those 2D-pictures:
We see two possible "cubes" that realise the coordinates, though the middle picture really realises some coordinates as corners.
If you know that the $C$ contains all corners of the cube you search, then the cube is the convex hull of $C$. There is a well etablished set of algorithms which calculate the convex hull, as Jaap Scherphuis already pointed out.
answered Aug 16 at 9:43
Babelfish
647115
edited Aug 16 at 9:49
answered Aug 16 at 9:43
Babelfish
647115
answered Aug 16 at 9:43
Babelfish
647115
answered Aug 16 at 9:43
Babelfish
647115
647115
add a comment |Â
add a comment |Â
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A convex hull algorithm?
– Jaap Scherphuis
Aug 16 at 9:23
Is there any guarantee that your set of coordinates includes points from the sides and corners? If not, the cube won't be unique. Just think of four points in the plane that form a quadrilateral. You could wrap them with other quadrilaterals. In the result, the coordinates would not longer be corners of the quadrilateral. On the other hand, if you know that all corner-points are part of your coordinate set, then any convex hull algorithm will yield the faces.
– Babelfish
Aug 16 at 9:24
Yes, some of the points will be in the faces of the faces. The convex hull algorithm looks promising though.
– user584683
Aug 16 at 9:30