"Johannes Korsawe" <johannes.korsawe.nospam@volkswagen.de> wrote in message <i5qho2$ihh$1@fred.mathworks.com>...
> Dear community,
>
> is there any tool to unwind (simply) warped (triangulated) 3d surfaces, e.g. the surface shell of a cylinder (height h, radius r), which should then result in a rectangle of height h and width 2*pi*r.
>
> I know that the resulting surface will be nonoverlapping only in some cases, especially not in the case of bidirectional warped surfaces.
>
> My ideas towards such an algorithm are the following:
>
> 1. Start from some triangle of the triangulated surface.
> 2. go through all edges and "flatten" the adjacent triangles by rotating the non-common cornerpoint around the sharted edge.
> 3. mark initial triangle as "processed" and the three adjacent triangles as "to be processed"
> 4. handle all not yet processed triangles in the similar way as in points 2 and 3
>
> using this as a draft for an algorithm, one would have to solve some severe inconstency as one vertex belongs to several triangles and therefore can be "rotated into the target plane" about several edges. This will result in several different projection/rotation points for this vertex. This multiplicity of results could be "solved" by using a mean value, but as this will happen during the algorithm sketched above, the handling of this vertex will also affect later rotation-results.
>
> So, is there any idea instead of this "algorithm" or any hint on how to solve this task?
Expect to see problems for this even with a singly curved
cylinder.
Imagine the path you take to a given vertex from your
starting triangle. The unrolled location of a vertex some
number of steps away from the start point will depend
on the specific sequence of triangles you choose to
unroll first. In fact, it is probably possible to choose
some degenerate case that causes some topological
strangeness.
And no matter what you do, in the end you must resolve
the topological issues when you have wrapped completely
around the surface. All of this gets worse on doubly curved
surfaces or surfaces with holes in them. The surface of a
torus or worse, a pretzel, would surely be fun here.
John
> Dear community,
>
> is there any tool to unwind (simply) warped (triangulated) 3d surfaces, e.g. the surface shell of a cylinder (height h, radius r), which should then result in a rectangle of height h and width 2*pi*r.
>
> I know that the resulting surface will be nonoverlapping only in some cases, especially not in the case of bidirectional warped surfaces.
>
> My ideas towards such an algorithm are the following:
>
> 1. Start from some triangle of the triangulated surface.
> 2. go through all edges and "flatten" the adjacent triangles by rotating the non-common cornerpoint around the sharted edge.
> 3. mark initial triangle as "processed" and the three adjacent triangles as "to be processed"
> 4. handle all not yet processed triangles in the similar way as in points 2 and 3
>
> using this as a draft for an algorithm, one would have to solve some severe inconstency as one vertex belongs to several triangles and therefore can be "rotated into the target plane" about several edges. This will result in several different projection/rotation points for this vertex. This multiplicity of results could be "solved" by using a mean value, but as this will happen during the algorithm sketched above, the handling of this vertex will also affect later rotation-results.
>
> So, is there any idea instead of this "algorithm" or any hint on how to solve this task?
Expect to see problems for this even with a singly curved
cylinder.
Imagine the path you take to a given vertex from your
starting triangle. The unrolled location of a vertex some
number of steps away from the start point will depend
on the specific sequence of triangles you choose to
unroll first. In fact, it is probably possible to choose
some degenerate case that causes some topological
strangeness.
And no matter what you do, in the end you must resolve
the topological issues when you have wrapped completely
around the surface. All of this gets worse on doubly curved
surfaces or surfaces with holes in them. The surface of a
torus or worse, a pretzel, would surely be fun here.
John