I have a few 1000s triangles connected in a 2D mesh grid. It represents water flow. This grid is a delaunay triangulation. I need to merge the triangles back into a minimal amount of simple polygons such that each polygon is constraint not to have interior holes. The output polygons should be the same shape.
Is there a known algorithm for accomplishing this?
answering my own question :)
I found the best way to do this is to use polygon union methods similar to disjoint subset merging. Here's a blog post on a fast implementation by taking advantage of spatial indices
http://lin-ear-th-inking.blogspot.com/2007/11/fast-polygon-merging-in-jts-using.html
Related
For my thesis I'm using a finite element flow solver to simulate the flow through a flume. The flow solver is capable of solving the flow in a 3D unstructured mesh constructed of tetrahedrons. However, the meshes I generate with Gmsh somehow seem to be too unstructured. Which leads too unsolvable and very slow runs.
At the moment I've tried to do simulations with both unstructured and structured meshes. Simulation with very coarse unstructured meshes go very well, however once I make the element size smaller, the flow solver only produces NaN values and doesn't run at all.
For the simulations with structured meshes I've used the transfinite technique to produce a very fine structured mesh. This mesh contains way more element than the unstructured one and the results are fine. However, in future runs I need to refine the mesh in certain areas which doesn't seem possible with the transfinite volume technique in 3D.
Does anyone have any what could possibly go wrong in this case? And is there a way to improve the quality of a 3D gmsh mesh? Can the structure of the mesh be improved somehow?
Thanks in advance!
Bart
I think the middle ground between a transfinite structured grid and a completely unstructured one would be one made of 8-node hexs. If your 3D case can be built from an extruded 2D case, you could try setting Mesh.Algorithm=8 to get right triangles (rather than equilaterals) and then use the Recombine Surface option to turn them into quads.
I have 3 sets of point cloud that represent one surface. I want to use these point clouds to construct triangular mesh, then use the mesh to represent the surface. Each set of point cloud is collected in different ways so their representation to this surface are different. For example, some sets can represent the surface with smaller "error". My questions are:
(1) What's the best way to evaluate such mesh-to-surface "error"?
(2) Is there a mature/reliable way to convert point cloud to triangular mesh? I found some software doing this but most requests extensive manual adjustment.
(3) After the conversion I get three meshes. I want to use a fourth mesh, namely Mesh4, to "fit" the three meshes, and get an "average" mesh of the three. Then I can use this Mesh4 as a representation of the underlying surface. How can I do/call this "mesh to mesh" fitting? Is it a mature technique?
Thank you very much for your time!
Please find below my answers for point 1 and 2:
as a metric for mesh-to-surface error you can use Hausdorff distance. For example, you could use Libigl to compare two meshes.
To obtain a mesh from a point cloud, have a look at PCL
all
I try to obtain one triangle mesh from one point cloud. The mesh is expected to be manifold, the triangles are well shaped or equilateral and the distribution of the points are adaptive in terms of the curvature.
There are valuable information provided on this website.
robust algorithm for surface reconstruction from 3D point cloud?
Mesh generation from points with x, y and z coordinates
I try Poisson reconstruction algorithm, but the triangles are not well shaped.
So I need to improve the quality of the triangles. I learn that centroidal voronoi tessellation(CVT) can achieve that, but I don't know whether the operation will introduce non-manifold vertices and self-intersection. I hope to get some information about it from you.
The mesh from the following post looks pretty good.
How to fill polygon with points regularly?
Delaunay refinement algorithm is used. Can delaunay refinement algorithm apply to triangle mesh directly? Do I first need to delaunay triangulation of the point cloud of the mesh, and then use the information from delaunay triangulation to perform delaunay refinement?
Thanks.
Regards
Jogging
I created the image in the mentioned post: You can insert all points into a Delaunay triangulation and then create a Zone object (area) consisting of these triangles. Then you call refine(pZone,...) to get a quality mesh. Other options are to create the Zone from constraint edges or as the result of a boolean operation. However, this library is made for 2D and 2.5D. The 3D version will not be released before 2014.
Do you know the BallPivoting approach?
I have a region bounded by a set of edges. I took those edges and added them as constraints to a Constrained_Delaunay_triangulation_2. I then performed a refinement step using refine_Delaunay_mesh_2(...). My understanding from
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Mesh_2_ref/Class_Triangulation_conformer_2.html
is that this may cause my original constraint segments to be split. That document mentions that I can instead use CGAL::Constrained_triangulation_plus_2 which allows my finding the relationship between the original constraints and the final edges. While this path is probably workable for my needs, I would prefer to refine the mesh such that the original boundary constraints are not split at all. Is there a setting for refine_Delaunay_mesh_2 that will disallow the splitting of these edges, or is there a related mesher that will accomplish this?
Thanks for any help.
Usually the constraints have to be split to enhance the quality of triangles in the mesh.
The 2d meshes can be modified not to split edges, though.
You can use classes or functions in the header <CGAL/Delaunay_mesher_no_edge_refinement_2.h>. That is not documented, but that is exactly the CGAL 2D mesher modified not to refine on constrained edges.
I have an array of sample points with their (X, Y, Z) coordinates. I use Delaunay Triangulation to generate an irregular network from them and then I use linear interpolation to plot contour lines at fixed values (e.g. 90, 95, 100, 105). The problem is that I need smooth contour lines to be generated with another algorithm. I've searched for some time now and found out that I need to use something like Kriging but I'm not that good at math to implement the algorithm from pure mathematical relations. Also I can't seem to find an implementation or explanation of the algorithm anywhere. Can anyone help me find one? Also, am I right with the chosen algorithm? Is there another one that can be easier to implement? Note that I don't care about precision.
https://dl.dropbox.com/u/15926260/ex.png
P.S. I've done a plot in Surfer showing the results that I'm looking for. On the right side is what I have done using triangulation and linear interpolation and on the left side is what I need to plot using a different algorithm (Kriging was used in Surfer).
Sorry for the spelling mistakes but I'm not a native language speaker.
Thank you!
You can try a regular (weighted) delaunay triangulation. In weighted delaunay triangulation triangle areas are more equal. IMO the kriging algorithm seems also to produce more equally contours. Weighted delaunay triangulation is also used to make smoother meshes.