Is that possible that poly2tri creates new points for the triangulation, or does it always use the given points only (the points on the contour and holes)?
When using a Contrained Delaunay Triangulation in 2D, the only points in your model will be those of the input polygons.
Adding points inside the domain will need a mesher like the one of CGAL. Python and Java bindings are also available.
You can give interior points to poly2tri but it does not create any new points.
Related
I'm trying to create this in Gamemaker. I already know the Voronoi vertices but i'm stuck with how to create polygons for each seed object. I need them to be independent so i can split it up later to apply texture mapping to them.
I've tried delaunay already but it doesn't seem as accurate as my voronoi generation. But being that the cicrumradius is the voronoi vertices anyways i feel like i don't need it. The problem with the Delaunay is that it only returns the points near the center of the diagram and doesn't return any points towards the Borders of the Box. The only good thing is that delaunay did skip an extra step and made it easier to return if the the seeds x and y are within the circumradius then just add them to the list of vertices
Is there any way to make a polygon from a plot of points from a data structure?
Pick the midpoint of each edge and the distance to each site then sort the result and pick the first and second (when they are equal) and save them into polygons. For the borders there is of course only 1 edge.
Duplicate:Getting polygons from voronoi edges
I understand how to use delaunay triangulation in 2d points?
But how to use delaunay triangulation in 3d points?
I mean I want to generate surface triangle mesh not tetrahedron mesh, so how can I use delaunay triangulation to generate 3d surface mesh?
Please give me some hint.
To triangulate a 3D point cloud you need the BallPivoting algorithm: https://vgc.poly.edu/~csilva/papers/tvcg99.pdf
There are two meanings of a 3D triangulation. One is when the whole space is filled, likely with tetrahedra (hexahedra and others may be also used). The other is called 2.5D, typically for terrains where the z is a property as the color or whatever, which doesn't influence the resulting triangulation.
If you use Shewchuk's triangle you can get the result.
If you are curious enough, you'll be able to select those tetrahedra that have one face not shared with other tetrahedra. These are the same tetrahedra "joined" with infinite/enclosing points. Extract those faces and you have your 3D surface triangulation.
If you want "direct" surface reconstruction then you undoubtly need to know in advance which vertices among the total given are in the surface. If you don't know them, perhaps the "maxima method" allows to find them out.
One your points cloud consists only of surface vertices, the triangulation method can be any one you like, from (adapted) incremental Chew's, Ruppert, etc to "ball-pivoting" method and "marching cubes" method.
The Delaunay tetrahedrization doesn't fit for two reasons
it fills a volume with tetrahedra, instead of defining a surface,
it fills the convex hull of the points, which is probably not what you expect.
To address the second problem, you need to accept concavities, and this implies that you need to specify a reference scale that tells what level of detail you want. This leads to the concept of Alpha Shapes, which are obtained as a subset of the faces.
Lookup "Alpha Shape" in an image search engine.
I have a GPX file with locations and altitude data.
I would like to create a 3D model and show this model using SceneKit.
I already tried the method using a NSBezierPath, but the problem is, that I can not add the Z data and it is more like a 2D route.
Right now I am creating a SCNBox for every single trackpoint - well, it works but it's not really that pretty and it kinda seems wrong.
I also thought about creating a 3D model (obj file) programatically, but this is too hard.
So, long story short: What is the best way to create a 3D geometry object with SceneKit when I got a list of points with X/Y/Z data?
Is there a way to "connect" SCNBoxes?
Regards,
Sascha
Try the SCNShape class. It allows you to create a 3D shape following a bezier path while controlling the Z axis as well:
"SceneKit creates a three-dimensional geometry by extruding a Bézier path, which extends in the x- and y-axis directions of its local coordinate space, along the z-axis by a specified amount."
I have some points on the edge(left image), and I want to construct a mesh(right), Is there any good algorithm to achieve it? many thanks!
image can see here http://ww3.sinaimg.cn/large/6a2c8e2bjw1dk8jr3t7eaj.jpg
To begin with, see Delauney triangulation. Look at this project: http://people.sc.fsu.edu/~jburkardt/c_src/triangulate/triangulate.html.
Edited because my original had too few details on edge-flipping, and when I tried to provided those details I found the TRIANGULATE project.
If the region is flat or quasi-flat look for Ear Clipping approach (http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf). In the case of curved surface you need point inside the region and therefore you may need Constrained Delaunay Triangulation (otherwise some edges may not be included in the triangulation).
There is delaunayn function in geometry package for R language (see doc)
It takes an array of boundary points (as in your case) to create a Delaunay mesh on it.
You could also save your geometry into some well-known format, and use one of mesh generators.
I want to create a Voronoi diagram on several pairs of
latitudes/longitudes, but want to use the great circle distance
between them, not the (inaccurate) Pythagorean distance.
Can I make qhull/qvoronoi or some other Linux program do this?
I considered mapping the points to 3D, having qvoronoi create a 3D
Voronoi diagram[1], and intersecting the result with the unit sphere, but
I'm not sure that's easy.
[1] I realize the 3D distance between two latitudes/longitudes (the
"through the Earth" path) isn't the same as the great circle distance,
but it's easy to prove that this transformation preserves relative
distances, which is all that matters for a Voronoi diagram.
I assume you've found this article. From that, it seems like you have the right idea by using a 3D embedding. Your question is then how to intersect the result with the sphere.
First of all you need to consider how you're going to represent the voronoi diagram. If you want to work in lat/long coordinates in a 2D plane, then your voronoi diagram will contain curved edges, so maybe it is best to just use a 3D representation.
If you use a program like qvoronoi, you should in theory only need the inifinite hyperplane data (generated by Fo). This gives you the equation of the plane and the two points it corresponds to. Usually you only need to use the voronoi diagram to test for inclusion within regions, and the hyperplanes should be enough for that.
See also this question: Algorithm to compute a Voronoi diagram on a sphere?