I'm new to CGAL and I'm trying to cut a cube with an arbitrary surface mesh in 3d (no self intersections, not closed/no volume). The goal is to get a volume which consists of one "side" of the cut cube, closed by the part of the surface inside the cube.
The surface itself consists of unordered triangles which should have the same winding order (consistent normal directions) but have no neighborhood information and could contain same points multiple times for different triangles.
I tried to use the clip function, like:
CGAL::Polygon_mesh_processing::clip(cube,surface,true);
Which of course does not work because the surface is not closed (as far as I understood). But It shows the idea on how the operation should work.
Boolean operations (https://doc.cgal.org/latest/Polygon_mesh_processing/index.html#title14)) cannot be used for this as well since they are calculated on volumes and the surface has no volume.
I also thought about extending the outside of the surface so that it is closed. This, however, does not seem like a good approach.
Sadly, my research on similar problems was not successful.
I'm pretty sure that there is a nice way to do this in CGAL. Maybe someone with more experience in CGAL knows how to do this.
What would be the best approach for getting this volume?
Regards
EDIT:
By removing redundant points in my surface mesh I was able to get clip to work. Nevertheless, I do not always get the right side of the volume, even though the winding order should yield normals which point to the outside.
Is it necessary to calculate the normals and pass them as an extra parameter (see here) of the surface before the cut in order to always get the same "inner" side of the volume?
Also, the clip function seems to be quite slow. I have to do this cut for a very high number of cubes and different surfaces.
I use CGAL as header only lib and without GMP and MPFR, since it crashed my other application. How big is the speedup using these libraries and are there any other tricks which can be used to speedup computation, e.g. using parallelization?
I saw that CGAL uses Intel's TBB which. But in the header files which are included by the clipping algorithm CGAL_LINKED_WITH_TBB is not tested.
Thanks
It was a problem with the clipping mesh. Clipping could not be done properly. I increased it size and now it always intersects the volume.
Related
I need to generate a tetrahedral (volume) mesh of thin-walled object object. Think of objects like a bottle or a plastic bowl, etc, which are mostly hollow. The volumetric mesh is needed for an FEM simulation. A surface mesh of the outside surface of the object is available from measurement, using e.g. octomap or KinectFusion. Therefore the vertex spacing is relatively regular. The inner surface of the object can be calculated from the outside surface by moving all points inside, since the wall thickness is known.
So far, I have considered the following approaches:
Create a 3D Delaunay triangulation (which would destroy the existing surface meshes) and then remove all tetrahedra which are not between the two original surfaces. For this check, it might be required to create an implicit surface representation of the 2 surfaces.
Create a 3D Delaunay triangulation and remove tetrahedra which are "inside" (in the hollow space) or "outside" (of the outer surface) with Alphashapes.
Close the outside and inside meshes and load them into tetgen as the outside hull and as a hole respectively.
These approaches seem to be a bit inelegant to me, and they still have some pitfalls. I would probably need several libraries/tools for them. For 1 and 2, probably tetgen or another FEM meshing tool would still be required to create well-conditioned tetrahedra. Does anyone have a more straight-forward solution? I guess this should also be a common problem in 3D printing.
Concerning tools/libraries, I have looked into PCL, meshlab and tetgen so far. They all seem to do only part of the job. Ideally, I would like to use only open source libraries and avoid tools which require manual intervention.
One way is to:
create triangular mesh of surface points,
extrude (move) that surface to inner for a given thickness. That produces volume (triangular prism) mesh of a wall,
each prism can be split in three tetrahedrons.
The problem I see is aspect ratio.
A single layer of tetrahedra will not reproduce shell or bending behavior very well. A single element through the thickness will already require a large mesh. Putting more than one will likely break the bank in order to keep aspect ratios and angles acceptable.
I'd prefer brick or thick shell elements to tetrahedra in this case. I think the modeling will be easier and the behavior will be more faithful to the physics.
Currently I'm working on a little project just for a bit of fun. It is a C++, WinAPI application using OpenGL.
I hope it will turn into a RTS Game played on a hexagon grid and when I get the basic game engine done, I have plans to expand it further.
At the moment my application consists of a VBO that holds vertex and heightmap information. The heightmap is generated using a midpoint displacement algorithm (diamond-square).
In order to implement a hexagon grid I went with the idea explained here. It shifts down odd rows of a normal grid to allow relatively easy rendering of hexagons without too many further complications (I hope).
After a few days it is beginning to come together and I've added mouse picking, which is implemented by rendering each hex in the grid in a unique colour, and then sampling a given mouse position within this FBO to identify the ID of the selected cell (visible in the top right of the screenshot below).
In the next stage of my project I would like to look at generating more 'playable' terrains. To me this means that the shape of each hexagon should be more regular than those seen in the image above.
So finally coming to my point, is there:
A way of smoothing or adjusting the vertices in my current method
that would bring all point of a hexagon onto one plane (coplanar).
EDIT:
For anyone looking for information on how to make points coplanar here is a great explination.
A better approach to procedural terrain generation that would allow
for better control of this sort of thing.
A way to represent my vertex information in a different way that allows for this.
To be clear, I am not trying to achieve a flat hex grid with raised edges or platforms (as seen below).
)
I would like all the geometry to join and lead into the next bit.
I'm hope to achieve something similar to what I have now (relatively nice undulating hills & terrain) but with more controllable plateaus. This gives me the flexibility of cording off areas (unplayable tiles) later on, where I can add higher detail meshes if needed.
Any feedback is welcome, I'm using this as a learning exercise so please - all comments welcome!
It depends on what you actually want and what you mean by "more controlled".
Do you want to be able to say "there will be a mountain on coordinates [11, -127] with radius 20"? Complexity of this this depends on how far you want to go. If you want just mountains, then radial gradients are enough (just add the gradient values to the noise values). But if you want some more complex shapes, you are in for a treat.
I explore this idea to great depth in my project (please consider that the published version is just a prototype, which is currently undergoing major redesign, it is completely usable a map generator though).
Another way is to make the generation much more procedural - you just specify a sequence of mathematical functions, which you apply on the terrain. Even a simple value transformation can get you very far.
All of these methods should work just fine for hex grid. If artefacts occur because of the odd-row shift, then you could interpolate the odd rows instead (just calculate the height value for the vertex from the two vertices between which it is located with simple linear interpolation formula).
Consider a function, which maps the purple line into the blue curve - it emphasizes lower located heights as well as very high located heights, but makes the transition between them steeper (this example is just a cosine function, making the curve less smooth would make the transformation more prominent).
You could also only use bottom half of the curve, making peaks sharper and lower located areas flatter (thus more playable).
"sharpness" of the curve can be easily modulated with power (making the effect much more dramatic) or square root (decreasing the effect).
Implementation of this is actually extremely simple (especially if you use the cosine function) - just apply the function on each pixel in the map. If the function isn't so mathematically trivial, lookup tables work just fine (with cubic interpolation between the table values, linear interpolation creates artefacts).
Several more simple methods of "gamification" of random noise terrain can be found in this paper: "Realtime Synthesis of Eroded Fractal Terrain for Use in Computer Games".
Good luck with your project
Im trying to transform a path along an arc.
My project is running on osX 10.8.2 and the painting is done via CoreAnimation in CALayers.
There is a waveform in my project which will be painted by a path. There are about 200 sample points which are mirrored to the bottom side. These are painted 60 times per second and updated to a song postion.
Please ignore the white line, it is just a rotation indicator.
What i am trying to achieve is drawing a waveform along an arc. "Up" should point to the middle. It does not need to go all the way around. The waveform should be painted along the green circle. Please take a look at the sketch provided below.
Im not sure how to achieve this in a performant manner. There are many points per second that need coordinate correction.
I tried coming up with some ideas of my own:
1) There is the possibility to add linear transformations to paths, which, i think, will not help me here. The only thing i can think of is adding a point, rotating the path with a transformation, adding another point, rotating and so on. But this would be very slow i think
2) Drawing the path into an image and bending it would surely lead to image-artifacts.
3) Maybe the best idea would be to precompute sample points on an arc, then save save a vector to the center. Taking the y-coordinates of the waveform, placing them on the sample points and moving them along the vector to the center.
But maybe i am just not seeing some kind of easy solution to this problem. Help is really appreciated and fresh ideas very welcome. Thank you in advance!
IMHO, the most efficient way to go (in terms of CPU usage) would be to use some form of pre-computed approach that would take into account the resolution of the display.
Cleverly precomputed values
I would go for the mathematical transformation (from linear to polar) and combine two facts:
There is no need to perform expansive mathematical computation
There is no need to render two points that are too close from each other
I have no ready-made algorithm for you, but you could use a pre-computed sin or cos table, and match the data range to the display size in order to work with integers.
For instance imagine we have some data ranging from 0 to 1E6 and we need to display the sin value of each point in a 100 pix height rectangle. We can use a pre-computed sin table and work with integers. This way displaying the sin value of a point would be much quicker. This concept can be refined to get a nicer result.
Also, there are some ways to retain only significant points of a curve so that the displayed curve actually looks like the original (see the Ramer–Douglas–Peucker algorithm on wikipedia). But I found it to be inefficient for quickly displaying ever-changing data.
Using multicore rendering
You could compute different areas of the curve using multiple cores (can be tricky)
Or you could use pre-computing using several cores, and one core to do finish the job.
I'm trying to develop an app which allows you to walk around, and where you walked will be drawn on a map. I have this all working fine, but I'm finding that even with a reasonably accurate GPS location the points still jump around a bit. When drawn on a map this has the effect of creating a squiggly or zig-zag line.
I'm looking for suggestions/strategies on how to smooth the data, so that the line drawn on the map is more of a smooth best fit, rather than an accurate point to point drawing.
There are many different types of smoothing algorithms you could apply to the data (for a few starting points, see this Wikipedia article). The only way to know for sure which is/are suitable for your application is to implement and test them.
Simple or weighted moving averages are fairly common (taking the last n samples and averaging them), but have the problem of lagging behind the data. A common one for filtering signal noise is a high-pass filter, which attenuates small (noisy) movements while passing through larger ones. Apple has some code for this in their AccelerometerGraph sample.
I'd suggest trying those out first as they're easy to implement, before looking at the move complex ones.
I am writing a physics simulation using Ogre and MOC.
I have a sphere that I shoot from the camera's position and it travels in the direction the camera is facing by using the camera's forward vector.
I would like to know how I can detect the point of collision between my sphere and another mesh.
How would I be able to check for a collision point between the two meshes using MOC or OGRE?
Update: Should have mentioned this earlier. I am unable to use a 3rd party physics library as we I need to develop this myself (uni project).
The accepted solution here flat out doesn't work. It will only even sort of work if the mesh density is generally high enough that no two points on the mesh are farther apart than the diameter of your collision sphere. Imagine a tiny sphere launched at short range on a random vector at a huuuge cube mesh. The cube mesh only has 8 verts. What are the odds that the cube is actually going to hit one of those 8 verts?
This really needs to be done with per-polygon collision. You need to be able to check intersection of polygon and a sphere (and additionally a cylinder if you want to avoid tunneling like reinier mentioned). There are quite a few resources for this online and in book form, but http://www.realtimerendering.com/intersections.html might be a useful starting point.
The comments about optimization are good. Early out opportunities (perhaps a quick check against a bounding sphere or an axis aligned bounding volume for the mesh) are essential. Even once you've determined that you're inside a bounding volume, it would probably be a good idea to be able to weed out unlikely polygons (too far away, facing the wrong direction, etc.) from the list of potential candidates.
I think the best would be to use a specialized physics library.
That said. If I think about this problem, I would suspect that it's not that hard:
The sphere has a midpoint and a radius. For every point in the mesh do the following:
check if the point lies inside the sphere.
if it does check if it is closer to the center than the previously found point(if any)
if it does... store this point as the collision point
Of course, this routine will be fairly slow.
A few things to speed it up:
for a first trivial reject, first see if the bounding sphere of the mesh collides
don't calc the squareroots when checking distances... use the squared lengths instead.(much faster)
Instead of comparing every point of the mesh, use a dimensional space division algorithm (quadtree / BSP)for the mesh to quickly rule out groups of points
Ah... and this routine only works if the sphere doesn't travel too fast (relative to the mesh). If it would travel very fast, and you sample it X times per second, chances are the sphere would have flown right through the mesh without every colliding. To overcome this, you must use 'swept volumes' which basically makes your sphere into a tube. Making the math exponentially complicated.