I have a set of points on an OPEN surface in 3D space.
I have identified a subset of points which lay on the boundary.
I mean to generate a triangulation of those points, which gives me an open surface and keeps my selected points on the boundary.
All references I found deal with (sometimes?) closed surfaces, e.g., CGAL.
See examples below.
In addition, some CGAL algorithms require oriented normals at each point, which I do not have.
Is there an available algorithm and code for this? (either CGAL Advancing_front_surface_reconstruction, properly handled, or any other)
See also this and this.
Example 1
I compiled and ran example reconstruction_surface_mesh.cpp from examples/Advancing_front_surface_reconstruction, out-of-the box (which uses file half.xyz as input for data points), and I obtained a closed surface:
I would like to get rid of the few triangles that close the surface.
I tried adding an extra point at the end of half.xyz, and I got
which is an open surface.
So far, with what I tested, I do not know:
How to indicate an open surface.
How to indicate which vertices lay at the boundary.
If this is a non-empty set (and it should have at least three vertices) this would imply an open surface.
Ideally, one would have a workflow which works without manual intervention.
Example 2
I compiled and ran example boundaries.cpp, out-of-the box (which also uses file half.xyz as input for data points).
The output is:
0 outliers:
Boundaries:
boundary
0.178269 0.438589 0.129521
0.0795598 0.419465 0.244812
0.0549683 0.377617 0.3119
-0.0295721 0.360972 0.329075
-0.111332 0.334417 0.342617
-0.186667 0.2953 0.346683
-0.2719 0.16555 0.375017
-0.336304 0.117058 0.339323
-0.393517 0.0775 0.285917
-0.421419 -0.126854 0.215271
-0.395217 -0.214417 0.20015
-0.354783 -0.2953 0.170767
-0.237067 -0.395867 0.172233
-0.178246 -0.438588 0.129553
0.0227767 -0.4873 0.0700833
0.220338 -0.438589 -7.23321e-06
0.293 -0.395867 0
0.36025 -0.334417 0
0.418077 -0.258382 6.0303e-05
0.46025 -0.17265 0
0.484417 -0.0425167 -0.0763333
0.485067 0.03875 -0.0782667
0.471547 0.117058 -0.076827
0.44605 0.197567 -0.0700833
0.4092 0.27125 -0.0433167
0.364885 0.329645 0
0.313633 0.377617 0.0441167
0.2509 0.41425 0.0879333
I did not find how to use this for
automatically removing triangles which would make my target boundary vertices not laying at the boundary.
Moreover, the output seems to be the list of boundary points, without the "spurious" triangles (I am not sure). I would like to specify this list.
The CGAL advancing front reconstruction algorithm does generate open surfaces in general.
Related
I am trying to create edges with bends for a layout. Normally, I am using a haystack edge in the graph but whenever an edge bend has to be created, the curve-style of the edge is changed to segments. Currently, I am only creating edges with single bends. I have tried the code provided in this post but it is not creating proper edges. Currently, I am using the code from cytoscape.js-edge-editing, since it is creating better results.
The main problem is that the segment-distances values which cause the bendpoint to be created at the wrong location. Since, the functions in the above provided codes are not creating proper bendpoints, what is the right way to go about this?
A sample problem is as shown:
An edge bend has to created created in the edge from n12 to n15 where n12 is the source. The values of segment-distances and segment-weights are shown in the console. Having a positive value of segment-distances creates the bendpoint at the wrong position. It was actually supposed to be to the right of n12 and to the top of n15.
Whereas in another scenario, as shown in the following figure, an edge bend has to be created in the edge from n3 and n2. And the positions of these nodes are quite similar to n12 and n15 wrt each other. Their edge is given the same values of segment-distances and segment-weights as for the edge in the previous figure. And yet, the bendpoint is created (not accurately) but almost near to the expected location. Whereas the same value of segment-distance creates the bendpoint at the opposite location in the previous scenario.
I do not understand why this is happening. Can someone please guide me as how to solve this problem?
Refer to edge-distances:
edge-distances : With value intersection (default), the line from source to target for segment-weights is from the outside of the source node’s shape to the outside of the target node’s shape. With value node-position, the line is from the source position to the target position. The node-position option makes calculating edge points easier — but it should be used carefully because you can create invalid points that intersection would have automatically corrected.
https://js.cytoscape.org/#style/segments-edges
The intersection point is different from the node centre point (position).
If you want right-angled edges, you should probably just use taxi edges: https://js.cytoscape.org/#style/taxi-edges
Using pyiron, I want to calculate the mean square displacement of the ions in my system. How do I see the total displacement (i.e. not folded back by periodic boundary conditions) without dumping very frequently and checking when an atom passes over the boundary and gets wrapped?
Try to compare job['output/generic/unwrapped_positions'][-1] and job.structure.positions+job.output.total_displacements[-1]. If they deliver the same values, it's definitely fine both ways. If not, you can post the relevant lines in your notebook here.
I'd like to add a few comments to Jan's answer:
While job['output/generic/unwrapped_positions'] returns the unwrapped positions parsed from the output files, job.output.total_displacements returns the displacement of atoms calculated from each pair of consecutive snapshots. So if an atom moves more than half the box length in any direction, job.output.total_displacements will give wrong coordinates. Therefore, job['output/generic/unwrapped_positions'] is generally more trustworthy, but it is not available in all the codes (since some codes simply do not provide an output for unwrapped positions).
Moreover, if an interactive job is used, it is possible that job.structure.positions does not return the initial positions, i.e. job.structure.positions+job.output.total_displacements won't be initial positions + displacements.
So, in short, my answer to your question would be rather "Use job['output/generic/unwrapped_positions'] and if it's not available, use job.structure.positions+job.output.total_displacements but be aware of potential problems you might be running into."
I am trying to model the interior of an epithelial space and am stuck on movement around the interior edges of a cylindrical space. Basically, I'm trying to implement StickyBorders and keep agents on those borders in a cylindrical space that I am creating.
Is there a way to use cylindrical coordinates in Repast Simphony? I found this example (https://www.researchgate.net/publication/259695792_An_Agent-Based_Model_of_Vascular_Disease_Remodeling_in_Pulmonary_Arterial_Hypertension) where they seem to have done something similar, but the paper doesn't explain methods in much depth, and I don't believe this is an example in the repast simphony models.
Currently, I have a class of epithelial cells that are set up to form a cylinder and other agents start just inside that cylinder. To move, they are choosing their most desired spot (similar to the Zombie code) then pointing to a new location in the direction of that desired location within one grid square of that original location. They check that new point before moving to it and make sure that there are at least two other epithelial cells in the immediate moore neighborhood, to ensure they stay against the wall.
GridPoint intendedpt = new GridPoint((int)Math.rint(alongX),(int)Math.rint(alongY),(int)Math.rint(alongZ));
GridCellNgh<EpithelialCell> nearEpithelium = new GridCellNgh<EpithelialCell>(mac_grid, intendedpt, EpithelialCell.class, 1,1,1);
List<GridCell<EpithelialCell>> EpiCells = nearEpithelium.getNeighborhood(false);
int nearbyEpiCellsCount=0;
for (GridCell<EpithelialCell> cell: EpiCells) {
nearbyEpiCellsCount++;
}
if (nearbyEpiCellsCount<2) {
System.out.println(this + " leaving epithelial wall /r");
RunEnvironment.getInstance().pauseRun();
//TODO: where to go if false
}
I am wondering if there is a way to either set the boundaries of the space to be a cylinder or to check which side of the agent is against the wall and restrict its movement in that direction.
The sticky border code (StickyBorders.java) essentially just checks if the point that the agent moves to is beyond any of the space's dimensions, and if so the point is clamped to that dimension. So, for example, if the space is 3x4 and an agent's movement would take it to 4,2, then that point becomes 3,2 and the agent is placed there. Can you do something like that in this case? If not, can you edit your question to explain why not and maybe that will help us understand better.
The approach we took in that model was to use a 3D grid space with custom borders and query methods. The space itself was still Cartesian - we just visualized it as a cylinder using custom display code. Using the Cartesian grid was an reasonable approximation for this application since the cell dimensions were significantly smaller that the vessel radius, so curvature effects were neglected. The boundary conditions on the vessel space were wrap around in the angular dimension, so that cells could move continuously around the circumference of the vessel, and the axial boundary conditions were also wrapped, as we assumed a long enough vessel length that this would be reasonable. The wall thickness dimension had hard boundaries at the basement membrane (y=0) and at the fluid interface (y=wall thickness).
Depending on which type of space you are using, you will need to implement a PointTranslator or GridPointTranslator that performs the border functions. If you want specific examples of the code I suggest you reach out to the author's directly.
I have several boxes (x,y,width,height) randomly scattered around, and some of them need to be linked from point (x1,y1) in box1 to point (x2,y2) in box2 by drawing a line. I am trying to figure a way to make such line avoid passing through any other boxes (other than box1 and box2) by drawing several straight interconnected lines to go around any box in the way (if it is not possible to go with one straight line). The problem is that I don't know an algorithm for such thing (let alone having a technical/common name for it). Would appreciate any help in the form of algorithm or expressed ideas.
Thanks
Assuming that the lines can't be diagonal, here's one simple way. It's based on BFS and will also find the shortest line connecting the points:
Just create a graph, containing one vertex for each point (x, y) and for each point the edges:
((x,y),(x+1,y)) ((x,y),(x-1,y)) ((x,y),(x,y+1)) ((x,y),(x,y-1))
But each of this edges must be present only if it doesn't overlap a box.
Now just do a plain BFS from point (x1,y1) to (x2,y2)
It's really easy to obtain also diagonal lines the same way but you will need 8 edges for each vertex, that are, in addition to the previouses 4:
((x,y),(x-1,y+1)) ((x,y),(x-1,y-1)) ((x,y),(x+1,y-1)) ((x,y),(x+1,y+1))
Still, each edge must be present only if it doesn't overlap a box.
EDIT
If you can't consider space divided into a grid, here's another possibility, it won't give you the very shortest path, though.
Create a graph, in which each box is a vertex and has an edge to any other box that can be reached without the line to overlap a third box. Now find the shortet path using dijkstra between box1 and box2 containing the two points.
Now consider each box to have a small countour that doesn't overlap any other box. This way you can link the entering and the exiting point of each box in the path found through dijistra, passing through the countour.
Put all (x,y) coords of the corners of the boxes in a set V
Add the start- and end coordinates to V.
Create a set of edges E connecting each corner that does not cross any box-side (except for the diagonals in the boxes).
How to check if a line crosses a box side can be done with this algorithm
Now use a path-finding algorithm of your choice, to find a path in the graph (V, E).
If you need a simple algorithm that finds the shortest path, just go with a BFS.
(This will produce a path that goes along the sides of some boxes. If this is undesirable, you could in step 1 put the points at some distance delta from the actual corners.)
If the edges may not be diagonal:
Create a large grid of lines that goes between the boxes.
Throw away the grid-edges that cross a box-side.
Find a path in the grid using a path-finding algorithm of your choice.
I have a projectile that I would like to pass through specific coordinates at the apex of its path. I have been using a superb equation that giogadi outlined here, by plugging in the velocity values it produces into chipmunk's cpBodyApplyImpulse function.
The equation has one drawback that I haven't been able to figure out. It only works when the coordinates that I want to hit have a y value higher than the cannon (where my projectile starts). This means that I can't shoot at a downward angle.
Can anybody help me find a suitable equation that works no matter where the target is in relation to the cannon?
As pointed out above, there isn't any way to make the apex be lower than the height of the cannon (without making gravity work backwards). However, it is possible to make the projectile pass through a point below the cannon; the equations are all here. The equation you need to solve is:
angle = arctan((v^2 [+-]sqrt(v^4 - g*(x^2+2*y*v^2)))/g*x)
where you choose a velocity and plug in the x and y positions of the target - assuming the cannon is at (0,0). The [+-] thing means that you can choose either root. If the argument to the square root function is negative (an imaginary root) you need a larger velocity. So, if you are "in range" you have two possible angles for any particular velocity (other than in the maximum range 45 degree case where the two roots should give the same answer).
I suspect one trajectory will tend to 'look' much more sensible than the other, but that's something to play around with once you have something working. You may want to stick with the apex grazing code for the cases where the target is above the cannon.