I am using the vtk package for python 2.7 to create some 3-dimensional stuff that I want to export to an .stl. Part of the geometry are sine waves with adjustable amplitudes. Here is my problem: When I generate the splines from point data (basically a point in every max, min and turning point) it does not look uniform!
This is what the spline looks like:
You can see that the middle amplitude looks kinda okay, while the rest is clearly distorted towards the center
Basically I only want the middle part to look like a perfect sine, because I cut away the remainder anyway.
When I use another program (Autodesk Inventor) to create splines manually from the same point data it creates a uniform sine wave. Is there a way to fix this problem?
Sorry for not providing any code, but I will give you the steps I do:
add points to vtkPoints object
create vtkParametricSpline with vtkPoints as input
use vtkSplineFilter to get a finer resolution of the spline
use vtkTubeFilter to create volume
use vtkClipClosedSurface to cut away what is not needed
In the end, parameterizing the line with a cosine function was the only way to avoid the weird spline behaviour. I tried avoiding it before, because it seemed over-engineered, but it turned out to be the better way.
New algorithm:
cosine function -> vtkPoints-> vtkLineSource -> vtkTubeFilter
Related
I have an output from a commercial program that contains the dihedral angles of a molecule in time. The problem comes from apparently a known quadrant issue when taking cosines, that your interval is -180 to 180, and I am not familiar with. If the dihedral would be bigger than 180, this commercial program (SHARC, for molecular dynamics simulations) understands that it is bigger than -180, creating jumps on the plots (you can see an example in the figure bellow).
Is there a correct mathematical way to convert these plots to smooth curves, even if it means to go to dihedrals higher than 180?
What I am trying is to create an python program to deal with each special case, when going from 180 to -180 or vice versa, how to deal with cases near 90 or 0 degrees, by using sines and cosines... But it is becoming extremely complex, with more than 12 nested if commands inside a for loop running through the X axis.
If it was only one figure, I could do it by hand, but I will have dozens of similar plots.
I attach an ascii file with the that for plotting this figure.
What I would like it to look like is this:
Thank you very much,
Cayo Gonçalves
Ok, I've found a pretty easy solution.
Numpy has the unwrap function. I just need to feed the function with a vector with the angles in radians.
Thank you Yves for giving me the name of the problem. This helped me find the solution.
This is called phase unwrapping.
As your curves are smooth and slowly varying, every time you see a large negative (positive) jump, add (subtract) 360. This will restore the original curve. (For the jump threshold, 170 should be good, I guess).
I have two sets of data points; effectively, one is from a preimage and the other from its image, but I do not know the rule between the two. This rule/function is nonlinear.
I've collected many data points of corresponding locations on both images, and I was wondering if anyone knew of a way to find a more complete mapping. That is, does anyone know the best way to find a mapping from R^2 to R^2 with an extensive set of sample points. This mapping is one-to-one and onto.
My goal is to use the data I've found to find a polynomial function that takes in some x,y coordinate from the preimage, and outputs the shifted coordinates.
edit: I have sample points along the domain and their corresponding points in the image, but not for every point in the domain. I want to be able to input any point (only integer values) in the domain and output the shifted point.
I don't think polynomial is easy (or easy to guarantee is a bijection). The obvious thing to do is to
Construct the delaunay triangulation of the known points in the domain.
For each delaunay triangle the mapping is just the linear mapping which interpolates the map on the vertices.
Then, when you have a random point, look up its delaunay triangle, and apply the requisite map.
I believe that all of the above can be done via scipy.spatial.delaunay.
The transformation you're trying to find sounds a lot like what's accomplished in Geographic Information Systems using a technique called rubber-sheeting https://en.wikipedia.org/wiki/Rubbersheeting
Igor Rivin's description of a process using a Delaunay triangulation is pretty much the solution that's used in such systems. Some systems will use a Barycentric coordinate system rather than a linear mapping to try to reduce the appearance of triangle-related artifacts in the transformed image.
What you are describing also sounds a bit like the "morphing" special effect used in video. Maybe a web search on that topic would turn up some leads for you.
I have unstructured (taken in no regular order) point cloud data (x,y,z) for a surface. This surface has bulges (+z) and depressions (-z) scattered around in an irregular fashion. I would like to generate some surface that is a function of the original data points and then be able to input a specific (x,y) and get the surface roughness value from it (z value). How would I go about doing this?
I've looked at scipy's interpolation functions, but I don't know if creating a single function for the entire surface is the correct approach? Is there a technical name for what I am trying to do? I would appreciate any suggestions/direction.
I don't know if creating a single function for the entire surface is the correct approach?
I guess this depends on your data. Let's assume the base form of your surface is spherical. Then you can model it as such.
If your surface is more complex then a sphere you might can still model the neighborhood of (x,y) as such. Maybe you could even consider your surface as plain in the near neighborhood of (x,y).
What you are trying to do, can be called surface fitting, or two-dimensional curve fitting. You would be able to find lots of available algorithms by searching for those terms. Now, the choice of the particular algorithm/method should be dictated:
by the origin of your data (there are specialized algorithms or variations of more common ones that are tailored for certain application areas)
by the future use of your data (depending on what you are going to do with it, maybe you need to be able to calculate derivatives easily, etc)
It is not easy to represent complicated data (especially the noisy one) using a single function. Thus there is a lot of research about it. However, in a lot of applications curve-fitting is very successful and very widely used.
I have been all over the internet trying to find the answer to this one and I've reached the end of my patience. What I am trying to achieve is pretty much what the standard bend deformer does but the only difference is I want it to unfold along a pre-defined curve. There are literally hundreds of tutorials about the bend deformer all doing the same thing, unfolding along a flat plane but none on how to do it along a curved surface. I have also tried paint effects with control curves to no avail and baking the bend deformer into the geometry then curving it afterwards. This last option didn't work as I no longer had the control I required. It seems from my search that probably the only way to do this would be through a Mel or Python script and I was wondering would anyone be able to help?
something like this?
Constrain -> Motion Patch -> Attach to Motion Patch + Flow Path Object
Lattice deformers themselves are skinnable, so you can run a skeleton or bend deformer through a lattice to maniuplate it's shape. This will also let you control the twist along the deformation. Animate the object you want to deform into the area of influence of the lattice to create the follow effect, while animating the deformation of the lattice itself at the same time to create the follow effect.
Or, you can just make the lattice follow the path using a spline IK control.
Given a contour outlining the edge of the letter S (in comic sans for example), how can I get a series of points along the spine of this letter in order to later represent this shape using lines, cubic spline or other curve-representing technique? I want to process and represent the shape using 30-40 points in Python/OpenCV.
Morphological skeletonization could help with this but the operation always seems to produce erroneous branches. Is there a better way to collapse the contour into just the 'S' shape of the letter?
In the example below you can see the erroneous 'serpent's tongue' like branches that are produced by morphological skeletonization. I don't know if it's fair to say they are erroneous if that's what the algorithm is supposed to be doing, but for me I would not like them to be there.
Below is the comic sans alphabet:
Another problem with skeletonization is that it is computationally expensive, but if you know a way of making it robust to forming 'serpent's tongue' like branches then I will give it a try.
Actually vectorizing fonts isn't trivial problem and quite tricky. To properly vectorize fonts using bezier curve you'll need tracing. There are many library you can use for tracing image, for example Potrace. I'm not knowledgeable using python but based on my experience, I have done similar project using c++ described below:
A. Fit the contour using cubic bezier
This method is quite simple although a lot of work should be done. I believe this also works well if you want to fit skeletons obtained from thinning.
Find contour/edge of the object, you can use OpenCV function findContours()
The entire shape can't be represented using a single cubic bezier, so divide them to several segments using Ramer-Douglas-Peucker (RDP). The important thing in this step, don't delete any points, use RDP only to segment the points. See colored segments on image below.
For each segments, where S is a set of n points S = (s0, s1,...Sn), fit a cubic bezier using Least Square Fitting
Illustration of least square fitting:
B. Resolution Resolution Independent Curve Rendering
This method as described in this paper is quite complex but one of the best algorithms available to display vector fonts:
Find contour (the same with method A)
Use RDP, differently from method A, use RDP to remove points so the contour can be simplified.
Do delaunay triangulation.
Draw bezier curve on the outer edges using method described in the paper
The following simple idea might be usefull.
Calculate Medial axis of the outer contour. This would ensure connectivity of the curves.
Find out the branch points. Depending on its length you can delete them in order to eliminate "serpent's tongue" problem.
Hope it helps.