I have solved a PDE's problem and I have the matrix with the values of the solution. The problem is that I don't know how to represent in the domain the solution. The domain is a rectangle with this vertices:
A(0,0)
B(1,1)
C(0,2)
D(-1,1)
I want to use 'meshgrid' without needing to evaluate every single point of the grid by myself. Someone can give me some help?
Thanks!
Related
I am stuck at a current project:
I have an input picture showing the ground with some shapes on it. I have to find a specific shape with a given template.
I have to use distance transformation into skeletonization. My question now is: How can I compare two skeletons? As far as I noticed and have been told, the most methods from the Image Processing Toolbox to match templates don't work, since they are not scale-invariant and rotation invariant.
Also some skeletons are really showing the shapes, others are just one or two short lines, with which I couldn't identify the shapes, if I didn't know what they should be.
I've used edge detection, and region growing on the input so there are only interessting shapes left.
On the template I used distance transformation and skeletonization.
Really looking forward to some tips.
Greetings :)
You could look into convolutions?
Basically move your template over your image and see if there is a match, and where.
The max value of your array [x,y] is the location of your object in the image.
Matlab has a built-in 2D convolution function for this
i am a newbie here.. please excuse me for asking a straight forward question as i did not have the right information to do so.
for my question above, can anyone help me to create various shape in matlab?
i know how to make a simple triangle, rectangle in matlab.
what i am looking for is how to create animal patterns in matlab. all i need is the boundary layer (outer layer).
like from a bird / butterfly. something like the picture below.
butterfly wing:
can anyone give me tips / links to help me.
and yes, i also did not have the coding. i am totally lost on how to make the pattern in matlab.
my real purpose was to add mesh pattern into the wings. i have the code for the mesh. all i need is the code on how to make the wing shape.
If you already have the image created by another program, you can import it to matlab using imread. If you then want to get a binary boundary, you can use im2bw.
threshold = 0.7; % you can play with this to get what you want
binary_img = im2bw(imread('PATH\TO\IMAGE.jpg'), threshold);
In matlab versions starting at 2016a there is another function called imbinarize you might want to have a look at.
As for creating patterns from scratch, as already mentioned in the comments, matlab should not be your choice. Unless, of course, you have a well defined mathematical equation or a problem solution to which becomes the boundary. For this you can look into fimplicit, fplot etc..
I have several binary images which represent a partial map of an area (~4m radius) and were taken ~0.2m apart, for example:
(Sorry for the different axis limit).
If you look closely, you'll see that the first image is about 20cm to the right.
I want to be able to create a map of the area from several pictures like this.
I've tried several methods, such as Matlab's register but couldn't find any good algorithm for this purpose. Any ideas on how to approach this?
Thanks in advance!
Two possible routes:
Use imregister. This does registration based on image intensity. You will probably want a rigid transform.
However, this will require your data to be an image (matrix), which it doesn't look like it currently is.
Alternatively, you can use control points. These are common (labelled) points in each image which provide a reference to determine the transform.
Matlab has a built in function to determine control points, cpselect. However, again this requires image data. You may be better of writing your own function to do this or just selecting control points manually.
Once you have control points you can determine the transform between them using fitgeotrans
The following problem:
Given is an arbitrary polygon. It shall be covered 100% with the minimum number of circles of a given radius.
Note:
1) Naturally the circles have to overlap.
2) I try to solve the problem for ARBITRARY polygons. But also solutions for CONVEX polygons are appreciated.
3) As far as Im informed, this problem is NP-hard ( an algorithm to find the minimum size set cover for the Set-cover problem )
Choose: U = polygon and S1...Sk = circles with arbitrary centers.
My solution:
Ive already read some papers and tried a few things on my own. The most promising idea that I came up with was in fact one already indicated in Covering an arbitrary area with circles of equal radius.
So I guess it’s best I quickly try to describe my own idea and then refine my questions.
The picture gives you already a pretty good idea of what I do
IDEA and Problem Formulation
1. I approximate the circles with their corresponding hexagons and tessellate the whole R2, i.e. an sufficiently large area; keyword hexagonally closest packaging. (cyan … tessellation, red dotted, centers of the cyan hexagons)
2. I put the polygon somewhere in the middle of this tessellated area and compute the number of hexagons that are needed to cover the polygon.
In the following Im trying to minimize N, which is number ofhexagons needed to cover the polygon, by moving the polygon around step by step, after each step “counting” N.
Solving the problem:
So that’s when it gets difficult (for me). I don’t know any optimizers that solve this problem properly, since they all terminate after moving the polygon around a bit and not observing any change.
My solution is the following:
First note that this is a periodic problem:
1. The polygon can be moved in horizontal direction x with a period of 3*r (side length = radius r) of the hexagon.
2. The polygon can be moved in vertical direction y with a period of r^2+r^2-2*rrcos(2/3*pi) of the hexagon.
3. The polygon can be rotated phi with a period of 2/3*pi.
That means, one has to search a finite area of possible solutions to find the optimal solution.
So what I do is, I choose a stepsize for (x,y,phi) and simply brute force compute all possible solutions, picking out the optimum.
Refining my questions
1) Is the problem formulated intelligently? Right now im working on an algorithm that only tessellates a very small area, so that as little hexagons as possible have to be computed.
2) Is there a more intelligent optimizer to solve the problem?
3) FINALLY: I also have difficulties finding appropriate literature, since I don’t guess I don’t know the right keywords to look for. So if anybody can provide me with literature, it would also be appreciated a lot.
Actually I could go on about other things ive tried but I think no one of u guys wants to spend the whole afternoon just reading my question.
Thx in advance to everybody who takes the time to think about it.
mat
PS i implement my algorithms in matlab
I like your approach! When you mention your optimization I think a good way to go about it is by rotating the hexagonal grid and translating it till you find the least amount of circles that cover the region. You don't need to rotate 360 since the pattern is symmetric so just 360/6.
I've been working on this problem for a while and have just published a paper that contains code to solve this problem! It uses genetic algorithms and BFGS optimization. You can find a link to the paper here: https://arxiv.org/abs/2003.04839
Edit: Answer rewritten (there's no limitation that circles couldn't go outside the polygon).
You might be interested in Covering a simple polygon with circles. I think the algorithm works or is extendable also to complex polygons.
1.Inscribe the given polygon in a minimum sized rectangle
2.Cover the rectangle optimally by circles (algorithm is available)
I am interested in using the CGContextEOFillPath feature provided by apple. I am guessing with the way the EOFill works, it probably has a way to take the filled in areas and calculate an area.
So my question is does anyone know of a way to use CGContextEOFillPath and find the area of the filled in sections.
If this isn't something that is easily done, maybe some pointers to a better way of doing this would be helpful. Though I need to use the EO style graphing.
Thanks.
What do you mean "Calculate the area"?
As in calculate the surface area of a complex shape?
It depends on your shapes.
Are they all polygons?
What about circles?
There are well known formulas for calculating the area of a polygon. (Wikipedia has it) Part of that calculation involves using an ABS() function because shapes drawn "counterclockwise" have the opposite sign as those drawn "clockwise". If you're looking to simulate the EO behavior, you can simply ignore the sign change, because, for you, it's desirable.
If you have more complicated shapes that involve curves, then you need to break the problem down into multiple parts - one part to solve for polygons - one to solve for circles - one to solve for other shapes, etc.