I have a list of 200 points I garnered from a graph digitization software I would like to transform into a smooth curve and then into Solidworks.
My points form an ellipse (airfoil shape to be more precise), so the commands I've tried in Matlab didn't have a circular curve.
My issues are:
* Obtaining a smooth curve that doesn't necessarily pass through all points, smooth being motus operandi.
* Being able to have a elliptical curve
* Somehow being able to export this curve into Solidwords
If anyone knows the right software, command line or anything that could get me started, I would be extremely thankful.
imacube
I've used Solid Works before. It's a very powerful tool. There should be some way to draw a curved spline through these points, such as a cubic spline.
If you are using a standard(ish) airfoil, then you can use a variety of tools to plot the points without having to use a graph digitization software.
Javafoil, for instance, is one of those. Even if you know the characteristics of your airfoil, you can use this to give you a smooth set of points.
Again, if your airfoil is a naca 4-series, then these are governed by a set of equations.
But I take it that the airfoil you want a more complicated one. Let me know if I can help anymore.
Related
I have image of robot with yellow markers as shown
The yellow points shown are the markers. There are two cameras used to view placed at an offset of 90 degrees. The robot bends in between the cameras. The crude schematic of the setup can be referred.
https://i.stack.imgur.com/aVyDq.png
Using the two cameras I am able to get its 3d co-ordinates of the yellow markers. But, I need to find the 3d-co-oridnates of the central point of the robot as shown.
I need to find the 3d position of the red marker points which is inside the cylindrical robot. Firstly, is it even feasible? If yes, what is the method I can use to achieve this?
As a bonus, is there any literature where they find the 3d location of such internal points which I can refer to (I searched, but could not find anything similar to my ask).
I am welcome to a theoretical solution as well(as long as it assures to find the central point within a reasonable error), which I can later translate to code.
If you know the actual dimensions, or at least, shape (e.g. perfect circle) of the white bands, then yes, it is feasible and possible.
You need to do the following steps, which are quite non trivial to do, and I won't do them here:
Optional but extremely suggested: calibrate your camera, and
undistort it.
find the equation of the projection of a 3D circle into a 2D camera, for any given rotation. You can simplify this by assuming the white line will be completely horizontal. You want some function that takes the parameters that make a circle and a rotation.
Find all white bands in the image, segment them, and make them horizontal (rotate them)
Fit points in the corrected white circle to the equation in (1). That should give you the parameters of the circle in 3d (radious, angle), if you wrote the equation right.
Now that you have an analytic equation of the actual circle (equation from 1 with parameters from 3), you can map any point from this circle (e.g. its center) to the image location. Remember to uncorrect for the rotations in step 2.
This requires understanding of curve fitting, some geometric analytical maths, and decent code skills. Not trivial, but this will provide a solution that is highly accurate.
For an inaccurate solution:
Find end points of white circles
Make line connecting endpoints
Chose center as mid point of this line.
This will be inaccurate because: choosing end points will have more error than fitting an equation with all points, ignores cone shape of view of the camera, ignores geometry.
But it may be good enough for what you want.
I have been able to extract the midpoint by fitting an ellipse to the arc visible to the camera. The centroid of the ellipse is the required midpoint.
There will be wrong ellipses as well, which can be ignored. The steps to extract the ellipse were:
Extract the markers
Binarise and skeletonise
Fit ellipse to the arc (found a matlab function for this)
Get the centroid of the ellipse
hsv_img=rgb2hsv(im);
bin=new_hsv_img(:,:,3)>marker_th; %was chosen 0.35
%skeletonise
skel=bwskel(bin);
%use regionprops to get the pixelID list
stats=regionprops(skel,'all');
for i=1:numel(stats)
el = fit_ellipse(stats(i).PixelList(:,1),stats(i).PixelList(:,2));
ellipse_draw(el.a, el.b, -el.phi, el.X0_in, el.Y0_in, 'g');
The link for fit_ellipse function
Link for ellipse_draw function
I have a set of (X, Y) coordinates which, when plotted produce a graph as in the pictures below. What I am trying to do, is to find the coordinates of the areas (corner points) circled in red.
I have been trying to find ways to accomplish this, as those actual turning points represents my area of interest. Please note that I do not have the actual equation for those coordinates.
I would find it grateful if someone could please advise me, or give me some directions on how to go about this, either by using Matlab, or even some other ideas using some C++ tools.
I manage to solve this using a combinaison of the Point Cloud Library and Matlab. The former helped me to separate the coordinates in line segments (RANSAC) and using the latter, I was able to get the Equation of each line segments (Curve Fitting), and simply compute the intersection point through some basic math calculation.
Anyone have any starting tips for me? I want to learn from this (ie Don't want to be lazy and have someone answer this for me).
I would like to develop my understanding of mathematical 3D surfaces. My own personal project is to produce a 3D surface/graph of the concourse structure in MATLAB.
I found a link with good pictures of its geometry here. I am not expecting to get it 100% perfectly but I'd like to come close!
At the end of this exercise I would like to have a mathematical definition of the geometry as well as a visual representation of the surface. This can involve cartesian equations, parametric equations, matrices, etc.
Any help would be very much appreciated!
To give some specific advice for MATLAB:
I would load in the 'section' image from the web page you have linked, and display this in a MATLAB figure window. You can then try plotting lines over the top until you find one that fits nicely. So you might do something like:
A = imread('~/Desktop/1314019872-1244-n364-1000x707.jpg');
imshow(A)
hold on
axis on
%# my guess at the function - obviously not a good fit
x = [550:900];
plot(x, 0.0001*x.^2 + 300)
Of course, you might want to move the position of the origin or crop the picture and so on.
As an arguably better alternative to this trial-and-error method, you could trace the outline of the section (e.g by clicking points with something like ginput), and then use one of MATLAB's curve-fitting tools (e.g. fit) to fit a function to the data.
The final 3D shape looks to me (at a casual glance) to be a 3D revolution of the section shape around a central axis. Use of a cylindrical coordinate system could therefore be a good idea.
The final plotting of your 3D shape could be done with a function such as surf or mesh.
I would start by defining a function that defines for each x, y coordinate whether there is a point z, and if so with which altitude.
The shape reminds me a bit of a log or a square root.
I have a binary image, i want to detect/trace curves in that image. I don't know any thing (coordinates, angle etc). Can any one guide me how should i start? suppose i have this image
I want to separate out curves and other lines. I am only interested in curved lines and their parameters. I want to store information of curves (in array) to use afterward.
It really depends on what you mean by "curve".
If you want to simply identify each discrete collection of pixels as a "curve", you could use a connected-components algorithm. Each component would correspond to a collection of pixels. You could then apply some test to determine linearity or some other feature of the component.
If you're looking for straight lines, circular curves, or any other parametric curve you could use the Hough transform to detect the elements from the image.
The best approach is really going to depend on which curves you're looking for, and what information you need about the curves.
reference links:
Circular Hough Transform Demo
A Brief Description of the Application of the Hough
Transform for Detecting Circles in Computer Images
A method for detection of circular arcs based on the Hough transform
Google goodness
Since you already seem to have a good binary image, it might be easiest to just separate the different connected components of the image and then calculate their parameters.
First, you can do the separation by scanning through the image, and when you encounter a black pixel you can apply a standard flood-fill algorithm to find out all the pixels in your shape. If you have matlab image toolbox, you can find use bwconncomp and bwselect procedures for this. If your shapes are not fully connected, you might apply a morphological closing operation to your image to connect the shapes.
After you have segmented out the different shapes, you can filter out the curves by testing how much they deviate from a line. You can do this simply by picking up the endpoints of the curve, and calculating how far the other points are from the line defined by the endpoints. If this value exceeds some maximum, you have a curve instead of a line.
Another approach would be to measure the ratio of the distance of the endpoints and length of the object. This ratio would be near 1 for lines and larger for curves and wiggly shapes.
If your images have angles, which you wish to separate from curves, you might inspect the directional gradient of your curves. Segment the shape, pick set of equidistant points from it and for each point, calculate the angle to the previous point and to the next point. If the difference of the angle is too high, you do not have a smooth curve, but some angled shape.
Possible difficulties in implementation include thick lines, which you can solve by skeleton transformation. For matlab implementation of skeleton and finding curve endpoints, see matlab image processing toolkit documentation
1) Read a book on Image Analysis
2) Scan for a black pixel, when found look for neighbouring pixels that are also black, store their location then make them white. This gets the points in one object and removes it from the image. Just keep repeating this till there are no remaining black pixels.
If you want to separate the curves from the straight lines try line fitting and then getting the coefficient of correlation. Similar algorithms are available for curves and the correlation tells you the closeness of the point to the idealised shape.
There is also another solution possible with the use of chain codes.
Understanding Freeman chain codes for OCR
The chain code basically assigns a value between 1-8(or 0 to 7) for each pixel saying at which pixel location in a 8-connected neighbourhood does your connected predecessor lie. Thus like mention in Hackworths suggestions one performs connected component labeling and then calculates the chain codes for each component curve. Look at the distribution and the gradient of the chain codes, one can distinguish easily between lines and curves. The problem with the method though is when we have osciallating curves, in which case the gradient is less useful and one depends on the clustering of the chain codes!
Im no computer vision expert, but i think that you could detect lines/curves in binary images relatively easy using some basic edge-detection algorithms (e.g. sobel filter).
like what i want is if i move my finger fast on the iphone screen , then i want like something that it make a proper curve using quartz 2d or opengl es whatever.
i want to draw a path in curve style......
i had seen that GLPaint(OpenglES) example ,but it will not help me alot , considering if your finger movement is fast.....
something like making a smooth curve.....
any one have some kind of example please tell me
thanks
Edit: Moved from answer below:
thanks to all.......
but i had tried the bezier curve algo with two control points but problem is first how to calculate the control points whether there is no predefined points....
as i mentioned my movement of finger is fast...... so most of the time i got straight line instead of curve, due to getting less number of touch points.......
now as mark said piecewise fashion, ihad tried it like considering first four touch points and render them on screen , then remove the first point then again go for next four points ex. step 1: 1,2,3,4 step 2: 2,3,4,5 like that where as in that approach i got an overlap , which is not the issue actually , but didn't get smooth curve........
but for fast movement of finger i have to find something else?????
Depending on the number of sample points you are looking at, there are two approaches that I would recommend:
Simple Interpolation
You can simply sample the finger location at set intervals and then interpolate the sample points using something like a Catmull-Rom spline. This is easier than it sounds since you can easily convert a Catmull-Rom spline into a series of cubic Bezier curves.
Here's how. Say you have four consecutive sample points P0, P1, P2 and P3, the cubic Bezier curve that connects P1 to P2 is defined by the following control points:
B0 = P1
B1 = P1 + (P2 - P0)/6
B3 = P2 + (P1 - P3)/6
B4 = P2
This should work well as long as your sample points aren't too dense and it's super easy. The only problem might be at the beginning and end of your samples since the first and last sample point aren't interpolated in an open curve. One common work-around is to double-up your first and last sample point so that you have enough points for the curve to pass through each of the original samples.
To get an idea of how Catmull-Rom curves look, you can try out this Java applet demonstrating Catmull-Rom splines.
Fit a curve to your samples
A more advance (and more difficult) approach would be to do a Least Squares approximation to your sample points. If you want try this, the procedure looks something like the following:
Collect sample points
Define a NURBS curve (including its knot vector)
Set up a system of linear equations for the samples & curve
Solve the system in the Least Squares sense
Assuming you can pick a reasonable NURBS knot vector, this will give you a NURBS curve that closely approximates your sample points, minimizing the squared distance between the samples and your curve. The NURBS curve can even be decomposed into a series of Bezier curves if needed.
If you decide to explore this approach, then the book "Curves and Surfaces for CAGD" by Gerald Farin, or a similar reference, would be very helpful. In the 5th edition of Farin's book, section 9.2 deals specifically with this problem. Section 7.8 shows how to do this with a Bezier curve, but you'd probably need a high-degree curve to get a good fit.
Naaff gives a great overview of the NURBS technique. Unfortunately, I think generating a smooth bezier on-the-fly might be too much for the iPhone. I write drawing apps, and getting a large number of touchesMoved events per second is quite a challenge to begin with. You really need to optimize your drawing code just to get good performance while recording individual points - much less constructing a bezier path.
If you end up going with a bezier or NURBS curve representation - you'll probably have to wait until the user has finished touching the screen to compute the smoothed path. Doing the math continuously as the user moves their finger (and then redrawing the entire recomputed path using Quartz) is not going to give you a high enough data collection rate to do anything useful...
Good luck!
Do something like Shadow suggested. Get the position of the touch with some frequency and then make a Bézier curve out of it. This is how paths are drawn with a mouse (or tablet) in programs like Illustrator.