In my Winforms application I have a small chart. Nothing fancy just a bunch of x/y points I connect with lines.
It would be nice to draw a curve instead of a lines to connect these points. But since mathematics was never my strong side I have no idea how to do that.
Any kind of sample or advice would be helpful.
This is very simple - no need for any math - just use Graphics.DrawCurve instead of DrawPolygon/DrawLine (see the very good help on this function).
Apologies for the thread resurrection, but I had to reply to this one:
Be clear in your mind what you want to achieve. I don't know the details of your project, but the methods being suggested are not appropriate for many applications. The correct solution depends on whether you intend the curves you're drawing to simply look nice, or to represent meaningful data. For the former, drawing a bezier curve is fine, but they are not mathematically meaningful and if you're trying to draw a graph to be interpreted with scientific rigour, they will mislead the user. For many applications what you'd want is a best-fit line. These have clear functional form, for example, a degree-2 polynomial (otherwise known as a parabola), a logarithmic curve, or a moving-average. All these are present in Excel and all have specific applications and are emphatically the wrong choice for anything outside their specific remit. The topic of statistical analysis of data is probably beyond the scope of a StackOverflow post - but to start with, look up 'linear regression', what you're describing is comprehensively dealt with by this area of mathematics.
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I often find myself fitting a scatter plot, and knowing that the 'true fit' should have only one inflection point. Any ideas for forcing a fit that will obey this?
I am using Matlab and Microsoft Excel
Many thanks
Option 1:
I like to use spline smoothing with Akaike information criteria, and while it is a hyper-parametric fit and has a large number of analytic candidate inflection points, the smoothed data at the sample points tends to reveal only what is within the data.
If your data doesn't actually have an inflection point, this is indicated. If it does, it is also usually captured. Statistical jargon for an important cousin to this is called a "non-informative prior".
Try slides 30-31 here: link.
Option 2:
If you have an older version of MatLab then you can specify the exact model easily in the "cftool" (not the same as sftool) then get m-file that gives how you put it into your own script. Pick a model appropriate to your data.
I want to implement some kind of improvement of DBSCAN algorithm, where user do not need to enter input parameters (minPts and Eps). My idea is to use the K-distances plot, but what is the best method to compute the 'knee' of this plot? How to count when there are 2 or more knees on the plot?
Where I can find the source code for some DBSCAN improvement, like AUTODBSCAN, VDBSCAN, PDBSCAN or DBSCAN-DLP? Im looking for some basics, but nowhere I can find a good help. Maybe you've seen somewhere sample source codes?
DBSCAN has already been improved to death.
In Google Scholar, it has 5361 citations, and probably 1000+ of these "improve" DBSCAN. And probably a dozen of these use the k-distance plot. But none of these are used in practise.
If you want to continue this line of research, best get updated on what has been done since.
In particular, have a look at OPTICS which does away with the Epsilon parameter completely (except for performance reasons when using indexes).
Also have a look at HDBSCAN* by one of the original DBSCAN authors, Joerg Sander. That will likely be the most important DBSCAN extension besides his work on OPTICS and GDBSCAN.
I have a curve which looks roughly / qualitative like the curves displayed in those 3 images.
The only thing I know is that the first part of the curve is hardware-specific supposed to be a linear curve and the second part is some sort of logarithmic part (might be a combination of two logarithmic curves), i.e. linlog camera. But I couldn't tell the mathematic structure of the equation, e.g. wether it looks like a*log(b)+c or a*(log(c+b))^2 etc. Is there a way to best fit/find out a good regression for this type of curve and is there a certain way to do this specifically in MATLAB? :-) I've got the student version, i.e. all toolboxes etc.
fminsearch is a very general way to find best-fit parameters once you have decided on a parametric equation. And the optimization toolbox has a range of more-sophisticated ways.
Comparing the merits of one parametric equation against another, however, is a deep topic. The main thing to be aware of is that you can always tweak the equation, adding another term or parameter or whatever, and get a better fit in terms of lower sum-squared-error or whatever other goodness-of-fit metric you decide is appropriate. That doesn't mean it's a good thing to keep adding parameters: your solution might be becoming overly complex. In the end the most reliable way to compare how well two different parametric models are doing is to cross-validate: optimize the parameters on a subset of the data, and evaluate only on data that the optimization procedure has not yet seen.
You can try the "function finder" on my curve fitting web site zunzun.com and see what it comes up with - it is free. If you have any trouble please email me directly and I'll do my best to help.
James Phillips
zunzun#zunzun.com
I have a set of 3D points which numbers up around 1 million points. I am looking to visualise these with matlab.
I have tried the following functions:
plot3
scatter3
But they are both very sluggish. Is there a more efficient way to visualise this level of points in matlab? Maybe a way to mesh the points?
If not can anyone suggest a plug-in or even a different program for visualising 3D points?
You're going to run into efficiency issues no matter what plugin/program you use if you want all million+ points to show up in a plot. My suggestion would be to downsample. Use the plot3 or scatter3 function on every other point, or every nth point, until you get a figure that is not sluggish. As long as the variance in your data isn't astronomical, downsampling a little bit shouldn't affect the overall distribution of points (given that you have a million+ points). And any software that is able to display that much data without being sluggish is most likely downsampling/binning or using some interpolation technique to do so (so you might as well have control over it).
fscatter3 from the file exchange, does what you like.
Is there a specific reason to actually have it display that many points?
I Googled around a bit and found some people who have had similar issues (someone suggested Avizo as an alternate program but I've never used it):
http://www.mathworks.com/matlabcentral/newsreader/view_thread/308948
mathworks.com/matlabcentral/newsreader/view_thread/134022 (not clickable because I don't have enough rep to post more than two links)
An alternate solution would be to generate a histogram if you're more interested in the density of the data:
http://blogs.mathworks.com/videos/2010/01/22/advanced-making-a-2d-or-3d-histogram-to-visualize-data-density/
I you know beforehand roughly the coordinates of the feature you are looking for, try passing the cloud through a simple pass-through-filter, which essentially crops your point cloud. I.e. if you know that the feature is at a x-coordinate > 5, remove all points with x-coordinate < 5.
This filter could for the first coordinated be realized as
data = data(data(1,:) > 5,:);
Provided that your 3d data is stored in an n by 3 matrix.
This, together with downsampling, could help you out. If you still find the performance lagging, consider using something like the PCD viewer in PointCloudLibrary, check half way down the page at
http://pointclouds.org/documentation/overview/visualization.php
It is a stand alone app you could launch from matlab. I find it's performance far better than the sluggish matlab plotting tools.
For anyone who is interested I ended up finding a Point cloud visualiser called Cloud Compare. It is extremely fast and allows selection and segmentation as well as filtering on point clouds.
OpenAL makes use of HRTF algorithms to fake surround sound with stereo headphones. However, there is an important dependency between HRTF and the shape of the users head and ears.
Simplified, this means: If your head / ears differ too much from the standard HRTF function they have implemented, the surround sound effect fades towards boring stereo.
I haven't yet found a way to adjust the various factors contributing to the HRTF algorithm, such as head diameter, pinna / external ear size, ear-to-ear distance, nose length and other important properties influencing the HRTF.
Is there any known way of setting these parameters for best surround sound experience?
I don't believe you can alter the HRTF in OpenAL. You certainly couldn't do it by putting in parametric values such as nose or pinna size. The only way to find out your HRTF is to put some very tiny, very accurate microphones in your ears, go into an anechoic chamber and take frequency response measurements at every angle around your head. Obviously this is time consuming, expensive and impractical. It would be fantastic to be able to work out your HRTF from measuring your head, but unfortunately acoustics isn't that deterministic and your ear is very sensitive to inaccuracies as you pointed out. I think the OpenAL HRTF is based on some KEMAR dummy head measurements (these perhaps?).
So, I think the short answer is that you can't alter the HRTF for OpenAL. Because HRTF is such a complex function that your ear is so sensitive to, there's no accurate way to approximate it with parametric values.
You might be able to make a "configuration game" out of optimizing the HRTF. I've been looking for an answer to the question if any of the virtual surround headsets or soundcards allow you adjust them to fit your personal HRTF.
Idea: You vary the different HRTF variables and play a sound. The user has to close his eyes and move the mouse into the direction he thought the sound came from. You measure how right he was.
You could use something like a thin plate spline or statistical curve fitting to plot the accuracy results and sample different regions of the multidimensional HRTF space to optimize the solution. This would be a kind of "brute force" method to find a solution that is not necessary accurate, but as good as the user has patience to optimize his personal HRTF.
According to a readme in the OpenALSoft sourcecode it uses a 32-sample convolution filter and you can create using custom HRTF samples.
It looks like it is now possible. I stumbled upon this comment which describes how to use hrtf_tables for approximations of your own ears. Google is showing me results for something called hrtf-paths as well but I'm not sure what that is.