How to draw Gaussian Distribution curve - algorithm

I want to draw a Gaussian Distribution curve, i know
p(x) = (1/σRoot(2π)) x exp (- (x-μ)2/2σ2),
i got the mean and standard deviation, but now i don't know how to proceed, how this bell-graph will be drawn, from where to get the co-ordinates, what's the use of above formula.
I searched a lot on internet and got nothing, every where it's given that how to draw it in excel or in matlab, but nowhere i found how those co-ordinates are got and how those curves are drawn.
if anyone can give me any idea on this it will be of great help.

A graph is simply a set of points plotted on the plane. So basically what you do is pick a set of x-coordinates that you want to plot the curve on. Then plug those x values into your function p(x) to get the y-coordinates.
Lastly, plot the resultant points.
Most graphing software (like your standard graphing calculator) will automate all this functionality for you.

Related

I am trying to find the slope of a polyline in autocad in a simpler way

My title pretty much says it all. I am trying to find the slope of a drawn polyline in a faster way than I am currently doing it. Right now I have to draw the line, check the distance in properties, than use the contours I have in the drawing to get my elevation, and than calculate slope off of that. This gets very dicey when dealing with very steep slopes due to the closeness of the contours. Thanks.
I would suggest using the standard AutoCAD DIST command - no programming required. This will return the distance, angle, and delta X, Y, & Z.

Matlab: polar coordinates grey scale plot

edit: I decided to split this question into two parts, because it were really two questions: 1. how to make a polar surface plot in MATLAB (this question) and 2. how to put fit polar data points into a coarse (and non-polar) matrix
I have a matrix that contains certain grey values (values between zero and one). These points are stored in a rectangular matrix, but really the data points are acquired by rotating the detector. This means that I actually have polar coordinates (I know the polar coordinates for every single pixel in my starting matrix).
I want to make a polar plot of the data points. I have the example of this below.
Because MATLAB stores images as matrices, the polar coordinates I have do not exactly match the 'bins' of the matrix. Therefore, we currently use an interpolation algorithm to put the polar coordinates into a square matrix. However, this is extremely slow. I see two methods to solve this issue:
let MATLAB directly plot the data points as polar.
calculate once how to convert from the start matrix to the end matrix and let MATLAB do this through matrix multiplication.
Some basic information:
Input matrix size: 512×960
Current output matrix size: 1024×1024
I think there is built in function for polar plot in matlab.
Z = [2+3i 2 -1+4i 3-4i 5+2i -4-2i -2+3i -2 -3i 3i-2i];
polarplot(Z,'*')
this command plots:
plot polar
See this link:
http://www.mathworks.com/help/matlab/ref/polarplot.html
To plot in grayscale, use "pcolor" and specify colormap to "gray"
www.mathworks.com/help/matlab/ref/ pcolor.html
The question was solved (apart from a minor flaw), partially because K.M. Shihab Uddin pointed me in the right direction. Unfortunately, using surf means continuously really plotting the image in a figure, and this is slow as well.
So I have X and Y values both in separate matrices and greyscale values (in a matrix called C) for every X and Y combination.
I found out that pcolor is just surf with a viewpoint from the top. So I used the following code to plot my graph.
surf(X,Y,C*255)
view([0,0,500])
However, this gave me a completely black image. This is because surf (and pcolor) create 960 grid lines radially in my case. The solution is to use:
surf(X,Y,img2*255,'EdgeColor','none')
view([0,0,500])
Now I have an almost perfect image, like I had before. Only, of my 960 radial lines, one is left white, so I still have to solve that. However, I feel this is a technical detail of the function surf, and answering this part does not belong in this question.
The resulting image

How to design an algorithm to linear interpolate points in 3D space and create an indented surface?

I am trying to develop a function that takes a matrix of input, out a contour plot as an output. There is a function in matlab which fits to my purpose. But for a self-examination method, I would like to do this myself. Like I said, my purpose is self-examination, I will not use this in an app or something.
Here is the deal, I have tried to do this with color maps, but what I got is a graph that seems like an uncalibrated TV channel:
(source: yeniakit.com.tr)
Graph is like that because, my function is discrete. I need to make this discreet function continuous.
I found a solution to this problem. Solution uses linear interpolation method to connect each point with each other. Surface created this way will have lots of rough edges but that is not a problem. Connecting the points in the space to create surfaces is OK, but those surfaces also has point on them. Computing such a thing would be very expensive, since a lot of computations involved. For example, lets say, I would like to create a surface by using 20x20 matrix. Rows and columns will be the x and y coordinates, values in each row and column will be the z coordinate.
I need to connect at least 3 dots to make a surface. Those surfaces have also points in them. I want to design such an algorithm that reduces the computations. How do I do that?

Comparing position of two sets of points on 2D image

I've got question about algorithms to compare if two sets of points are in a similar place on the image.
They don't create similar shapes likes circles, rectangles etc, but they are something like irregular clouds.
For example:
The first cloud of points is learning set of desired area on image and we are checking if second cloud is in similar position.
I was thinking of drawing simple shapes to form points (like rectangles which will accumulate all points) and checking if one is in another or distance between centers of figures, but this method doesn't seem to be very accurate.
Are there better algorithms to solve this problem?
Image Moments
Don't worry about the fancy name, it's just a standard method in image processing to do exactly what you require.
Image moment of power n w.r.t. x and m w.r.t. y is actually the
integration of (pixel value * xPosition^n * xPosition^m) over the
entire image.
So (0, 0)th order moment i.e moment(0, 0) is actually area of the cloud.
Similarly, moment(1, 0)/moment(0, 0) is X coordinate of centroid of the cloud.
And, moment(0, 1)/moment(0, 0) is Y coordinate of centroid of the cloud.
Higher order moments give additional features/information peculiar to shape of the clouds.
Now you can easily compare the arbitrary shapes.
These functions are available in opencv and matlab.
Hope this helps.
Good luck.
Sets will have quite similar shapes (it will be set of points of human skeleton from kinect > sensor) and I want to check if person is sitting in the same place as it was learned in the > first place
Then you will probably be able to derive a correspondence between two points (i.e. you will know that a given point is SHOULDER_RIGHT or ELBOW_LEFT or...). If that is the case you can simply calculate the SUM(SQRT((Xi1-Xi2)^2+(Yi1-Yi2)^2) for each i-th pair of points (X1,Y1) and (X2,Y2) (same goes if you can obtain the third dimension Z).
The value thus obtained will have a minimum of zero when the two sets of points are perfectly coinciding.

Shape casting a capsule against convex polyhedra

Let's say I have a upright capsule shape (swept sphere) that I would like to cast it along a velocity vector. I would like to be able to find the point of contact and a surface normal for any convex shapes it would intersect along this path. I would also like to find the distance the swept caspule traveled to the point of first contact.
Heres a quick diagram of a capsule being casted against a large convex polyhedra (only one face is drawn)
What kind of algorithm or process could do this? I assume it would be similar to a sphere-cast, but i can't find much on that either.
Since you are considering capsules and convex polyhedra, I suppose you could use something based on GJK. You would get the point of contact and a surface normal during a collision, and the minimum distance between the objects and the associated witness points if there is no collision.
You can also take a look at this publication on Interactive and Continuous Collision Detection for Avatars in Virtual Environments.
Right if its the same as your diagram then finding where it collides is the easy part. Get the circles x and y coordinates and plus '+' the radius of the circle. If that point is at the line of the path then its a collision. The line will have to be found using the line equation here y = mx+c.
The distance can be calculated by setting an intial values of x and y. and then when the object hits set final variables to x and y again. then just the lenght of a line formula to calculate the distance travelled.
The problem is im going on what i know from C++ and i dont know what your programming in.
i think you wanted something else but cant work out what that is from paragraph.

Resources