how to count the number of scatter points in a each sector region of the 6 concentric circles ?

I have found the scatter points in a graph but i need to find the number of scatter points lies inside of the sector region of the circle in the form of percentage ? i have attached the sample answer graph for this question(fig2).

Answer 1

[Image Analyst]

If you have the x and y points then you can get the angle of each point using atand

angles = atand(y ./ x)

Then you can take the histogram

counts = histcounts(angles, 8)
percents = 100 * counts / numel(x)

[ejjagiri]

I have x and y but its 75*201 matrix

[Image Analyst]

What does each row and column represent? For example if column 1 is x and column 2 is y, what do the other 199 columns represent?

Attach your matrix with the paperclip icon.

So do you want a count for each radius range and each of 4 angle sectors. Then you need to compute the radius of each point.

radii = sqrt(x.^2 + y.^2);

and compute edges for the angles and radii and then use

help histogram2

 HISTOGRAM2  Plots a bivariate histogram.
    HISTOGRAM2(X,Y) plots a bivariate histogram of X and Y. X and Y can be 
    arrays of any shape, but they must have the same size. HISTOGRAM2 
    determines the bin edges using an automatic binning algorithm that 
    returns uniform bins of an area chosen to cover the range of values in 
    X and Y and reveal the shape of the underlying distribution. 
 
    HISTOGRAM2(X,Y,NBINS), where NBINS is a scalar or 2-element vector, 
    specifies the number of bins to use. A scalar specifies the same number 
    of bins in each dimension, whereas the 2-element vector [nbinsx nbinsy] 
    specifies a different number of bins for the X and Y dimensions.
 
    HISTOGRAM2(X,Y,XEDGES,YEDGES), where XEDGES and YEDGES are vectors, 
    specifies the edges of the bins.
 
    The value [X(k),Y(k)] is in the (i,j)th bin if XEDGES(i) <= X(k) < 
    XEDGES(i+1) and YEDGES(j) <= Y(k) < YEDGES(j+1). The last bins in the
    X and Y dimensions will also include the upper edge. For example, 
    [X(k),Y(k)] will fall into the i-th bin in the last row if 
    XEDGES(end-1) <= X(k) <= XEDGES(end) && YEDGES(i) <= Y(k) < YEDGES(i+1).
 
    HISTOGRAM2(...,'BinWidth',BW) where BW is a scalar or 2-element vector, 
    uses bins of size BW. A scalar specifies the same bin width for each 
    dimension, whereas the 2-element vector [bwx bwy] specifies different 
    bin widths for the X and Y dimensions. To prevent from accidentally 
    creating too many bins, a limit of 1024 bins can be created along each 
    dimension when specifying 'BinWidth'. If BW is too small such that more 
    than 1024 bins are needed in either dimension, HISTOGRAM2 uses larger 
    bins instead.
 
    HISTOGRAM2(...,'XBinLimits',[XBMIN,XBMAX]) plots a histogram 
    with only elements between the bin limits inclusive along the X axis, 
    X>=BMINX & X<=BMAXX.  Similarly, 
    HISTOGRAM2(...,'YBinLimits',[YBMIN,YBMAX]) uses only elements between 
    the bin limits inclusive along the Y axis, Y>=YBMIN & Y<=YBMAX.
 
    HISTOGRAM2(...,'Normalization',NM) specifies the normalization scheme 
    of the histogram values. The normalization scheme affects the scaling 
    of the histogram along the Z axis. NM can be:
                   'count'   The height of each bar is the number of 
                             observations in each bin. The sum of the
                             bar heights is generally equal to NUMEL(X) 
                             and NUMEL(Y), but is less than if some 
                             of the input data is not included in the bins..
             'probability'   The height of each bar is the relative 
                             number of observations (number of observations
                             in bin / total number of observations), and
                             the sum of the bar heights is less than or equal
                             to 1.
            'countdensity'   The height of each bar is, (the number of 
                             observations in each bin) / (area of bin). The 
                             volume (height * area) of each bar is the number
                             of observations in the bin, and the sum of
                             the bar volumes is less than or equal to NUMEL(X) 
                             and NUMEL(Y).
                     'pdf'   Probability density function estimate. The height 
                             of each bar is, (number of observations in bin)
                             / (total number of observations * area of bin).
                             The volume of each bar is the relative number of
                             observations, and the sum of the bar volumes 
                             is less than or equal to 1.
                'cumcount'   The height of each bar is the cumulative 
                             number of observations in each bin and all
                             previous bins in both the X and Y dimensions. 
                             The height of the last bar is less than or equal 
                             to NUMEL(X) and NUMEL(Y).
                     'cdf'   Cumulative density function estimate. The height 
                             of each bar is the cumulative relative number
                             of observations in each bin and all previous 
                             bins in both the X and Y dimensions. The height 
                             of the last bar is less than or equal to 1.
 
    HISTOGRAM2(...,'DisplayStyle',STYLE) specifies the display style of the 
    histogram. STYLE can be:
                    'bar3'   Display histogram using 3-D bars. This is the 
                             default.
                    'tile'   Display histogram as a rectangular array of 
                             tiles with colors indicating the bin values.
 
    HISTOGRAM2(...,'BinMethod',BM), uses the specified automatic binning 
    algorithm to determine the number and width of the bins.  BM can be:
                    'auto'   The default 'auto' algorithm chooses a bin 
                             size to cover the data range and reveal the 
                             shape of the underlying distribution.
                   'scott'   Scott's rule is optimal if X and Y are close 
                             to being jointly normally distributed, but 
                             is also appropriate for most other 
                             distributions. It uses a bin size of 
                             [3.5*STD(X(:))*NUMEL(X)^(-1/4)
                             3.5*STD(Y(:))*NUMEL(Y)^(-1/4)]
                      'fd'   The Freedman-Diaconis rule is less sensitive to 
                             outliers in the data, and may be more suitable 
                             for data with heavy-tailed distributions. It 
                             uses a bin size of [2*IQR(X(:))*NUMEL(X)^(-1/4) 
                             2*IQR(Y(:))*NUMEL(Y)^(-1/4)] where IQR is the 
                             interquartile range.
                'integers'   The integer rule is useful with integer data, 
                             as it creates a bin for each pair of integer 
                             X and Y. It uses a bin width of 1 along each 
                             dimension and places bin edges halfway 
                             between integers. To prevent from accidentally 
                             creating too many bins, a limit of 1024 bins 
                             can be created along each dimension with this 
                             rule. If the data range along either dimension 
                             is greater than 1024, then larger bins are 
                             used instead.
 
    HISTOGRAM2(...,NAME,VALUE) set the property NAME to VALUE. 
      
    HISTOGRAM2('XBinEdges', XEDGES, 'YBinEdges', YEDGES, 'BinCounts', COUNTS) 
    where COUNTS is a matrix of size [length(XEDGES)-1, length(YEDGES)-1],
    manually specifies the bin counts. HISTOGRAM2 plots the counts and does 
    not do any data binning.
 
    HISTOGRAM2(AX,...) plots into AX instead of the current axes.
        
    H = HISTOGRAM2(...) also returns a Histogram2 object. Use this to 
    inspect and adjust the properties of the histogram.
 
    Class support for inputs X, Y, XEDGES, YEDGES:
       float: double, single
       integers: uint8, int8, uint16, int16, uint32, int32, uint64, int64
       logical
 
    See also HISTCOUNTS2, HISTCOUNTS, HISTOGRAM, DISCRETIZE,
    matlab.graphics.chart.primitive.Histogram2

    Documentation for histogram2
       doc histogram2

    Other uses of histogram2

       matlab.graphics.chart.primitive/histogram2    tall/histogram2

Answer 2

[KSSV]

Let (x,y) be your scattered points.

C = [mean(x) mean(y)]  ; % center of circle. This would be (0,0)
R = 200 ;   % RAdius of circle 
d = sqrt((C(1)-x).^2+(C(2)-y).^2) ;  % distance of each point from circle center 
idx = d <= R ;   % points lying inside circle of radii R 
nR = nnz(idx)*100/length(x)   % percentage of points lying inside circle of radius R