Description of sldrawellipse

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sldrawellipse

PURPOSE

SLDRAWELLIPSE Draws an ellipse on current axis

SYNOPSIS

function h = sldrawellipse(center, shape, n, varargin)

DESCRIPTION

SLDRAWELLIPSE Draws an ellipse on current axis

 $ Syntax $
   - sldrawellipse(center, shape)
   - sldrawellipse(center, shape, n)
   - sldrawellipse(center, shape, n, ...)
   - h = sldrawellipse(...)

 $ Description $
   - sldrawellipse(center, shape) draws an ellipse specified by
     its center and shape on current axis. center is a vector of
     length 2, storing the x and y coordinate of the center. 
     shape have following two forms:
     1. [a, b, theta], here a and b are the half-lengths of two axis,
        theta is the radians of first axis relative to x-axis, in 
        anti-clockwise manner.
     2. C, a 2 x 2 covariance matrix, the ellipse is the set of points
        with mahalanobis distance to the center being equal to 1.
        ellipse eqn: x^T C x = 1
     3. {C, r}, C is a 2 x 2 covariance matrix, the ellipse is the set 
        of points with mahalanobis distance to the center being equal to 
        r. ellipse eqn: x^T C x = r^2.

   - sldrawellipse(center, shape, n) draws the ellipse using specified
     number of samples. If n is not specified or empty, then n takes
     the default value 300.
          
   - sldrawellipse(center, shape, n, ...) draws the ellipse with the 
     plotting properties specified by additional arguments. By default,
     it uses 'b-'.

   - h = sldrawellipse(...) returns the handle to the line
     drawn on the axis.

 $ History $
   - Created by Dahua Lin on Apr 23, 2006
   - Modified by Dahua Lin, on Aug 26, 2006
       - from sldraw_ellipse to sldrawellipse
   - Modified by Dahua Lin, on Sep 10, 2006
       - replace sladd by sladdvec to increase efficiency

CROSS-REFERENCE INFORMATION

This function calls:

• sladdvec SLADDVEC adds a vector to columns or rows of a matrix
• slsymeig SLSYMEIG Compute the eigenvalues and eigenvectors for symmetric matrix
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

• sldrawmultiellipse SLDRAWMULTIELLIPSE Draws multiple ellipses on axies

SUBFUNCTIONS

• function [S, R] = get_transform_from_geo(a, b, theta)
• function [S, R] = get_transform_from_cov(C)

SOURCE CODE

0001 function h = sldrawellipse(center, shape, n, varargin)
0002 %SLDRAWELLIPSE Draws an ellipse on current axis
0003 %
0004 % $ Syntax $
0005 %   - sldrawellipse(center, shape)
0006 %   - sldrawellipse(center, shape, n)
0007 %   - sldrawellipse(center, shape, n, ...)
0008 %   - h = sldrawellipse(...)
0009 %
0010 % $ Description $
0011 %   - sldrawellipse(center, shape) draws an ellipse specified by
0012 %     its center and shape on current axis. center is a vector of
0013 %     length 2, storing the x and y coordinate of the center.
0014 %     shape have following two forms:
0015 %     1. [a, b, theta], here a and b are the half-lengths of two axis,
0016 %        theta is the radians of first axis relative to x-axis, in
0017 %        anti-clockwise manner.
0018 %     2. C, a 2 x 2 covariance matrix, the ellipse is the set of points
0019 %        with mahalanobis distance to the center being equal to 1.
0020 %        ellipse eqn: x^T C x = 1
0021 %     3. {C, r}, C is a 2 x 2 covariance matrix, the ellipse is the set
0022 %        of points with mahalanobis distance to the center being equal to
0023 %        r. ellipse eqn: x^T C x = r^2.
0024 %
0025 %   - sldrawellipse(center, shape, n) draws the ellipse using specified
0026 %     number of samples. If n is not specified or empty, then n takes
0027 %     the default value 300.
0028 %
0029 %   - sldrawellipse(center, shape, n, ...) draws the ellipse with the
0030 %     plotting properties specified by additional arguments. By default,
0031 %     it uses 'b-'.
0032 %
0033 %   - h = sldrawellipse(...) returns the handle to the line
0034 %     drawn on the axis.
0035 %
0036 % $ History $
0037 %   - Created by Dahua Lin on Apr 23, 2006
0038 %   - Modified by Dahua Lin, on Aug 26, 2006
0039 %       - from sldraw_ellipse to sldrawellipse
0040 %   - Modified by Dahua Lin, on Sep 10, 2006
0041 %       - replace sladd by sladdvec to increase efficiency
0042 %
0043 
0044 
0045 %% parse and verify arguments
0046 
0047 if nargin < 2
0048     raise_lackinput('sldraw_ellipse', 2);
0049 end
0050 
0051 if length(center) ~= 2
0052     error('sltoolbox:invaliddims', 'center should be a vector of length 2');    
0053 end
0054 center = center(:);
0055 
0056 if nargin < 3 || isempty(n)
0057     n = 300;
0058 end
0059 
0060 %% convert the shape to transform (scale and rotation)
0061 
0062 if isnumeric(shape) && length(shape) == 3 % [a, b, theta] form
0063     
0064     [S, R] = get_transform_from_geo(shape(1), shape(2), shape(3));                
0065     
0066 elseif isnumeric(shape) && isequal(size(shape), [2, 2]) % C form
0067     
0068     [S, R] = get_transform_from_cov(shape);
0069     
0070 elseif iscell(shape) && length(shape) == 2 % {C, r} form
0071     
0072     [S, R] = get_transform_from_cov(shape{1});
0073     S = S * shape{2};
0074     
0075 end
0076 
0077 T = R * S;
0078 
0079 %% make the points forming the ellipse
0080 
0081 % make a circle first
0082 t = linspace(0, 2*pi, n);
0083 X = [cos(t); sin(t)];
0084 
0085 % transform the circle to an ellipse
0086 X = T * X;
0087 X = sladdvec(X, center, 1);
0088 
0089 % draw the circle
0090 hold on;
0091 h = plot(X(1,:), X(2,:), varargin{:});
0092 
0093 
0094 %% The functions for making transforms from shapes
0095 
0096 function [S, R] = get_transform_from_geo(a, b, theta)
0097 
0098 S = [a 0; 0 b];
0099 R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
0100 
0101 function [S, R] = get_transform_from_cov(C)
0102 
0103 [S, R] = slsymeig(C);
0104 S = max(S, 0);  % a zero guard
0105 S = diag(sqrt(S));
0106 
0107 
0108 
0109     
0110     
0111 
0112

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