drawParabola

DRAWPARABOLA Draw a parabola on the current axis.

   drawParabola(PARABOLA);
   Draws a vertical parabola, defined by its vertex and its parameter.
   Such a parabola admits a vertical axis of symetry.

   The algebraic equation of parabola is given by:
      (Y - YV) = A * (X - VX)^2
   Where XV and YV are vertex coordinates and A is parabola parameter.

   A parametric equation of parabola is given by:
      x(t) = t + VX;
      y(t) = A * t^2 + VY;

   PARABOLA can also be defined by [XV YV A THETA], with theta being the
   angle of rotation of the parabola (in degrees and Counter-Clockwise).

   drawParabola(PARABOLA, T);
   Specifies which range of 't' are used for drawing parabola. If T is an
   array with only two values, the first and the last values are used as
   interval bounds, and several values are distributed within this
   interval.

   drawParabola(..., NAME, VALUE);
   Can specify one or several graphical options using parameter name-value
   pairs.

   drawParabola(AX, ...);
   Specifies handle of the axis to draw on.

   H = drawParabola(...);
   Returns an handle to the created graphical object.


   Example:
     figure(1); clf; hold on;
     axis equal; axis([0 100 0 100])
     % draw parabola with default parameterization bounds 
     drawParabola([50 50 .2 30]);
     % draw parabola with more specific bounds and drawing style
     drawParabola([50 50 .2 30], [-3 3], 'color', 'r', 'linewidth', 2);
   

   See Also:
   drawCircle, drawEllipse

0001 function varargout = drawParabola(varargin)
0002 %DRAWPARABOLA Draw a parabola on the current axis.
0003 %
0004 %   drawParabola(PARABOLA);
0005 %   Draws a vertical parabola, defined by its vertex and its parameter.
0006 %   Such a parabola admits a vertical axis of symetry.
0007 %
0008 %   The algebraic equation of parabola is given by:
0009 %      (Y - YV) = A * (X - VX)^2
0010 %   Where XV and YV are vertex coordinates and A is parabola parameter.
0011 %
0012 %   A parametric equation of parabola is given by:
0013 %      x(t) = t + VX;
0014 %      y(t) = A * t^2 + VY;
0015 %
0016 %   PARABOLA can also be defined by [XV YV A THETA], with theta being the
0017 %   angle of rotation of the parabola (in degrees and Counter-Clockwise).
0018 %
0019 %   drawParabola(PARABOLA, T);
0020 %   Specifies which range of 't' are used for drawing parabola. If T is an
0021 %   array with only two values, the first and the last values are used as
0022 %   interval bounds, and several values are distributed within this
0023 %   interval.
0024 %
0025 %   drawParabola(..., NAME, VALUE);
0026 %   Can specify one or several graphical options using parameter name-value
0027 %   pairs.
0028 %
0029 %   drawParabola(AX, ...);
0030 %   Specifies handle of the axis to draw on.
0031 %
0032 %   H = drawParabola(...);
0033 %   Returns an handle to the created graphical object.
0034 %
0035 %
0036 %   Example:
0037 %     figure(1); clf; hold on;
0038 %     axis equal; axis([0 100 0 100])
0039 %     % draw parabola with default parameterization bounds
0040 %     drawParabola([50 50 .2 30]);
0041 %     % draw parabola with more specific bounds and drawing style
0042 %     drawParabola([50 50 .2 30], [-3 3], 'color', 'r', 'linewidth', 2);
0043 %
0044 %
0045 %   See Also:
0046 %   drawCircle, drawEllipse
0047 %
0048 
0049 %   ---------
0050 %   author : David Legland
0051 %   INRA - TPV URPOI - BIA IMASTE
0052 %   created the 02/06/2006.
0053 %
0054 
0055 %   HISTORY
0056 %   2010-11-17 rewrite, change parametrisation, update doc
0057 %   2011-03-30 use degrees for angle
0058 %   2011-10-11 add management of axes handle
0059 
0060 % Extract parabola
0061 if nargin < 1
0062     error('geom2d:drawParabola:IllegalArgument', ...
0063         'Please specify parabola representation');
0064 end
0065 
0066 % extract handle of axis to draw on
0067 if isAxisHandle(varargin{1})
0068     ax = varargin{1};
0069     varargin(1) = [];
0070 else
0071     ax = gca;
0072 end
0073 
0074 % input parabola is given as a packed array
0075 parabola = varargin{1};
0076 varargin(1) = [];
0077 x0 = parabola(:,1);
0078 y0 = parabola(:,2);
0079 a  = parabola(:,3);
0080 
0081 % check if parabola orientation is specified
0082 if size(parabola, 2) > 3
0083     theta = parabola(:, 4);
0084 else
0085     theta = zeros(length(a), 1);
0086 end
0087 
0088 % extract parametrisation bounds
0089 bounds = [-100 100];
0090 if ~isempty(varargin)
0091     var = varargin{1};
0092     if isnumeric(var)
0093         bounds = var;
0094         varargin(1) = [];
0095     end
0096 end
0097 
0098 % create parametrisation array
0099 if length(bounds) > 2
0100     t = bounds;
0101 else
0102     t = linspace(bounds(1), bounds(end), 100);
0103 end
0104 
0105 % create handle array (in the case of several parabola)
0106 h = zeros(size(x0));
0107 
0108 % draw each parabola
0109 for i = 1:length(x0)
0110     % compute transformation
0111     trans = ...
0112         createTranslation(x0(i), y0(i)) * ...
0113         createRotation(deg2rad(theta(i))) * ...
0114         createScaling(1, a);
0115     
0116     % compute points on the parabola
0117     [xt, yt] = transformPoint(t(:), t(:).^2, trans);
0118 
0119     % draw it
0120     h(i) = plot(ax, xt, yt, varargin{:});
0121 end
0122 
0123 % process output arguments
0124 if nargout > 0
0125     varargout = {h};
0126 end
0127