www.pudn.com > IrisLocate.rar > plot_circle.m
% 431-400 Year Long Project
% LA1 - Medical Image Processing 2003
% Supervisor : Dr Lachlan Andrew
% Group Members : Alister Fong 78629 a.fong1@ugrad.unimelb.edu.au
% Lee Siew Teng 102519 s.lee1@ugrad.unimelb.edu.au
% Loh Jien Mei 103650 j.loh1@ugrad.unimelb.edu.au
%
% File and function name : plot_circle.m
% Version : 4.0
% Date of completion : 20 August 2003
% Written by : Alister Fong 78629 a.fong1@ugrad.unimelb.edu.au
%
% Inputs :
% X - The X coordinates of the center of this circle
% Y - The Y coordinates of the center of this circle
% Radius - The radius of this circle >= 0
% intervals (optional) - The number of evenly spaced points along the X axis
% inclusive of the start and end coordinates
% (needed by 'interval' algorithm)
% algorithm (optional) - Allows the choice of the following algorithms
% = 'angle' (default)
% Calculates the node points by its angle
% = 'interval'
% Takes the number of intervals and spaces the
% X coordinates out according to the integer
% value of intervals
% = 'bresenham'
% Uses the "Bresenham's incremental circle algorithm"
% on Page 84-85, Chapter 2, "Procedural Elements for
% Computer Graphics, Second Edition" by David F. Rogers,
% UniM Engin 006.6 ROGE,
% Produces a digital integer approximation of a circle
% that is suitable for plotting a circle in a matrix
% = 'bresenhamSolid'
% Uses the "Bresenham's incremental circle algorithm"
% that have been modified to produce a solid circle instead
% instead of the circumference
%
% Outputs :
% output_coord - Results in a [M x 2] matrix :
% The coordinates desired:
% X coordinates are output_coord(:,1) and
% Y coordinates are output_coord(:,2)
% and the first and last coordinates are the same to
% ensure that a complete closed circle is formed
%
% Description :
% To calculate the coordinates needed to draw a circle given the details of the
% circle, for use by the 'plot' function
%
% Usage >> output_coord = plot_circle(X,Y,Radius); or
% output_coord = plot_circle(X,Y,Radius,intervals,algorithm);
% plot(output_coord(:,1),output_coord(:,2),'r*-');
%
% >> output_coord = plot_circle(X,Y,Radius,'bresenham');
% output_image = zeros(500);
% [M,N] = size(output_coord);
% for q = 1:1:M
% output_image(output_coord(q,1),output_coord(q,2)) = 1;
% end
% imshow(output_image);
function output_coord = plot_circle(X,Y,Radius,varargin)
outputX = [];
outputY = [];
temp_mod = 1;
cal_mode = 'angle'; %default
intervals = NaN;
% =============================================================
% Check optional inputs
% =============================================================
if (length(varargin) > 0)
for a = 1:1:length(varargin)
if isstr(varargin{a}) == 1
if ((strcmp(varargin{a},'angle') == 1)|...
(strcmp(varargin{a},'interval') == 1)|...
(strcmp(varargin{a},'bresenham') == 1)|...
(strcmp(varargin{a},'bresenhamSolid') == 1)...
)
cal_mode = varargin{a};
end
elseif isfinite(varargin{a}) == 1
intervals = varargin{a};
else
error('Invalid arguments');
end
end
end
% =============================================================
% Initialization of 'interval'
% =============================================================
if strcmp(cal_mode,'interval') == 1
% Satisfies requirement for calculation by the given intervals
if isnan(intervals) == 1
error('No interval given');
end
temp_mod = mod(intervals,2);
interval = (intervals - temp_mod) / 2;
interval_size = (Radius+Radius)/intervals;
valueX = 0;
if temp_mod == 1
outputX = [0];
outputY = [Radius];
else
valueX = (-1/2)*interval_size;
end
cal_mode = 'interval';
end
% =============================================================
% Calculate the 1st quardrant
% =============================================================
% ************************************************************
% by the angle, scaled by the given radius
% ************************************************************
if strcmp(cal_mode,'angle') == 1
increment_angle = pi*(1/Radius);
curr_angle = pi/2;
loop=0;
while curr_angle>0
loop=loop+1;
outputX = [outputX(:);sqrt(Radius^2-(Radius*sin(curr_angle))^2)];
outputY = [outputY(:);sqrt(Radius^2-(Radius*cos(curr_angle))^2)];
curr_angle = curr_angle-increment_angle;
end
outputX = [outputX(:);Radius];
outputY = [outputY(:);0];
elseif strcmp(cal_mode,'interval') == 1
% ************************************************************
% by the given x-interval
% ************************************************************
valueX = valueX + interval_size;
while valueX < Radius
outputX = [outputX(:);valueX];
outputY = [outputY(:);sqrt((Radius*Radius)-(valueX*valueX))];
valueX = valueX + interval_size;
end
outputX = [outputX(:);Radius];
outputY = [outputY(:);0];
elseif (strcmp(cal_mode,'bresenham') == 1) | (strcmp(cal_mode,'bresenhamSolid') == 1)
X = round(X);
Y = round(Y);
Radius = round(Radius);
% ************************************************************
% Taken from Chapter 2, Page 84-85, David F. Rogers,
% "Procedural Elements for Computer Graphics,Second Edition"
% ************************************************************
x_i = 0;
y_i = Radius;
theta_i=2*(1-Radius);
Limit = 0;
while y_i >= Limit
% Set Pixel
if (strcmp(cal_mode,'bresenham') == 1)
% Plot the circumference
outputX = [outputX(:);x_i];
outputY = [outputY(:);y_i];
elseif (strcmp(cal_mode,'bresenhamSolid') == 1)
% Create a solid circle
tempY = [0:1:y_i]';
tempX = tempY;
tempX(:) = x_i;
outputX = [outputX(:);tempX];
outputY = [outputY(:);tempY];
else
error('Invalid option');
end
% determine if case 1 or 2, 4 or 5, or 3
if theta_i < 0
delta = 2*(theta_i + y_i) - 1;
% determine whether case 1 or 2
if delta <= 0
% move horizontally
x_i = x_i + 1;
theta_i = theta_i + (2*x_i) + 1;
else
% move diagonally
x_i = x_i + 1;
y_i = y_i - 1;
theta_i = theta_i + (2*(x_i - y_i)) + 2;
end
elseif theta_i > 0
delta_prime = 2*(theta_i - x_i) -1;
% determine whether case 4 or 5
if delta_prime <= 0
% move diagonally
x_i = x_i + 1;
y_i = y_i - 1;
theta_i = theta_i + (2*(x_i - y_i)) + 2;
else
% move vertically
y_i = y_i - 1;
theta_i = theta_i - (2*y_i) + 1;
end
elseif theta_i == 0
% move diagonally
x_i = x_i + 1;
y_i = y_i - 1;
theta_i = theta_i + (2*(x_i - y_i)) + 2;
end
end
end
% =============================================================
% Calculate the 2nd quardrant
% =============================================================
length_outputX = length(outputX);
if temp_mod == 1
% Avoids duplicate coordinates
outputX = [outputX([length_outputX:-1:2])*(-1);outputX(:)];
outputY = [outputY([length_outputX:-1:2]);outputY(:)];
else
outputX = [outputX([length_outputX:-1:1])*(-1);outputX(:)];
outputY = [outputY([length_outputX:-1:1]);outputY(:)];
end
% =============================================================
% Calculate the 3rd and 4th quardrant and to close the loop
% =============================================================
length_outputY = length(outputY)-1;
outputX = [outputX(:);outputX([length_outputY:-1:1])];
outputY = [outputY(:);outputY([length_outputY:-1:1])*(-1)];
% =============================================================
% Shift the circle to the desired center
% =============================================================
outputX = outputX+X;
outputY = outputY+Y;
output_coord = [outputX,outputY];
% If a solid is asked for make sure there are no duplicates
if (strcmp(cal_mode,'bresenhamSolid') == 1)
output_coord = unique(output_coord,'rows');
end