Plotting a Circle through three points. (Final version at top and early progression versions progressing down.

final_plot3circles.m

%PLOTTING A CIRCLE THROUGH 3 RANDOM POINTS OR USER INPUT POINTS

%Makes random array for random 3 points
randompoints = randi(10,2,3); 

%loop to check whether all 3 points line up, if they do it re-generates the
%points.
while  ((randompoints(2,2))-(randompoints(2,1)))/((randompoints(1,2))-(randompoints(1,1)))== ((randompoints(2,3)-randompoints(2,2))/((randompoints(1,3))-randompoints(1,2)))
randompoints = randi(10,2,3);
end

%sets variables for check
p1 = [randompoints(1,1),randompoints(2,1)];
p2 = [randompoints(1,2),randompoints(2,2)];
p3 = [randompoints(1,3),randompoints(2,3)];

% checks for any two points lieing on the same location
% re-generates if any are same
while (p1 == p2) | (p1 == p3) | (p2 == p3)
    randompoints = randi(10,2,3);
    p1 = [randompoints(1,1),randompoints(2,1)];
    p2 = [randompoints(1,2),randompoints(2,2)];
    p3 = [randompoints(1,3),randompoints(2,3)];
end


%re sets variables to use for another check, need to be reset because they
%may have changed because of previous checks.
x1=randompoints(1,1);
y1=randompoints(2,1);

x2=randompoints(1,2);
y2=randompoints(2,2);

x3=randompoints(1,3);
y3=randompoints(2,3);

%Test to check whether any points are horizontally alligned, which then
%changes the order they are accessed in So that the program can correctly
%calculate the circle.
while (y2-y1)/(x2-x1)==0 || (y3-y2)/(x3-x2)==0
    randompoints = [x2 x3 x1; y2 y3 y1];
    
x1=randompoints(1,1);
y1=randompoints(2,1);

x2=randompoints(1,2);
y2=randompoints(2,2);

x3=randompoints(1,3);
y3=randompoints(2,3);
end

%plots each random points and sets up graph axis.
plot(randompoints(1,1),randompoints(2,1),'r.') %plotting all 3 points on graph
hold all
plot(randompoints(1,2),randompoints(2,2),'g.')
plot(randompoints(1,3),randompoints(2,3),'b.')
axis([0 20 0 20]) % cleaning up the graph to look nicer
grid on


%find the equation of the lines and perpendicular lines.
gradientAB = (y2-y1)/(x2-x1);
yintAB = (y1-(gradientAB*x1));

gradientBC = (y3-y2)/(x3-x2);
yintBC = (y2-(gradientBC*x2));

gradientperpAB = -1/gradientAB;                     
xmidAB = (x1+x2)/2; 
ymidAB = (y1+y2)/2;
yintperpAB = ymidAB +(-1*gradientperpAB*xmidAB);

gradientperpBC = -1/gradientBC;                    
xmidBC = (x2+x3)/2;                                 
ymidBC = (y2+y3)/2;                                 
yintperpBC = ymidBC +(-1*gradientperpBC*xmidBC);

%find centre coordinates of circle
xorigin= (yintperpBC - yintperpAB) / (gradientperpAB - gradientperpBC);    %finds the x value of the origin of the cirlce
yorigin=xorigin*gradientperpAB + yintperpAB;                              %finds the y value of the origin of the circle         

plot(xorigin,yorigin,'k.')

%find radius of circle
radius=sqrt((xorigin-x1)^2+(yorigin-y1)^2);

%   
%
%  Credit for below code to plot a cirlce goes to:
%  http://www.mathworks.com/matlabcentral/answers/3058-plotting-circles
%
ang=0:0.01:2*pi; 
xp=radius*cos(ang);
yp=radius*sin(ang);
plot(xorigin+xp,yorigin+yp,'k');
hold off
% END OF PROGRAM

plot3circles1.m

% Plotting a Circle through three random points
%
%                         __________________________
% 3 random points --->   | calculate circle formula | -----> plot circle
%                        |__________________________|
%
%
clear
clc
close all
%
%
% Outline 1: Randomize 3 points
%
randompoints = round(10*rand(2,3)) %random array from 0 - 10 
%
x1=randompoints(1,1)% random points from array to make first coord
y1=randompoints(2,1)
%
x2=randompoints(1,2)%random points from array to make second coord
y2=randompoints(2,2)
%
x3=randompoints(1,3)%random points from array to make third coord
y3=randompoints(2,3)
%
plot(randompoints(1,1),randompoints(2,1),'r.') %plotting all 3 points on graph
hold all
plot(randompoints(1,2),randompoints(2,2),'g.')
plot(randompoints(1,3),randompoints(2,3),'b.')


%plot(x1,y1,'r.')

%plot(x2,y2,'g.')
%plot(x3,y3,'b.')
grid on
%
% Outline 2: Find Equation of AB line
%
gradientAB = (y2-y1)/(x2-x1)        %gradient of the line AB
yintAB = (y1-(gradientAB*x1))       %y-intercept of line AB
%
% Outline 3: Find equation of Perpendicular line to AB
%
gradientperpAB = -1/gradientAB                      %gradient of perpendicular line
xmidAB = (x1+x2)/2                                  %finds the middle of the the AB line
ymidAB = (y1+y2)/2                                  %
yintperpAB = ymidAB -(gradientperpAB*xmidAB)        %gets the y int of the perpendicular line
%
% Outline 4: Find Equation of BC line
%
gradientBC = (y3-y2)/(x3-x2)        %gradient of the line AB         
yintBC = (y2-(gradientBC*x2))       %y-intercept of line AB
%
% Outline 5: Find Equation of perpendicular line to BC
%
gradientperpBC = -1/gradientBC                      %gradient of perpendicular line
xmidBC = (x2+x3)/2                                  %finds the middle of the the AB line
ymidBC = (y2+y3)/2                                  
yintperpBC = ymidBC -(gradientperpBC*xmidBC)        %gets the y int of the perpendicular line
% Outline 6: Simultaneously solve the intersect point of the two lines
%
xorigin = (yintperpBC-yintperpAB)/(gradientperpAB-gradientperpBC)   %finds the x value of the origin of the cirlce
yorigin = xorigin*gradientperpAB + yintperpBC                       %finds the y value of the origin of the circle
%
% Outline 7: find radius from this point which is the origin
%
%
% Outline 8: Plot the circle    
%
%
% Outline 9: fix the graph
%
%
% Outline 10: CREATE GUI???
%
%

plot3circles2.m

% Plotting a Circle through three random points
%
%                         __________________________
% 3 random points --->   | calculate circle formula | -----> plot circle
%                        |__________________________|
%
%
clear
clc
close all
%
%
% Outline 1: Randomize 3 points
%
randompoints = round(10*rand(2,3)) %random array from 0 - 10 
%
x1=randompoints(1,1)% random points from array to make first coord
y1=randompoints(2,1)
%
x2=randompoints(1,2)%random points from array to make second coord
y2=randompoints(2,2)
%
x3=randompoints(1,3)%random points from array to make third coord
y3=randompoints(2,3)
%
plot(randompoints(1,1),randompoints(2,1),'r.') %plotting all 3 points on graph
hold all
plot(randompoints(1,2),randompoints(2,2),'g.')
plot(randompoints(1,3),randompoints(2,3),'b.')


%plot(x1,y1,'r.')

%plot(x2,y2,'g.')
%plot(x3,y3,'b.')
grid on
%
% Outline 2: Find Equation of AB line
%
gradientAB = (y2-y1)/(x2-x1)        %gradient of the line AB
yintAB = (y1-(gradientAB*x1))       %y-intercept of line AB
%
% Outline 3: Find equation of Perpendicular line to AB
%
gradientperpAB = -1/gradientAB                      %gradient of perpendicular line
xmidAB = (x1+x2)/2                                  %finds the middle of the the AB line
ymidAB = (y1+y2)/2                                  %
yintperpAB = ymidAB -(gradientperpAB*xmidAB)        %gets the y int of the perpendicular line
%
% Outline 4: Find Equation of BC line
%
gradientBC = (y3-y2)/(x3-x2)        %gradient of the line AB         
yintBC = (y2-(gradientBC*x2))       %y-intercept of line AB
%
% Outline 5: Find Equation of perpendicular line to BC
%
gradientperpBC = -1/gradientBC                      %gradient of perpendicular line
xmidBC = (x2+x3)/2                                  %finds the middle of the the AB line
ymidBC = (y2+y3)/2                                  
yintperpBC = ymidBC -(gradientperpBC*xmidBC)        %gets the y int of the perpendicular line
% Outline 6: Simultaneously solve the intersect point of the two lines
%
xorigin = (yintperpBC-yintperpAB)/(gradientperpAB-gradientperpBC)   %finds the x value of the origin of the cirlce
yorigin = xorigin*gradientperpAB + yintperpBC                       %finds the y value of the origin of the circle
%
% Outline 7: find radius from this point which is the origin
%
radius=sqrt((xorigin-x1)^2+(yorigin-y1)^2)
%
% Outline 8: Plot the circle    
%
circle(xorigin,yorigin,radius)
%
% Outline 9: fix the graph
%
%
% Outline 10: CREATE GUI???
%
%

plot3circles3.m

% Plotting a Circle through three random points
%
%                         __________________________
% 3 random points --->   | calculate circle formula | -----> plot circle
%                        |__________________________|
%
%
clear
clc
%
%
% Outline 1: Randomize 3 points
%
randompoints = round(10*rand(2,3)) %random array from 0 - 10 
%
 x1=randompoints(1,1)% random points from array to make first coord
y1=randompoints(2,1)
%
x2=randompoints(1,2)%random points from array to make second coord
y2=randompoints(2,2)
%
x3=randompoints(1,3)%random points from array to make third coord
y3=randompoints(2,3)
%
plot(randompoints(1,1),randompoints(2,1),'r.') %plotting all 3 points on graph
hold all
plot(randompoints(1,2),randompoints(2,2),'g.')
plot(randompoints(1,3),randompoints(2,3),'b.')

axis([0 20 0 20])

%plot(x1,y1,'r.')

%plot(x2,y2,'g.')
%plot(x3,y3,'b.')
grid on
%





% Outline 2: Find Equation of AB line
%
gradientAB = (y2-y1)/(x2-x1)        %gradient of the line AB
yintAB = (y1-(gradientAB*x1))       %y-intercept of line AB
%



% Outline 4: Find Equation of BC line
%
gradientBC = (y3-y2)/(x3-x2)        %gradient of the line AB         
yintBC = (y2-(gradientBC*x2))       %y-intercept of line AB
%



% Outline 3: Find equation of Perpendicular line to AB
%
gradientperpAB = -1/gradientAB                      %gradient of perpendicular line
xmidAB = (x1+x2)/2                                  %finds the middle of the the AB line
ymidAB = (y1+y2)/2                                  %
yintperpAB = ymidAB -(gradientperpAB*xmidAB)        %gets the y int of the perpendicular line
%


% Outline 5: Find Equation of perpendicular line to BC
%
gradientperpBC = -1/gradientBC                      %gradient of perpendicular line
xmidBC = (x2+x3)/2                                  %finds the middle of the the AB line
ymidBC = (y2+y3)/2                                  
yintperpBC = ymidBC -(gradientperpBC*xmidBC)        %gets the y int of the perpendicular line




% Outline 6: Simultaneously solve the intersect point of the two lines
%

xorigin = (yintperpBC-yintperpAB)/(gradientperpAB-gradientperpBC)   %finds the x value of the origin of the cirlce
yorigin = xorigin*gradientperpAB - yintperpBC                       %finds the y value of the origin of the circle
%
% Outline 7: find radius from this point which is the origin
%
radius=sqrt((xorigin-x1)^2+(yorigin-y1)^2)
%
% Outline 8: Plot the circle    
%
%  Code for plotting a circle taken from:
%  http://www.mathworks.com/matlabcentral/answers/3058-plotting-circles
%
% function circle(x,y,r)
% x and y are the coordinates of the center of the circle
% r is the radius of the circle
% 0.01 is the angle step, bigger values will draw the circle faster but
% you might notice imperfections (not very smooth)
ang=0:0.01:2*pi; 
xp=radius*cos(ang);
yp=radius*sin(ang);
plot(xorigin+xp,yorigin+yp,'k');


%
% Outline 9: fix the graph
%
%
% Outline 10: CREATE GUI???
%
%
hold off

plot3circles4.m

% Plotting a Circle through three random points
%
%                         __________________________
% 3 random points --->   | calculate circle formula | -----> plot circle
%                        |__________________________|
%
%
clear
clc
%
%
% Outline 1: Randomize 3 points
%
randompoints = round(10*rand(2,3)) %random array from 0 - 10 

%this while loop makes the generation of the random points exclude any
%points which are in a straight line to eliminate errors.
while  ((randompoints(2,2))-(randompoints(2,1)))/((randompoints(1,2))-(randompoints(1,1)))== ((randompoints(2,3)-randompoints(2,2))/((randompoints(1,3))-randompoints(1,2)))
    randompoints = round(10*rand(2,3))
end 

%
x1=randompoints(1,1)% random points from array to make first coord
y1=randompoints(2,1)
%
x2=randompoints(1,2)%random points from array to make second coord
y2=randompoints(2,2)
%
x3=randompoints(1,3)%random points from array to make third coord
y3=randompoints(2,3)
%
plot(randompoints(1,1),randompoints(2,1),'r.') %plotting all 3 points on graph
hold all
plot(randompoints(1,2),randompoints(2,2),'g.')
plot(randompoints(1,3),randompoints(2,3),'b.')
axis([0 20 0 20]) % cleaning up the graph to look nicer
grid on
%
% Outline 2: Find Equation of AB line
%
gradientAB = (y2-y1)/(x2-x1)        %gradient of the line AB
yintAB = (y1-(gradientAB*x1))       %y-intercept of line AB
%
% Outline 4: Find Equation of BC line
%
gradientBC = (y3-y2)/(x3-x2)        %gradient of the line AB         
yintBC = (y2-(gradientBC*x2))       %y-intercept of line AB
%
% Outline 3: Find equation of Perpendicular line to AB
%
gradientperpAB = -1/gradientAB                      %gradient of perpendicular line
xmidAB = (x1+x2)/2                                  %finds the middle of the the AB line
ymidAB = (y1+y2)/2                                  %
yintperpAB = ymidAB +(-1*gradientperpAB*xmidAB)     %gets the y int of the perpendicular line
%
% Outline 5: Find Equation of perpendicular line to BC
%
gradientperpBC = -1/gradientBC                      %gradient of perpendicular line
xmidBC = (x2+x3)/2                                  %finds the middle of the the AB line
ymidBC = (y2+y3)/2                                  
yintperpBC = ymidBC +(-1*gradientperpBC*xmidBC)        %gets the y int of the perpendicular line
gradienta = gradientAB
gradientb = gradientBC
%Outline 6: Simultaneously solve the intersect point of the two lines
%
xorigin= (yintperpBC - yintperpAB) / (gradientperpAB - gradientperpBC)    %finds the x value of the origin of the cirlce
yorigin=xorigin*gradientperpAB + yintperpAB                               %finds the y value of the origin of the circle         
%
% Outline 7: find radius from this point which is the origin
%
radius=sqrt((xorigin-x1)^2+(yorigin-y1)^2)
%
% Outline 8: Plot the circle    
%
%  Credit for code to plot a cirlce goes to:
%  http://www.mathworks.com/matlabcentral/answers/3058-plotting-circles
%
ang=0:0.01:2*pi; 
xp=radius*cos(ang);
yp=radius*sin(ang);
plot(xorigin+xp,yorigin+yp,'k');
hold off
% END OF PROGRAM