Plotting a Circle through three points.

circle3points

% Plotting a Circle through three random points
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% 3 random points --->   | calculate circle formula | -----> plot circle
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clear
clc
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% Outline 1: Randomize 3 points
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randompoints = round(10*rand(2,3)) %random array from 0 - 10 
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x1=randompoints(1,1)% random points from array to make first coord
y1=randompoints(2,1)
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x2=randompoints(1,2)%random points from array to make second coord
y2=randompoints(2,2)
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x3=randompoints(1,3)%random points from array to make third coord
y3=randompoints(2,3)
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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
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% Outline 2: Find Equation of AB line
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gradientAB = (y2-y1)/(x2-x1)        %gradient of the line AB
yintAB = (y1-(gradientAB*x1))       %y-intercept of line AB
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% Outline 4: Find Equation of BC line
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gradientBC = (y3-y2)/(x3-x2)        %gradient of the line AB         
yintBC = (y2-(gradientBC*x2))       %y-intercept of line AB
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% Outline 3: Find equation of Perpendicular line to AB
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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
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% Outline 5: Find Equation of perpendicular line to BC
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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
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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         
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% Outline 7: find radius from this point which is the origin
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radius=sqrt((xorigin-x1)^2+(yorigin-y1)^2)
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% Outline 8: Plot the circle    
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%  Credit for code to plot a cirlce goes to:
%  http://www.mathworks.com/matlabcentral/answers/3058-plotting-circles
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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

randompoints = round(10*rand(2,3))
You could try an alternative way of creating random points
randompoints = randi(10,2,3)