P1: Given Scripts/Functions

MakeConic

  function Z = MakeConic(A,B,C,D,E,F)
% Represents the conic defined by
%
%     Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

Z = struct('A',A,'B',B,'C',C,'D',D,'E',E,'F',F);

P1A

% Script P1A
%
% Plots the coeficients A, B, C, D, E, and F as the conic
%
%            2x^2 + xy + 3y^2 - x + y - 2
%
% is rotated around the origin (0,0).

close all
n = 200;
Kappa = MakeConic(2,1,3,-1,1,-2);
phi = linspace(0,2*pi,n)';
P = zeros(n,6);

% Store the A, B, C, D, E, and F values in the columns of P
for k=1:n
   Z = RotateConic(Kappa,phi(k));
   P(k,:) = [Z.A Z.B Z.C Z.D Z.E Z.F];
end

% Plot the A, B, and C values

plot(phi,P(:,1),'-',phi,P(:,2),':',phi,P(:,3),'--')
xlabel('phi (the counter-clockwise rotation angle)')
legend('A','B','C')
title('Values of A, B, C when 2x^2 + xy + 3y^2 - x + y - 2 is rotated \phi radians')


% Plot the D, E, and F values

figure
plot(phi,P(:,4),'-',phi,P(:,5),':',phi,P(:,6),'--')
xlabel('phi (the counter-clockwise rotation angle)')
legend('D','E','F')
title('Values of D, E, F when 2x^2 + xy + 3y^2 - x + y - 2 is rotated \phi radians')

P1B

% Script P1B
clc
disp(' A  B  C  D  E  F      a       b       h       k      phi')
disp('-----------------------------------------------------------')
for A = 0:1
   for B = 0:2
      for C = 0:2
         for D = [-1 1]
            for E = [-1 1]
               for F = [-1 1]
                  Kappa = MakeConic(A,B,C,D,E,F);
                  Eta = MakeEllipse(Kappa);
                  if ~isempty(Eta)
                     a = Eta.a; b = Eta.b; h = Eta.h; k = Eta.k; phi = Eta.phi;
                     s1 = sprintf('%2d %2d %2d %2d %2d %2d',A,B,C,D,E,F);
                     s2 = sprintf('%6.3f  %6.3f  %6.3f  %6.3f  %6.3f',a,b,h,k,phi);
                     disp([s1 '   ' s2])
                  end
               end
            end
         end
      end
   end
end

P1C

% Script P1C
% Illustrates ShowEllipse

close all

% Display the ellipse (x/3)^2 + (y/2)^2  = 1
% and what is obtained by rotating it counterclockwise pi/6, pi/3, and pi/2
% radians.

for i=1:4
   subplot(2,2,i)
   ShowEllipse(MakeEllipse(RotateConic(MakeConic(1/9,0,1/4,0,0,-1),(i-1)*pi/6)))
   title(sprintf('angle  = %3d degrees',(i-1)*30))
end

% Display 2x^2 + xy + 3y^2 -x + y -2 = 0

figure
Eta = MakeEllipse(MakeConic(2,1,3,-1,1,-2));
ShowEllipse(Eta)
title(sprintf('a = %6.4f  b = %6.4f   (h,k) = (%6.4f,%6.4f)  phi = %6.4f',...
                Eta.a, Eta.b, Eta.h, Eta.k, Eta.phi))