Problem 6 (1 point. Instructor\'s Initials Write an m-file that graphs an ellips
ID: 3196826 • Letter: P
Question
Problem 6 (1 point. Instructor's Initials Write an m-file that graphs an ellipse of the form x2, y2 a? + = 1 rotated by an angle provided by the user. The user will also provide the values for a and b. Attach a copy of the m-file to the lab. Hints 1. Start by creating an unrotated ellipse, then use a rotation matrix to tilt it. 2. To create the unrotated ellipse, start by determining x as a function of angle from 0 to 180 degrees. Then determine y as a function of x. This will give you the top half of the ellipse. From there you should be able to figure out how to create the bottom half of the ellipse. -15 -15 -05 0 05 1 15Explanation / Answer
function h=ellipse(ra,rb,ang,x0,y0,C,Nb)
% Ellipse adds ellipses to the current plot
%
% ELLIPSE(ra,rb,ang,x0,y0) adds an ellipse with semimajor axis of ra,
% a semimajor axis of radius rb, a semimajor axis of ang, centered at
% the point x0,y0.
%
% The length of ra, rb, and ang should be the same.
% If ra is a vector of length L and x0,y0 scalars, L ellipses
% are added at point x0,y0.
% If ra is a scalar and x0,y0 vectors of length M, M ellipse are with the same
% radii are added at the points x0,y0.
% If ra, x0, y0 are vectors of the same length L=M, M ellipses are added.
% If ra is a vector of length L and x0, y0 are vectors of length
% M~=L, L*M ellipses are added, at each point x0,y0, L ellipses of radius ra.
%
% ELLIPSE(ra,rb,ang,x0,y0,C)
% adds ellipses of color C. C may be a string ('r','b',...) or the RGB value.
% If no color is specified, it makes automatic use of the colors specified by
% the axes ColorOrder property. For several circles C may be a vector.
%
% ELLIPSE(ra,rb,ang,x0,y0,C,Nb), Nb specifies the number of points
% used to draw the ellipse. The default value is 300. Nb may be used
% for each ellipse individually.
%
% h=ELLIPSE(...) returns the handles to the ellipses.
%
% as a sample of how ellipse works, the following produces a red ellipse
% tipped up at a 45 deg axis from the x axis
% ellipse(1,2,pi/8,1,1,'r')
%
% note that if ra=rb, ELLIPSE plots a circle
%
% written by D.G. Long, Brigham Young University, based on the
% CIRCLES.m original
% written by Peter Blattner, Institute of Microtechnology, University of
% Neuchatel, Switzerland, blattner@imt.unine.ch
% Check the number of input arguments
if nargin<1,
ra=[];
end;
if nargin<2,
rb=[];
end;
if nargin<3,
ang=[];
end;
%if nargin==1,
% error('Not enough arguments');
%end;
if nargin<5,
x0=[];
y0=[];
end;
if nargin<6,
C=[];
end
if nargin<7,
Nb=[];
end
% set up the default values
if isempty(ra),ra=1;end;
if isempty(rb),rb=1;end;
if isempty(ang),ang=0;end;
if isempty(x0),x0=0;end;
if isempty(y0),y0=0;end;
if isempty(Nb),Nb=300;end;
if isempty(C),C=get(gca,'colororder');end;
% work on the variable sizes
x0=x0(:);
y0=y0(:);
ra=ra(:);
rb=rb(:);
ang=ang(:);
Nb=Nb(:);
if isstr(C),C=C(:);end;
if length(ra)~=length(rb),
error('length(ra)~=length(rb)');
end;
if length(x0)~=length(y0),
error('length(x0)~=length(y0)');
end;
% how many inscribed elllipses are plotted
if length(ra)~=length(x0)
maxk=length(ra)*length(x0);
else
maxk=length(ra);
end;
% drawing loop
for k=1:maxk
if length(x0)==1
xpos=x0;
ypos=y0;
radm=ra(k);
radn=rb(k);
if length(ang)==1
an=ang;
else
an=ang(k);
end;
elseif length(ra)==1
xpos=x0(k);
ypos=y0(k);
radm=ra;
radn=rb;
an=ang;
elseif length(x0)==length(ra)
xpos=x0(k);
ypos=y0(k);
radm=ra(k);
radn=rb(k);
an=ang(k)
else
rada=ra(fix((k-1)/size(x0,1))+1);
radb=rb(fix((k-1)/size(x0,1))+1);
an=ang(fix((k-1)/size(x0,1))+1);
xpos=x0(rem(k-1,size(x0,1))+1);
ypos=y0(rem(k-1,size(y0,1))+1);
end;
co=cos(an);
si=sin(an);
the=linspace(0,2*pi,Nb(rem(k-1,size(Nb,1))+1,:)+1);
% x=radm*cos(the)*co-si*radn*sin(the)+xpos;
% y=radm*cos(the)*si+co*radn*sin(the)+ypos;
h(k)=line(radm*cos(the)*co-si*radn*sin(the)+xpos,radm*cos(the)*si+co*radn*sin(the)+ypos);
set(h(k),'color',C(rem(k-1,size(C,1))+1,:));
end;