MATLAB: Ellipse in parametric form

ellipseMATLABmatlab functiontheta

I'm trying to create an ellipse in parametric form. I have just two Foci along the major axis. So, how shall I get r1, r2 etc.

   point1  = 10  8
    point2 = 25  20

The syntax is

t = linspace(0, 2*pi, 200);
xt = r1 * cos(t) + xc;
yt = r2 * sin(t) + yc;
cot = cos(theta); sit = sin(theta);
x = xt * cot - yt * sit;
y = xt * sit - yt * cot;
plot(x, y, '-');

Best Answer

You cannot determine the ellipse with only the foci. You also need to know r1. Once you know that however, you can determine r2 readily,

xc_yc=(point1+point2)/2;
c=norm(point1-xc_yc);
r2 = r1^2-c^2;

Related Solutions

MATLAB: Generate random moving nodes inside two intersecting circle

clc; clear all ;
N1 = 100 ; N2 = 50 ;
th = linspace(0,2*pi,N1)' ;
r1 = 1. ; r2 = 1. ;   % radii of circles 
c1 = [0 0] ;          % center of first cirlce 
c2 = [1.5 0] ;        % center of second circle 
a1 = repmat(c1,[N1 1])+[r1*cos(th)  r1*sin(th)] ;
a2 = repmat(c2,[N1 1])+[r2*cos(th)  r2*sin(th)] ;
%
plot(a1(:,1),a1(:,2),'r') ;
hold on
plot(a2(:,1),a2(:,2),'r') ;
axis equal
%%Get points of fitst circle lying in second circle
in12 = inpolygon(a1(:,1),a1(:,2),a2(:,1),a2(:,2)) ;
P1 = a1(in12,:) ;
plot(a1(in12,1),a1(in12,2),'.b') ;
%%Get points of second circle lying in first circle
in21 = inpolygon(a2(:,1),a2(:,2),a1(:,1),a1(:,2)) ;
P2 = a2(in21,:) ;
plot(a2(in21,1),a2(in21,2),'.b') ;
%%form the oval / intersection boundary 
R = [P1 ;P2] ;
%%Form a suare grid around ovel region 
x = linspace(c1(1),c2(1),N2) ;
y = linspace(-r1,r2,N2) ;
[X,Y] = meshgrid(x,y) ;
XX = X(:) ; YY = Y(:) ;
%%Get the random points  inside the region 
l = 1 ;
ax = min(R(:,1)) ; bx = max(R(:,1)) ;
ay = min(R(:,2)) ; by = max(R(:,2)) ;
while l ==1 
      x = (bx-ax).*rand(1,1) + ax;
      y = (by-ay).*rand(1,1) + ay;
    in = inpolygon(x,y,R(:,1),R(:,2)) ;
    if in 
        plot(x,y,'.g') ;
        drawnow
    end
end

MATLAB: Define an ellipse with a given angle and find if a point lies inside its boundaries

The most easy approach is defining the ellipse by the two foci F1 and F2. Then an ellipse is the set of points, which sum of distances to F1 and F2 is 2*a, where a is the semi-major axis length. Convert this to the polar form to draw the ellipse, but use this to determine points inside:

P      = [x, y];  % A point in 2D
dist   = norm(P - F1) + norm(P - F2);
inside = (dist <= 2*a);

Best Answer

Related Solutions

MATLAB: Generate random moving nodes inside two intersecting circle

MATLAB: Define an ellipse with a given angle and find if a point lies inside its boundaries

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