5.4 How to draw an ellipse?

5.4.1 draw an ellipse centered at origin and given its semi-major/minor $(a,b)$

draw an ellipse centered at $(0,0)$ with $a=2,b=1$ being its semi-major and minor.

The ellipse equation for the above is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Mathematica a = 2; b = 1; Graphics[Circle[{0, 0}, {a, b}], Axes -> True]

 

Matlab a=2; b=1; t=linspace(0,2*pi,50); plot(a*cos(t),b*sin(t)) axis equal

 

5.4.2 draw an ellipse centered at $(x,y$) and given its semi-major/minor $(a,b)$

draw an ellipse centered at $(1,2)$ with $a=2,b=1$ being its semi-major and minor. The ellipse equation for the above is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Mathematica a = 2; b = 1; Graphics[ { Circle[{1, 2}, {a, b}], Point[{1, 2}] }, Axes -> True ]

 

Matlab close all; a=2; b=1; t=linspace(0,2*pi,50); plot(a*cos(t)+1,b*sin(t)+2) axis equal xlim([-1,4]); ylim([0,4]);

 

5.4.3 draw an ellipse centered at origin and given its semi-major/minor $(a,b)$ and rotated at angle $\theta$

draw an ellipse centered at $(0,0)$ with $a=2,b=1$ being its semi-major and minor titlted at angle $\theta =30\text{degrees}$ anti-clockwise.

The ellipse equation for the above is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. After drawing it, we rotate it.

Mathematica a = 2; b = 1; Graphics[ Rotate[ {Circle[{0, 0}, {a, b}], Line[{{-a, 0}, {a, 0}}], Line[{{0, -b}, {0, b}}] } , 30 Degree ] , Axes -> True ]

 

Matlab Matlab does not have rotate function, so use the rotation tranformation matrix. close all; a = 2; b = 1; t = linspace(0,2*pi,50); rotateAngle = 30*pi/180; mat = [cos(rotateAngle) -sin(rotateAngle) sin(rotateAngle) cos(rotateAngle)]; %2x2 times 2x50 = 2x50 data = mat*[a*cos(t);b*sin(t)]; plot(data(1,:),data(2,:)) axis equal