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