Calculating a spiral in MATLAB

Question

We have these logarithmic spirals which are circling around the centre of the coordinate system:

x = e^bθ cos(θ)

y = e^bθ sin(θ)

where the e^bθ is the distance between the point (which is on the spiral) and the centre; and the θ is the angle between the line connecting the point and the origin and the axis x.

Consider a spiral where the angle is θ ϵ <0,10π> and the parameter is b=0.1. By thickening points on the spirals (and the angle θ) calculate the circumference with the relative precision better than 1%. Draw the spiral!

I'm preparing for a (MATLAB) test and I'm stuck with this exercise. Please help, any hint is appreciated.

Answer 1

Start by computing a list of x,y for your range of theta and value of b. For more accurate results, have your theta increment in smaller steps (I chose 5000 arbitrarily). Then, its simply computing the distance for each pair of consecutive points and summing them up.

t = linspace(0,10*pi,5000);
b = 0.1;
x = exp(b*t).*cos(t);
y = exp(b*t).*sin(t);
result = sum(sqrt((x(2:end) - x(1:end-1)).^2 + (y(2:end)-y(1:end-1)).^2))