function handle parameterization interval

Hello everyone,

yesterday I got help from the community for my problem. I try to make a parameterized function of a straight line - radius - straight line (three segments). For simplicity I'd like to enter it in one single function handle as f(t) and adapt the parameter t with intervals. My function looks like this:

geo.x = @(t) t(t<=l_1) * 1 + geo.radius * cos(t(t>= l_1 & t<=l_2) / geo.radius + 1.5*pi) + t(t>=l_2) * cosd(geo.psi);

with l_1 = length of the first interval, l_2 first and second interval and l_3 length of the whole polyline. Due to any reason, matlab cant handle this, when I want to execute the function with the parameter (t = linspace 0,l_3) and returns the following error:

Error using  + 
Matrix dimensions must agree.

Error in @(t)t(t<=l_1)*1+geo>=l_1&t<=l_2)/geo.radius+1.5*pi)+t(t>=l_2)*cosd(geo.psi)

Can anyone tell me, where my mistake is located?

Thanks in advance! Georg

Answer 1

[Mischa Kim]

Georg, you could use something like

l_1    = 1;
l_2    = 2;
radius = 0.5;
psi    = 0.2;
t      = -1:0.01:5;
geo = @(t) [t(t<=l_1) * 1 , radius * cos(t(t> l_1 & t<l_2) / radius + 1.5*pi) , t(t>=l_2) * cosd(psi)];
plot(t,geo(t))

Note, the function is not quite the same as yours. Essentially, you break up the function into intervals which you then concatenate into one vector.

[Georg Söllinger]

Hello Mischa,

thanks for your fast answer. Well,the problem is, that I would prefer a single vector, as I would like to proceed with some other operations, where a single function without discontinuities would be preferable. E.g. I want to calculate the normal on the polyline with atan(y(t2)-y(t1))/(x(t2)-x(t1)) and an intersection point with a circle. Programming those operations would be much easier if only having a single function. Isn't there a way to achieve that?