Creating one curve from different curves

I would like to merge three curves to only one. the first curve is a sector of an ellipse from pi to 4/3*pi. the second curve is upper half circle from 4/3*pi to 5/3*pi, and the third is again a sector of an ellipse from 5/4*pi to 2pi.

This is sketch:

[Rik]

Do you mean just as lines, or do you want a piecewise function?

[Ziv Abramovic]

a piecewise function

Answer 1

[Rik]

There are at least 3 methods I could think of, each with their own pros and cons:

figure(1),clf(1)

%% with the symbolic toolbox
syms x
cond1= x<-2;
val1= -x;
cond2= x>=-2 & x<5;
val2= x.^2-2;
cond3= x>=5;
val3= 23+sin((x-5)*3);
f=piecewise(cond1,val1,cond2,val2,cond3,val3);

figure(1)
ax=subplot(1,3,1);cla(ax);
fplot(f,[-10 10])

%% with an anonymous function
%(note that this doesn't work if a val is NaN, even if the cond is false)

cond1=@(x) x<-2;
val1=@(x) -x;
cond2=@(x) x>=-2 & x<5;
val2=@(x) x.^2-2;
cond3=@(x) x>=5;
val3=@(x) 23+sin((x-5)*3);

f=@(x) 0 + ...
    cond1(x).*val1(x) + ...
    cond2(x).*val2(x) + ...
    cond3(x).*val3(x);

figure(1)
ax=subplot(1,3,2);cla(ax);
fplot(f,[-10 10])

%% with array operations
%(also works if a val is NaN when the cond is false)

x=linspace(-10,10,200);

y=zeros(size(x));

cond=x<-2;
val= -x;
y(cond)=val(cond); % or if val is still an anonymous function: y(cond)=val(x(cond));
cond= x>=-2 & x<5;
val= x.^2-2;
y(cond)=val(cond);
cond= x>=5;
val= 23+sin((x-5)*3);
y(cond)=val(cond);

figure(1)
ax=subplot(1,3,3);cla(ax);
plot(x,y)