I want to compute length of parametric curve r(t)=<x(t),y(t)> where t in [a,b]. Please help me to write an FREEFEM code where user can give any parametric curve. I should able to compute the length.

You have two possibilities:

- Construct the corresponding parametric curve as an inner border of your mesh. Basically the command
`border`

builds a parametric curve. - Or you ca use
`levelset`

in you integration.

See the following code:

int Npts = 40; int NptsIn=20;

border circle1(t=0,2 * pi){x=cos(t); y=sin(t); label=0;};

border circle2(t=0,2 * pi){x=0.5 * cos(t); y=0.5 * sin(t); label=1;};

mesh Th=buildmesh(circle1(Npts)+circle2(NptsIn)) ;

real length1 = int1d(Th,1)(1.0);

real length2 = int1d(Th,levelset= (x^2 + y^2 -0.5^2) )(1.);

cout << length1 <<endl;

cout << length2 <<endl;

`length1`

is computed along the inner border

`length2`

is computed on the parametric curve giver by the levelset

in both cases you have the same length of an inner circleâ€¦