function [xx,yy]=curve_int(x,y,k,N)
% Builds a parametric representation (x(t),y(t))of a curve passing 
% through the points (x(i),y(i)) at t(i), 0=t(1)<...<t(end)=1
% ARGUMENTS:
%    x,y - two vectors of the same size, point coordinates
%    k   - parametrization parameter: the distances between 
%          t(i) and t(i+1) are proportional to (chord length)^k;
%          the typical values are:
%          k=0 - uniform,   k=1 - linear,    k=0.5 - centripetal;
%    [the chord length is the distance between the points i and (i+1)]
%    N   - the output xx,yy should be x(t),y(t) for tt=linspace(0,1,N)
% METHOD: The program should return the values sx(tt) and sy(tt) of the 
%         two interpolating cubic splines: sx(t(i))=x(i),  sy(t(i))=y(i)
%         (use the "not-a-knot" or "natural" boundary conditions)
% 
