Going from piecewise polynomials to CasADi BSplines

test.m

close all

% casadi.interpolant creates 'knots' and 'coefficients' out of data and passes it on to casadi.Function.bspline
% Here, we supply knots and coefficients directly to casadi.Function.bspline


%% Example 1: discontinuous example, just to make clear the interpretation
% of the pp = piecewise polynomial form clear

% 4 intervals: 0-1, 1-2, 2-4, 4-6
breaks = [0,1,2,4,6];

coeffs = [1 0 0 ...  % on interval 1: x^2         (local coordinates)
          0 1 0 ...  % on interval 2: x           (local coordinates)
          0 0 1 ...  % on interval 3: 1           (local coordinates)
          1 2 -1];    % on interval 4: x^2+x*x-1  (local coordinates)

pp = ppmak(breaks,coeffs);

x = linspace(0,6,1000);
plot(x,fnval(pp,x));
hold on

sp = fn2fm(pp,'B-');

spline = casadi.Function.bspline('spline',{sp.knots},sp.coefs,[sp.order-1]);

% Note not really meant for discontinuities/knots with multiplicity>1 inside the interval
plot(x,full(spline(x)),'x')

legend('Matlab pp','CasADi spline')

%% Example 2: now a spline that is smooth

breaks = [0,1,2,4,6];

coeffs = [-2 2 1 ... % on interval 1: -2*x^2+2*x+1 (local coordinates)
          2 -2 1 ... % on interval 2: x^2-2*x+1    (local coordinates)
          -3/8 2 1 ... 
          -7/8 0.5 3.5];

pp = ppmak(breaks,coeffs);

figure()
x = linspace(0,6,100);
plot(x,fnval(pp,x));
hold on

sp = fn2fm(pp,'B-');
spline = casadi.Function.bspline('spline',{sp.knots},sp.coefs,[sp.order-1]);

plot(x,full(spline(x)),'x')

legend('Matlab pp','CasADi spline')