bezier_differentiated.mac

/*

https://github.com/t-o-k/Maxima-bezier/bezier_differentiated.mac

Copyright (c) 2020 Tor Olav Kristensen, http://subcube.com

Use of this source code is governed by the GNU Lesser General Public License version 3, 
which can be found in the LICENSE file.

*/

kill(all);

load("bezier");

define(
    g(u, v),
    bezier_function_2a(
        matrix(
            [ 4, 2, 3, 5 ],
            [ 5, 3, 2, 4 ],
            [ 2, 5, 4, 3 ],
            [ 3, 4, 5, 2 ]
        ),
        u, v
    )
);

define(der_u_g(u, v), diff(g(u, v), u));

define(der_v_g(u, v), diff(g(u, v), v));

define(der2_u_g(u, v), diff(g(u, v), u, 2));

define(der2_v_g(u, v), diff(g(u, v), v, 2));

define(der_u_der_v_g(u, v), diff(diff(g(u, v), u), v));

define(der_v_der_u_g(u, v), diff(diff(g(u, v), v), u));

expand(g(u, v));

expand(der_u_g(u, v));

expand(der_v_g(u, v));

expand(der2_u_g(u, v));

expand(der2_v_g(u, v));

expand(der_u_der_v_g(u, v));

expand(der_v_der_u_g(u, v));

define(
    f(s, t),
    bezier_function_2a(
        matrix(
            [ a_11, a_12, a_13, a_14 ],
            [ a_21, a_22, a_23, a_24 ],
            [ a_31, a_32, a_33, a_34 ]
        ),
        s, t
    )
);

expand(f(s, t));

expand(f(0, 0));

expand(f(0, 1));

expand(f(1, 0));

expand(f(1, 1));

expand(f(u, 0));

expand(f(u, 1));

expand(f(0, v));

expand(f(1, v));