/* wxMaxima Commands to plot a Bezier curve as a parametric plot.
 *
 * Usage: Copy and paste this file into the command window.
 *
 * M.V.Wickerhauser
 * 2019-10-10
 */ 

/* Fix three control points. */
P0: [1,1];
P1: [1,3];
P2: [3,2];
P3: [2,1];

/* ...so use Bernstein polynomials of degree 3. */
B30:binomial(3,0)*(1-t)^3;
B31:binomial(3,1)*(1-t)^2*t;
B32:binomial(3,2)*(1-t)*t^2;
B33:binomial(3,3)*t^3;

/* Bezier curve B is a vector valued function of the parameter t. */
B: P0*B30+P1*B31+P2*B32+P3*B33;  /* X(t) = B[1], Y(t) = B[2] */

/* Plot the Bezier curve with "parametric" plot2d() and 0<t<1. */
plot2d([parametric, B[1], B[2], [t,0,1]]);

/* Alternatively, use the package "bernstein": */

load("bernstein");  /* includes contributed function bernstein_poly() */
CP:[[1,1],[1,3],[3,2],[2,1]];  /* control points CP[1],...,CP[4] */
degN: length(CP)-1;       /* degree N = (number of control pts) - 1 */
Bez:sum(CP[k+1]*bernstein_poly(k,3,t),k,0,degN); /* Bezier curve */
plot2d([parametric, Bez[1], Bez[2], [t,0,1]]);  /* X=Bez[1], Y=Bez[2] */