Parametric curves and surfaces applet

This is an applet to demonstrate and give some examples of parametric curves and surfaces.

Click the "Bezier curve" button and the top panel should change to allow you to enter the control points. The four control points p_i of the Bezier curve define the curves shape by the equation:
r(t) = S(i=0 to 3) p_i B_i(t)
where the B_i(t) are special blending functions used by Mr. Bezier to construct his smooth curves.
Initially the control points have been placed at (0,0,0) (1,0,0) (2,0,0) and (3,0,0), but you can move them to anywhere you want by selecting the control point from the drop down list, entering the x, y, and z coordinates, and clicking "Set control point".

Click the "Fourier curve" button. The general Fourier curve is defined by the equations,
x(t) = S(i=0 to inf.) a_i cos it + b_i sin it
y(t) = S(i=0 to inf.) c_i cos it + d_i sin it
z(t) = S(i=0 to inf.) f_i cos it + g_i sin it
You can enter the coefficients (up to i = 20) in the top panel.For example, to construct the cardiod:
x = (cos t)(1 - sin t)
y = (sin t)(1 - sin t)
z = 0
using, cos t sin t = (1/2) sin 2t
and, sin² t = (1/2)(1 - cos 2t)
we get,
x = cos t - 0.5 sin 2t
y = -0.5 + 0.5 cos 2t + sin t
so next to "x cos coeffs" select 1 from the drop down list, enter 1.0 in the text field and click the "x cos coeffs" button to enter the value, and you've done the "cos t" term. The other four terms can be done in the same way. (The number, n say, in the drop down list refers to the coefficient of t, cos nt or sin nt)