![]() U_int, v_int: the interval between consecutive u’s and v’s. ![]() drawing a curve / surface for each u and each v. Object(u,v): the usual command you use to draw curves / surfaces, but parametrized by u,v, i.e. Sequence (Sequence (,u, u_start, u_end, u_int), v, v_start, v_end,v_int) Or, if the object being drawn is parametrized by 2 variables, GeoGebra will first draw the object(t_start), then object(t_start + t_int) and so on until object(t_end) T_int: the interval between consecutive t’s. ![]() T_start, t_end: the start and end values of t in your curve. Object(t): the usual command you use to draw curves / surfaces, but parametrized by t, i.e. This is the kind of command you want for simulating linear transformations. This is the command to use if you want to construct multiple lines / curves / any object at the same time. If you want to have different colors at different points, you will have to go through a rather painful route, and as a result, I used Mathematica when I wanted to color different points of a surface a different color for complex analysis. The whole line / curve / surface is a single object, and it can only be of the same color. The only limitation that I came across (that I really want GeoGebra to be able to make it much more convenient to remedy) is when it comes to customization. But perhaps when it comes to things like a torus, I will need it! GeoGebra also has a built-in sphere tool, so for my purposes, I haven’t used this command yet. For simple surfaces where you can parametrize into z = f(x,y), you can simply input the formula into GeoGebra and it will handle it. I don’t think I have used this command for surfaces before in my videos. U_start, u_end, v_start, v_end: the start and end values of u, v in your surface. X(u,v), y(u,v), z(u,v): the expression of x, y, z coordinates, with u,v as variables Surface (x(u,v), y(u,v), z(u,v), u, ustart, uend, v, vstart, v_end) The only difference is that we have two variables to parametrize a surface rather than 1 to parametrize a curve: If you want to plot surfaces instead, then there is a similar command.
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