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# 'draw'-Gnuplot interface:object parametric

Once you have opened a Maxima session, load package draw:

load("draw") $ To read the documentation on object parametric, write the following sentence: describe(parametric)$


## Parametric curves in R2

Parametric and explicit functions:

draw2d(
color = ReD,   /* case insensitive */
explicit(exp(x),x,-1,3),

color = "#0000Ff",
key   = "This is the parametric one!!",
parametric(2*cos(rrr),rrr^2,rrr,0,2*%pi))$ Transforming a parametric function: para : parametric(2*cos(r),r,r,0,2*%pi)$

draw2d(
para,
transform = [v+6,u,u,v],
color     = red,
para)$ ## Parametric curves in R3 Parametric 3D curves can be rendered with a colored 4th dimension. This feature is a contribution by Joan Pau Beltran: draw3d( terminal = wxt, color = blue, nticks = 60, line_width = 3, enhanced3d = (u-1)^2, parametric(cos(5*u)^2,sin(7*u),u-2,u,0,2))$


A parametric curve is defined in terms of one parameter; we can define color numbers with respect to it. Also, we can define color numbers in terms of coordinates (x, y, z):

set_draw_defaults(
nticks     = 60,
line_width = 3,
view       = [63,74])$par_fun: parametric(sin(u)^2,cos(u),u,u,0,4*%pi)$

c1: gr3d(
/* we can select any parameter name */
enhanced3d = [(k-1)^2,k],
par_fun) $c2: gr3d( /* coordinate names are also arbitrary */ enhanced3d = [if yy>= 0 then 1 else 0, xx, yy, zz], par_fun)$

draw(dimensions = [350,700],
c1,
c2,
columns    = 1)\$