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Function: parploth
Section: graphic
C-Name: parploth
Prototype: V=GGJD0,M,D0,L,p\nParametric|1; Recursive|2; no_Rescale|4; no_X_axis|8; no_Y_axis|16; no_Frame|32; no_Lines|64; Points_too|128; Splines|256; no_X_ticks|512; no_Y_ticks|1024; Same_ticks|2048; Complex|4096
Description:
(,gen,gen,closure,?0,?0):vec parploth($2, $3, $4, $5, $6, $prec)
Help: parploth(X=a,b,expr,{flags=0},{n=0}): plot of expression expr, X goes
from a to b in high resolution. Both flags and n are optional. Binary digits
of flags mean: 1=Parametric, 2=Recursive, 4=no_Rescale, 8=no_X_axis,
16=no_Y_axis, 32=no_Frame, 64=no_Lines (do not join points), 128=Points_too
(plot both lines and points), 256=Splines (use cubic splines),
512=no_X_ticks, 1024= no_Y_ticks, 2048=Same_ticks (plot all ticks with the
same length), 4096=Complex (the two coordinates of each point are encoded
as a complex number). n specifies number of reference points on the graph
(0=use default value). Returns a vector for the bounding box.
Doc: high precision plot of the function $y=f(x)$ represented by the expression
\var{expr}, $x$ going from $a$ to $b$. This opens a specific window (which is
killed whenever you click on it), and returns a four-component vector giving
the coordinates of the bounding box in the form
$[\var{xmin},\var{xmax},\var{ymin},\var{ymax}]$.
\misctitle{Important note} \kbd{parploth} may evaluate \kbd{expr} thousands of
times; given the relatively low resolution of plotting devices, few
significant digits of the result will be meaningful. Hence you should keep
the current precision to a minimum (e.g.~9) before calling this function.
$n$ specifies the number of reference point on the graph, where a value of 0
means we use the hardwired default values (1000 for general plot, 1500 for
parametric plot, and 8 for recursive plot).
If no $\fl$ is given, \var{expr} is either a scalar expression $f(X)$, in which
case the plane curve $y=f(X)$ will be drawn, or a vector
$[f_1(X),\dots,f_k(X)]$, and then all the curves $y=f_i(X)$ will be drawn in
the same window.
\noindent The binary digits of $\fl$ mean:
\item $1 = \kbd{Parametric}$: \tev{parametric plot}. Here \var{expr} must
be a vector with an even number of components. Successive pairs are then
understood as the parametric coordinates of a plane curve. Each of these are
then drawn.
For instance:
\bprog
parploth(X=0,2*Pi,[sin(X),cos(X)], "Parametric")
parploth(X=0,2*Pi,[sin(X),cos(X)])
parploth(X=0,2*Pi,[X,X,sin(X),cos(X)], "Parametric")
@eprog\noindent draw successively a circle, two entwined sinusoidal curves
and a circle cut by the line $y=x$.
\item $2 = \kbd{Recursive}$: \tev{recursive plot}. If this flag is set,
only \emph{one} curve can be drawn at a time, i.e.~\var{expr} must be either a
two-component vector (for a single parametric curve, and the parametric flag
\emph{has} to be set), or a scalar function. The idea is to choose pairs of
successive reference points, and if their middle point is not too far away
from the segment joining them, draw this as a local approximation to the
curve. Otherwise, add the middle point to the reference points. This is
fast, and usually more precise than usual plot. Compare the results of
\bprog
parploth(X=-1,1, sin(1/X), "Recursive")
parploth(X=-1,1, sin(1/X))
@eprog\noindent
for instance. But beware that if you are extremely unlucky, or choose too few
reference points, you may draw some nice polygon bearing little resemblance
to the original curve. For instance you should \emph{never} plot recursively
an odd function in a symmetric interval around 0. Try
\bprog
parploth(x = -20, 20, sin(x), "Recursive")
@eprog\noindent
to see why. Hence, it's usually a good idea to try and plot the same curve
with slightly different parameters.
The other values toggle various display options:
\item $4 = \kbd{no\_Rescale}$: do not rescale plot according to the
computed extrema. This is used in conjunction with \tet{plotscale} when
graphing multiple functions on a rectwindow (as a \tet{plotrecth} call):
\bprog
s = plothsizes();
plotinit(0, s[2]-1, s[2]-1);
plotscale(0, -1,1, -1,1);
plotrecth(0, t=0,2*Pi, [cos(t),sin(t)], "Parametric|no_Rescale")
plotdraw([0, -1,1]);
@eprog\noindent
This way we get a proper circle instead of the distorted ellipse produced by
\bprog
parploth(t=0,2*Pi, [cos(t),sin(t)], "Parametric")
@eprog
\item $8 = \kbd{no\_X\_axis}$: do not print the $x$-axis.
\item $16 = \kbd{no\_Y\_axis}$: do not print the $y$-axis.
\item $32 = \kbd{no\_Frame}$: do not print frame.
\item $64 = \kbd{no\_Lines}$: only plot reference points, do not join them.
\item $128 = \kbd{Points\_too}$: plot both lines and points.
\item $256 = \kbd{Splines}$: use splines to interpolate the points.
\item $512 = \kbd{no\_X\_ticks}$: plot no $x$-ticks.
\item $1024 = \kbd{no\_Y\_ticks}$: plot no $y$-ticks.
\item $2048 = \kbd{Same\_ticks}$: plot all ticks with the same length.
\item $4096 = \kbd{Complex}$: is a parametric plot but where each member of
\kbd{expr} is considered a complex number encoding the two coordinates of a
point. For instance:
\bprog
parploth(X=0,2*Pi,exp(I*X), "Complex")
parploth(X=0,2*Pi,[(1+I)*X,exp(I*X)], "Complex")
@eprog\noindent will draw respectively a circle and a circle cut by the line
$y=x$.
\synt{parploth}{GEN a,GEN b,GEN code, long flag, long n, long prec}.
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