[X, - 3, 3] [Y, - 3, 3]
are the x range and y range respectively.
[TRANSFORM_XY, FALSE] if not false, should be the output of
make_transform([x,y,z], [f1(x,y,z),f2(x,y,z),f3(x,y,z)])
which produces a transformation from 3 space to 3 space, which will be applied to the graph. A built in one is polar_xy which gives the same as
make_transform([r,th,z],[r*cos(th),r*sin(th),z])
[RUN_VIEWER,TRUE] if not false, means run the viewer software dont just output a data file.
[GRID,30,30] means plot3d should divide the x range into 30 intervals and similarly the y range.
[COLOUR_Z,false] aplies to colouring done with plot_format ps.
[PLOT_FORMAT,ZIC] is for plot3d and currently ZIC, GNUPLOT, PS, and GEOMVIEW are supported.
There are good quality public domain viewers for these formats. They are izic, gnuplot, ghostview, and geomview.
izic is available by ftp from zenon.inria.fr. Contact one of
{fournier,kajler,mourrain}@sophia.inria.fr.
It has beautiful colour gouraud shading, and very fast wireframe. It runs on X windows.
geomview is from the geometry institute in minnesota, and is available by anonymous ftp from there. It is currently not quite as pretty as izic, but provides excellent support for multiple objects and multiple lights.
gnuplot is everywhere as is ghostview. We also provide mgnuplot a tcl interface for gnuplot, which lets you rotate the plots using the mouse and a scale.
plot3d(2^(-u^2+v^2),[u,-5,5],[v,-7,7]);
would plot z = 2^(-u^2+v^2) with u and v varying in [-5,5] and [-7,7] respectively, and with u on the x axis, and v on the y axis.
An example of the second pattern of arguments is
plot3d([cos(x)*(3+y*cos(x/2)),sin(x)*(3+y*cos(x/2)),y*sin(x/2)], [x,-%pi,%pi],[y,-1,1],['grid,50,15])
which will plot a moebius band, parametrized by the 3 expressions given as the first argument to plot3d. An additional optional argument [grid,50,15] gives the grid number of rectangles in the x direction and y direction.
/* REal part of z ^ 1/3 */ plot3d(r^.33*cos(th/3),[r,0,1],[th,0,6*%pi], ['grid,12,80],['plot_format,ps], ['transform_xy,polar_to_xy],['view_direction,1,1,1.4], ['colour_z,true])
Here the View_direction indicates the direction from which we take a projection. We actually do this from infinitely far away, but parallel to the line from view_direction to the origin. This is currently only used in 'ps' plot_format, since the other viewers allow interactive rotating of the object.
Another example is a moebius band:
plot3d([cos(x)*(3+y*cos(x/2)), sin(x)*(3+y*cos(x/2)),y*sin(x/2)], [x,-%pi,%pi],[y,-1,1],['grid,50,15]);
or a klein bottle:
plot3d([5*cos(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3.0) - 10.0, -5*sin(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3.0), 5*(-sin(x/2)*cos(y)+cos(x/2)*sin(2*y))], [x,-%pi,%pi],[y,-%pi,%pi],['grid,40,40])
or a torus
plot3d([cos(y)*(10.0+6*cos(x)), sin(y)*(10.0+6*cos(x)), -6*sin(x)], [x,0,2*%pi],[y,0,2*%pi], ['grid,40,40])
We can output to gnplot too:
plot3d(2^(x^2-y^2),[x,-1,1],[y,-2,2],[plot_format,gnuplot])
plot2d(sin(x),[x,-5,5]); plot2d(sec(x),[x,-2,2],[y,-20,20],[nticks,200]);
A point set may be of the form
[x0,y0,x1,y1,x2,y2,...] or [[x0,y0],[x1,y1],....]
A point set may also contain symbols which give labels or other information.
xgraph_curves([pt_set1,pt_set2,pt_set3]);
would graph the three point sets as three curves.
pt_set:append(["NoLines: True","LargePixels: true"], [x0,y0,x1,y1,...])
would make the point set [and subsequent ones], have no lines between points, and to use large pixels. See the man page on xgraph for more options to specify.
pt_set:append([concat("\"","x^2+y")],[x0,y0,x1,y1,...])
would make there be a "label" of "x^2+y" for this particular
point set. The "
at the beginning is what tells
xgraph this is a label.
pt_set:append([concat("TitleText: Sample Data")],[x0,...])
would make the main title of the plot be "Sample Data" instead of "Maxima PLot".
A temporary file `xgraph-out
' is used.
SET_PLOT_OPTION([grid,30,40])
would change the default grid used by plot3d. Note that if the symbol grid has a value, then you should quote it here:
SET_PLOT_OPTION(['grid,30,40])
so that the value will not be substituted.
Draws a curve connecting the points in PTLIST. The latter may be of the form [x0,y0,x1,y1,...] or [[x0,y0],[x1,y1],...] The function JOIN is handy for taking a list of x's and a list of y's and splicing them together. PSDRAW_CURVE simply invokes the more primitive function PSCURVE. Here is the definition:
(defun $psdraw_curve (lis) (p "newpath") ($pscurve lis) (p "stroke"))
?DRAW2D may also be used to produce a list
points1:?draw2d(1/x,[.05,10],.03)
COM will be inserted in the poscript file eg
pscom("4.5 72 mul 5.5 72 mul translate 14 14 scale");