Re: [NTG-context] function machine
Mojca, I've used clip currentpicture to cpath before, then saved the result, draw the grid, draw the axes, then draw the saved clipped picture. But, you're right, I can't use drawdblarrow then. In our classes, the drawdblarrow is important, having the same meaning as the ellipsis in 1, 3, 5, 7, 9, ..., that is, "etc." In the case of a parabola opening upward, the arrow on the right half would indicate that the graph continues opening upward and to the right indefinitely. This is an important distinction from say a line segment that "stops" at one end, especially when asked to determine the domain and range of a function from its graph. The clipping path is a huge convenience for an instructor crafting plots for an exam, activity, or lesson. Otherwise, the instructor would have to calculate the points where the graph leaves the bounding box (less painful if you use Matlab, Maple, or Mathematica, or a graphing calculator), a time consuming task. I am not so concerned about a plot that might lie entirely outside the clipping window. That just requires, as on the graphing calculator, that one adjust the window (different xmin, xmax, xscl, ymin, ymax, and yscl). I just need to be able to clip the plot and retain the part that lies inside the clipping window, then use drawdblarrow on the part that remains. My clip routine won't (cutbefore, reverse, cutbefore) won't work on something like y=sqrt(3-x) for two reasons: 1. A domain problem (easily solved by adjusting the drawfcn command to include two more parameters: beginx, endx. 2. The clip routine is not general enough to handle this situation. So, there's room for improvement if you want to use this routine on irrational, rational, and logarithmic functions. On Dec 28, 2005, at 8:57 AM, Mojca Miklavec wrote: Please, put this example on the wiki (together with some sample images that can be created, with or without some cheating). The community would be greatful for that. Hans, Taco, et al, This is getting pretty close to the limit of my expertise. The good stuff of it is stolen from Metafun and mp-func.mp. Because of the way I handle clipping the path, p:=p cutbefore cpath; p:=reverse p; p:=p cutbefore cpath; this will only work on functions (like lines, quadratics, and polynomials, maybe sinusoids) that both enter and leave the region inside the clipping path. If I understand it properly (that you only want to draw the content inside the square, while the function may be a circle or something lying completely outside the region), you could also use something like clip currentpicture to cpath; although you may have to change the code that draws double arrow then. Mojca ___ ntg-context mailing list ntg-context@ntg.nl http://www.ntg.nl/mailman/listinfo/ntg-context ___ ntg-context mailing list ntg-context@ntg.nl http://www.ntg.nl/mailman/listinfo/ntg-context
Re: [NTG-context] function machine
Please, put this example on the wiki (together with some sample images that can be created, with or without some cheating). The community would be greatful for that. > Hans, Taco, et al, > > This is getting pretty close to the limit of my expertise. The good > stuff of it is stolen from Metafun and mp-func.mp. > > Because of the way I handle clipping the path, > >p:=p cutbefore cpath; >p:=reverse p; >p:=p cutbefore cpath; > > this will only work on functions (like lines, quadratics, and > polynomials, maybe sinusoids) that both enter and leave the region > inside the clipping path. If I understand it properly (that you only want to draw the content inside the square, while the function may be a circle or something lying completely outside the region), you could also use something like clip currentpicture to cpath; although you may have to change the code that draws double arrow then. Mojca ___ ntg-context mailing list ntg-context@ntg.nl http://www.ntg.nl/mailman/listinfo/ntg-context
Re: [NTG-context] function machine
David Arnold wrote: \startMPinclusions ... \stopMPinclusions you can consider putting that code into an environment file easier to maintain Hans ___ ntg-context mailing list ntg-context@ntg.nl http://www.ntg.nl/mailman/listinfo/ntg-context
[NTG-context] function machine
Hans, Taco, et al,
This is getting pretty close to the limit of my expertise. The good
stuff of it is stolen from Metafun and mp-func.mp.
Because of the way I handle clipping the path,
p:=p cutbefore cpath;
p:=reverse p;
p:=p cutbefore cpath;
this will only work on functions (like lines, quadratics, and
polynomials, maybe sinusoids) that both enter and leave the region
inside the clipping path.
I proceed the in the order I do because I want the axes layered atop
the grid and the functions layered atop the grid and axes.
It's actually a pretty cool routine for teachers as it almost works
like a TI83 calculator. Just change xmin, xmax, xscl, ymin, ymax, and
yscl to determine domain and range and tick marks, then adjust the
number of points for a smooth graph, then set the width of the figure
you want. There's an option to label the axes differently from the
usual x and y, if needed.
Finally, thanks to Hans' expertise, the drawfcn routine allows for a
parametric definition of the intended curve.
All you need to do to make another graphic is copy and paste
everything between \startMPpage ... \stopMPpage and adjust the
parameters described above. Now you have a second plot.
You can run texexec with
texexec filename
or
texexec --page=2 filename
if you only want your second graphic. When I compile all, I write an
xml database file (very cool) and use
\usemodule[fig-base]
\usefigurebase[figures/figlibSection1]
in my document. Very cool working arrangement.
Here's some lines from my xml file:
College of the Redwoods Mathematics Departmentorganization>
Intermediate Algebra Text
Chapter 1
Figures for Section 1
section1figs-mpgraph.1
yeqx2
College of the Redwoods Mathematics Department
section1figs-mpgraph.2
yeq2x2
College of the Redwoods Mathematics Department
...
And here's my function machine. I'd love to hear any suggestions for
improvement. Thanks to all who have helped me the last week (Taco has
been especially patient). I've learned a lot.
%output=pdf
\setupcolors[state=start]
\definecolor[gridlines][s=0.7]
\startMPinclusions
color gridlines; gridlines:=\MPcolor{gridlines};
vardef create_grid (expr l,r,h,b,t,v,wid,ht)=
save ux, uy; numeric ux, uy;
(r-l)*ux=wid; (t-b)*uy=ht;
for k=b step v until t:
draw (l*ux,k*uy)--(r*ux,k*uy) withcolor \MPcolor{gridlines};
endfor;
for k=l step h until r:
draw (k*ux,b*uy)--(k*ux,t*uy) withcolor \MPcolor{gridlines};
endfor;
enddef;
vardef create_axes (expr l,r,b,t,wid,ht) (text xlbl,ylbl) =
save ux, uy; numeric ux, uy;
(r-l)*ux=wid; (t-b)*uy=ht;
textextoffset:=3pt;
drawdblarrow (1.05*l*ux,0)--(1.05*r*ux,0);
draw textext.rt(xlbl) shifted (1.05*r*ux,0);
draw textext.bot(decimal r) shifted (r*ux,0);
drawdblarrow (0,1.05*b*uy)--(0,1.05*t*uy);
draw textext.top(ylbl) shifted (0,1.05*t*uy);
draw textext.lft(decimal t) shifted (0,t*uy);
enddef;
vardef drawfcn (expr ind,dep,l,r,b,t,wid,ht,n) text txt =
save x, dx, ux, uy; numeric x, dx, ux, uy;
dx:=(r-l)/n;
(r-l)*ux=wid; (t-b)*uy=ht;
save cpath; path cpath; cpath:=(l,b)--(r,b)--(r,t)--(l,t)--cycle;
save p; path p; hide (x:=l;) p:=(scantokens(ind),scantokens(dep));
for xx:=l step dx until r:
hide (x:=xx;) p:=p--(scantokens(ind),scantokens(dep));
endfor;
hide(x:=r;) p:=p--(scantokens(ind),scantokens(dep));
p:=p cutbefore cpath;
p:=reverse p;
p:=p cutbefore cpath;
p:=p xyscaled (ux,uy);
drawdblarrow p txt;
enddef;
\stopMPinclusions
\starttext
\startMPpage
%initialize window parameters
numeric xmin, xmax, xscl, ymin, ymax, yscl;
xmin:=-10;
xmax:=10;
xscl:=1;
ymin:=-10;
ymax:=10;
yscl:=1;
%initialize number of points
numeric num_points;
num_points:=100;
%initialize dimensions of image
numeric width, height;
width=3in;
height=3in;
%create the grid
create_grid(xmin,xmax,xscl,ymin,ymax,yscl,width,height);
%create the axes
create_axes(xmin,xmax,ymin,ymax,width,height)("$x$")("$y$");
%draw the function
%drawf(xmin,xmax,ymin,ymax,width,height,num_points);
drawfcn("x","x*x",xmin,xmax,ymin,ymax,width,height,100) ;
%to add another function with extra formatting, try:
% drawfcn("x","(x+1)*(x+1)",xmin,xmax,ymin,ymax,width,height,100)
% withpen pencircle scaled 2pt dashed evenly withcolor red;
\stopMPpage
\stoptext
%%% Local Variables:
%%% mode: conTeXt-en
%%% End:
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