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Barycentric coordinates

I'd like to draw a triangle and mark a point P
in it with barycentric coordinates (3/4,1/6,1/12).
How to do this with Maple?

Best regards,
Rainer Rosenthal
r.rosenthal@web.de
0
Rainer
4/16/2006 9:48:36 PM
comp.soft-sys.math.maple 4344 articles. 2 followers. Post Follow

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Perhaps this will do for you.
> restart:
> with(plots):
> P[1],P[2],P[3]:=[3,5],[-1,4],[7,-3]:
> B:=[3/4,1/6,1/12]:
> C:=add(B[i]*P[i],i=1..3):
>
> T:=plot([P[1],P[2],P[3],P[1]], style=line, color=red, scaling = constrained,axes=normal):
> Pt:=plot([C], style=point,symbol=circle,color=blue):
> Text:=textplot([op(C+[-.2,.2]),convert(B,string)],align={ABOVE,RIGHT}):
> 
> display([Text,T,Pt]);

0
Edwin
4/17/2006 2:37:12 AM
Edwin Clark schrieb:
> Perhaps this will do for you.

Many thanks, it really did! I added the normalization
and was able to display the picture I wanted:
Point [17,3,8] in an equilateral triangle.

My new version including three Easter-eggs as a
little present for you:

  restart:
  barycentric := proc(tri,raw)
   sum(evalf(tri[j])*raw[j]/sum(raw[i],i=1..3),j=1..3)
  end proc:
  with(plots):
  P[1],P[2],P[3]:=[0,0],[1,0],[1/2,sqrt(3)/2]:
  B := [17,3,8]:
  C := barycentric(P,B):
  T:=plot([P[1],P[2],P[3],P[1]],
    style=line,color=red,scaling=constrained,axes=normal):
  Pt:=plot([C], style=point,symbol=circle,color=blue):
  Text:=textplot([op(C+[0.02,0.02]),convert(B,string)],align={ABOVE,RIGHT}):
  display([Text,T,Pt]);
  #
  # Thanks to Edwin Clark --- some Easter-eggs
  #
  p1 := plot([sin(x),x,x=0..2*Pi], color=red, axes=normal):
  p2 := plot([sin(x)*0.7,x,x=0..2*Pi], color=blue, axes=normal):
  p3 := plot([sin(x)*0.2,x,x=Pi..2*Pi], color=green, axes=normal):
  q1 := changecoords(p1, polar): q2 := changecoords(p2, polar):
  q3 := changecoords(p3, polar):
  display([q1,q2,q3]);


Best regards,
Rainer Rosenthal
r.rosenthal@web.de
0
Rainer
4/17/2006 8:50:06 AM
Reply:

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