test/experimental/quadrilateral.py

   1 # this example is adapted from a MetaPost example by Hans Hagen
   2
   3 import sys; sys.path.insert(0, "../..")
   4 from pyx import *
   5 from solve import scalar, vector, solver
   6
   7 # define the inner quadrilateral
   8 p = vector([0, 0])
   9 q = vector([2, 5])
  10 r = vector([8, 6])
  11 s = vector([5, -1])
  12
  13 # some points of the outer squares are equal to points of the inner quadrilateral
  14 z11 = p
  15 z12 = q
  16 z21 = q
  17 z22 = r
  18 z31 = r
  19 z32 = s
  20 z41 = s
  21 z42 = p
  22
  23 # complete the definition of the outer squares
  24 z1diff = z12 - z11
  25 z2diff = z22 - z21
  26 z3diff = z32 - z31
  27 z4diff = z42 - z41
  28
  29 z13 = vector([z12.x-z1diff.y, z12.y+z1diff.x])
  30 z14 = vector([z11.x-z1diff.y, z11.y+z1diff.x])
  31 z23 = vector([z22.x-z2diff.y, z22.y+z2diff.x])
  32 z24 = vector([z21.x-z2diff.y, z21.y+z2diff.x])
  33 z33 = vector([z32.x-z3diff.y, z32.y+z3diff.x])
  34 z34 = vector([z31.x-z3diff.y, z31.y+z3diff.x])
  35 z43 = vector([z42.x-z4diff.y, z42.y+z4diff.x])
  36 z44 = vector([z41.x-z4diff.y, z41.y+z4diff.x])
  37
  38 # define the centers of the outer squares
  39 z1 = 0.5*(z11 + z13)
  40 z2 = 0.5*(z21 + z23)
  41 z3 = 0.5*(z31 + z33)
  42 z4 = 0.5*(z41 + z43)
  43
  44 # define the crossing point by some equations
  45 z0 = vector(2)
  46 solver.eq(z0, z1 + scalar()*(z3-z1))
  47 solver.eq(z0, z2 + scalar()*(z4-z2))
  48
  49 # finally draw the result
  50
  51 def line(p1, p2):
  52     return path.line(float(p1.x), float(p1.y), float(p2.x), float(p2.y))
  53
  54 def square(p1, p2, p3, p4):
  55     return path.path(path.moveto(float(p1.x), float(p1.y)),
  56                      path.lineto(float(p2.x), float(p2.y)),
  57                      path.lineto(float(p3.x), float(p3.y)),
  58                      path.lineto(float(p4.x), float(p4.y)),
  59                      path.closepath())
  60
  61 c = canvas.canvas()
  62
  63 c.stroke(square(z11, z12, z13, z14))
  64 c.stroke(square(z21, z22, z23, z24))
  65 c.stroke(square(z31, z32, z33, z34))
  66 c.stroke(square(z41, z42, z43, z44))
  67
  68 c.stroke(line(z11, z13), [style.linestyle.dashed, style.linewidth.Thin])
  69 c.stroke(line(z12, z14), [style.linestyle.dashed, style.linewidth.Thin])
  70 c.stroke(line(z21, z23), [style.linestyle.dashed, style.linewidth.Thin])
  71 c.stroke(line(z22, z24), [style.linestyle.dashed, style.linewidth.Thin])
  72 c.stroke(line(z31, z33), [style.linestyle.dashed, style.linewidth.Thin])
  73 c.stroke(line(z32, z34), [style.linestyle.dashed, style.linewidth.Thin])
  74 c.stroke(line(z41, z43), [style.linestyle.dashed, style.linewidth.Thin])
  75 c.stroke(line(z42, z44), [style.linestyle.dashed, style.linewidth.Thin])
  76
  77 c.stroke(square(p, q, r, s), [color.rgb.red, style.linewidth.THick])
  78
  79 c.stroke(line(z1, z3), [color.rgb.green])
  80 c.stroke(line(z2, z4), [color.rgb.green])
  81
  82 c.fill(path.circle(float(z0.x), float(z0.y), 0.1), [color.rgb.blue])
  83
  84 c.writeEPSfile("quadrilateral")
  85