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This section shows how to draw functions expressed in non cartesian coordinates.

Two functions defined in polar coordinates.

draw2d(terminal   = eps,
       grid       = true,
       nticks     = 300,
       line_type  = solid,
       key        = "Rhodonea curve",
         polar(5*sin(10*theta),theta,0,%pi*2),
       line_type  = dots,
       key        = "Fermat spiral",  /* don't write "Fermat's" !! */
          polar(sqrt(theta),theta,0,10*%pi),
       key        = "",       /* we avoid two equal entries in legend */
          polar(-sqrt(theta),theta,0,10*%pi) )$

Option grid = true makes reference to a rectangular grid on the plane. If we are plotting a function in polar coordinates, maybe we prefere a polar grid. In this case, option user_preamble will be of great help.

draw2d(terminal      = png,
       pic_width     = 400,
       pic_height    = 400,
       file_name     = "polargrid",
       user_preamble = "set grid polar",
       nticks        = 200,
       xrange        = [-5,5],
       yrange        = [-5,5],
       color         = red,
       line_width    = 3,
       title         = "Hyperbolic Spiral",
         polar(10/theta,theta,1,10*%pi) )$

---

Function defined in spherical coordinates. In this example, variable a is the azimuth and variable z is the zenith. The expression is for the radius.

draw3d(
  surface_hide = true,
  axis_3d      = false,
  color        = salmon,
  spherical(sin(z)*cos(2*a),a,0,2*%pi,z,0,%pi))$

---

A geometrical model for genus Nautilus.

draw3d(
  color        = green,
  surface_hide = true,
  axis_3d      = false,
  xtics        = none,
  ytics        = none,
  ztics        = none,
  spherical(a+z,a,0,3*%pi,z,0,%pi))$

---

Three geometric objects defined in cylindrical coordinates.

draw3d(
  surface_hide = true,
  axis_3d      = false,
  xtics        = none,
  ytics        = none,
  ztics        = none,
  color        = blue,
  cylindrical(z,z,-2,2,a,0,2*%pi), /*cone*/
  color        = brown,
  cylindrical(3,z,-2,2,az,0,%pi),  /*cylinder*/
  color        = green,
  cylindrical(sqrt(25-z^2),z,-5,5,a,0,%pi) /*sphere*/ )$

---

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