...
> Now the next trick will be to draw an arbitrary curve on said
> surface.
...


See my code below for a way to draw simple functions on an
uv-mapped surface.

It shouldn't be very difficult to add a coordinate grid to
the surface pigment too.


Tor Olav


// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

#declare LW = 0.01; // Line Width

#declare SelFn =
  function(A) {
    select(A, select(A + LW/2, 0, 1), select(A - LW/2, 1, 0))
  }

#declare OneLineFn = function(u, v) { SelFn(v - u) }

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

#declare DrawFn =
  function(u) { 0.5 + 0.25*sin(4*pi*u) + 0.25*cos(5*pi*u) }

//#declare DrawFn = function(u) { 0.5 + 0.5*sin(2*pi*u) }


bicubic_patch {
  type 0
  flatness 0.01
  u_steps 4
  v_steps 4

  <0, 0, 0>, <1, 0, 0>, <2, 0, 0>, <3, 0, 0>,
  <0, 1, 0>, <1, 1, 0>, <2, 1, 0>, <3, 1, 0>,
  <0, 2, 0>, <1, 2, 0>, <2, 2, 0>, <3, 2, 0>,
  <0, 3, 0>, <1, 3, 0>, <2, 3, 0>, <3, 3, 0>

  uv_mapping
  texture {
    pigment {
      function { OneLineFn(DrawFn(u), v) }
      color_map {
        [ 0 color rgb <1, 1, 1> ]
        [ 1 color rgb <1, 0, 0> ]
      }
    }
  }
}

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

camera {
  location <1.5, 1.5, -4>
  look_at <1.5, 1.5, 0>
}


light_source {
  <1, 1, -3>*100
  color rgb <1, 1, 1>
  shadowless
}

background { color blue 0.5 }

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

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