// bug: won't work: field#1(2)[] F = bspln3 ⊛ image("../data/ddro.nrrd") - isoval;
// field#2(2)[] F = bspln3 ⊛ image("../data/ddro.nrrd") - isoval;


/*
 $DDRO_HOME/branches/vis12/bin/diderotc --exec bug027.diderot \
 && ./bug027 \
 && unu jhisto -i x.nrrd -b 800 800 -min 0 0 -max 1 1 \
     | unu 2op neq - 0 \
     | unu quantize -b 8 -o bug027.png
*/

input real isoval = 0.5;
/* BUG: it looks like the type promotion from field#2 to field#1
  doesn't work with subtracting a constant
error converting OffsetField
uncaught exception Fail [Fail: bogus operator OffsetField]
  raised at common/phase-timer.sml:76.50-76.52
  raised at common/phase-timer.sml:76.50-76.52
  raised at high-to-mid/high-to-mid.sml:297.85-297.87
  raised at high-to-mid/high-to-mid.sml:294.32-294.78
*/
field#1(2)[] F = bspln3 ⊛ image("../data/ddro.nrrd") - isoval;

int grid = 150;
int stepsMax = 10;
real epsilon = 0.000001;

strand RootFind(vec2 x0) {
   output vec2 x = x0;
   int steps = 0;
   update {
      // Stop if we're no longer inside or taken too many steps.
      if (!inside(x, F) || steps > stepsMax)
         die;
      vec2 grad = ∇F(x);
      // subsequent expressions are undefined if |∇F| is zero
      if (|grad| == 0.0)
         die;
      // the Newton-Raphson step
      vec2 delta = normalize(grad) * F(x)/|grad|;
      // we've converged if the change is small enough
      if (|delta| < epsilon)
         stabilize;
      x -= delta;
      steps += 1;
   }
}

initially { RootFind([lerp(0, 1, -0.5, ui, grid-0.5),
                      lerp(0, 1, -0.5, vi, grid-0.5)])
            | vi in 0..(grid-1), ui in 0..(grid-1) };

/*
 different in 3D:
 vec2 -> vec3
 field#1(2)[] F -> field#1(3)[] F
 initially over 3D grid
*/

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/*
 different in 3D:
 vec2 -&gt; vec3
 field#1(2)[] F -&gt; field#1(3)[] F
 initially over 3D grid
*/</div>
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