/*

../../../bin/diderotc giso3d.diderot \
&& ./giso3d \
&& unu crop -i giso3d.txt -min 0 0 -max 1 M | \
   unu jhisto -b 600 600 -min -1.2 -1.2 -max 1.2 1.2 -t float | \
   unu 1op log1p | \
   unu quantize -b 8 -o giso3d.png \
&& open giso3d.png

*/

field#4(3)[] V= c4hexic ⊛ load("parab0.nrrd");

field#3(3)[3] N = ∇V/|∇V|;
//field#3(3)[3,3] P = identity[3] - N⊗N;
field#2(3)[3,3] P = identity[3] - N⊗N;
field#2(3)[3,3] H = ∇⊗∇V;
field#2(3)[3,3] G = -(P•H•P)/|∇V|; // HEY why is field#3 allowed? should want field#2

// compilation stalls out with either of these
field#2(3)[] F = trace(G) - -3;
//field#2(3)[] F = G:G - 9;

// (to try later after this is fixed: isosurfaces of flowline curvature)

int grid = 30;
int stepsMax = 10;
real epsilon = 0.000001;

strand RootFind(real xi,real xj, real xk) {
   output vec3 x = [xi,xj,xk];
   int steps = 0;
   update {
      // Stop if we're no longer inside or taken too many steps.
      if (!inside(x, V) || steps > stepsMax)
         die;
      // subsequent expressions are undefined if |∇F| is zero
      if (|∇F(x)| == 0.0)
         die;
      // the Newton-Raphson step
      vec3 delta = normalize(∇F(x)) * F(x)/|∇F(x)|;
      // we've converged if the change is small enough
      if (|delta| < epsilon)
         stabilize;
      x -= delta;
      steps += 1;
   }
}

initially { RootFind(lerp(-2, 2, -0.5, ui, grid-0.5),
                     lerp(-2, 2, -0.5, vi, grid-0.5),
                     lerp(-2, 2, -0.5, wi, grid-0.5))
            | wi in 0..(grid-1), vi in 0..(grid-1), ui in 0..(grid-1) };