input real isoval = 0.5;
input real thick = 0.8;
field#2(3)[3,3] V = bspln3 ⊛ image("tball.nrrd");
field#0(3)[3,3,3] G=∇⊗V;
field#2(3)[3] hackRGB = bspln3 ⊛ image("const-curl3d.nrrd");
function vec3 color(vec3 x) = hackRGB(x);
vec3 cutVec = [-1,-0.03,0.02];
real cutPos = -1.5;
real refStep = 1;
input vec3 camEye = [440.499, 66.673, 175.265];
input vec3 camAt = [69.6939, 103.067, 41.4651];
input vec3 camUp = [-0.0808311, 0.0976636, 0.991932];
input real camNearAtRel = -90;
input real camFarAtRel = 90;
input real camFOV = 17;
input int iresU = 520;
input int iresV = 370;
input real phongKa = 0.3;
input real phongKd = 0.7;
input real rayStep = 0.4;
input vec3 lightVsp = [-2.0, -2.5, -8.0];
real camDist = |camAt - camEye|;
real camNear = camNearAtRel + camDist;
real camFar = camFarAtRel + camDist;
vec3 camN = normalize(camAt - camEye);  // away from eye
vec3 camU = normalize(camN × camUp);    // right
vec3 camV = camN × camU;                // down
real camVmax = tan(camFOV*π/360)*camDist;
real camUmax = camVmax*iresU/iresV;
vec3 light = transpose([camU,camV,camN])•normalize(lightVsp);

function real alpha(real v, real g) = 1.0 if (v > 0) else clamp(0, 1, 1.3*(1 - |v|/(g*thick)));

strand raycast(int ui, int vi) {
  real rayU = lerp(-camUmax, camUmax, -0.5, ui, iresU-0.5);
  real rayV = lerp(-camVmax, camVmax, -0.5, vi, iresV-0.5);
  real rayN = camNear;
  vec3 rayVec = (camDist*camN + rayU*camU + rayV*camV)/camDist;
  real transp = 1;
  vec3 rgb = [0, 0, 0];
  output vec4 rgba = [0, 0, 0, 0];

  update {
    vec3 x = camEye + rayN*rayVec;
    if (inside(x,V) && (x - camAt)•normalize(cutVec) > cutPos) {
      real val = 0;
      vec3 grad = [0,0,0];
      real m=|V(x)|;
      tensor[3,3,3] g=G(x);
      tensor[3] t1=(1/2)*(V(x):g+g:V(x))/m;
    vec3 t2=[g[0,0,0]+g[0,1,1]+g[0,2,2],g[1,0,0]+g[1,1,1]+g[1,2,2],g[2,0,0]+g[2,1,1]+g[2,2,2]];
    tensor [3,3] E = V(x) - trace(V(x))*identity[3]/3;
    tensor[3,3,3] t3= g-t2⊗identity[3]/3;
    real t4=|E|;
    tensor [3] t5=(1/2)*(t3:E +E:t3)/(E:E);
    val=sqrt(3.0/2.0)*t4/m - isoval;
    vec3 t6 =m*t5;
    vec3 t7 = t4*t1;
    grad =sqrt(3.0/2.0)*(t6- t7)/(m*m);
      real a = alpha(val, |grad|);
      if (a > 0) {
        a = 1 - pow(1-a, rayStep);
        real depth = lerp(1.1, 0.8, camNear, rayN, camFar);
        real shade = max(0, normalize(grad)•light);
        vec3 thisrgb = (phongKa + phongKd*shade)*color(x);
        if ((x - camAt)•normalize(cutVec) < cutPos + 1.1*rayStep) {
          thisrgb = phongKd*color(x);
        }
        rgb += transp*a*depth*thisrgb;
        transp *= 1 - a;
      }
    }
    if (transp < 0.01) {  // early ray termination
      transp = 0;
      stabilize;
    }
    if (rayN > camFar) {
      stabilize;
    }
    rayN = rayN + rayStep;
  }
  stabilize {
    real a = 1-transp;
    if (a > 0) rgba = [rgb[0]/a, rgb[1]/a, rgb[2]/a, a];
  }
}
initially [ raycast(ui, vi) | vi in 0..iresV-1, ui in 0..iresU-1 ];