// derivs3
//
// for debugging transforms of derivatives from index to world, in 3D.
//
// Can output image of errors in reconstructed values, or reconstructed
// gradients, according to which of (1), (2), (3) is uncommented below.
// In all cases, output is processed with:
//
// unu reshape -i mip.txt -s 3 300 300 | unu quantize -b 8 -min 0 -max 1 -o derivs2.png
//
// This should produce an *ALL BLACK IMAGE* (modulo a few near-black
// pixels due to numerical precision issues)

// F: full isotropic resolution
image(3)[] Fimg = image ("../data/parab/parab3-150.nrrd");
field#1(3)[] F0 = Fimg ⊛ ctmr;
field#2(3)[] F = Fimg ⊛ bspln3;

// FX: one fifth as many samples along X
image(3)[] FXimg = image ("../data/parab/parab3-x30.nrrd");
field#1(3)[] F0X = FXimg ⊛ ctmr;
field#2(3)[] FX = FXimg ⊛ bspln3;

// FY: one fifth as many samples along Y
image(3)[] FYimg = image ("../data/parab/parab3-y30.nrrd");
field#1(3)[] F0Y = FYimg ⊛ ctmr;
field#2(3)[] FY = FYimg ⊛ bspln3;

// FZ: one fifth as many samples along Z
image(3)[] FZimg = image ("../data/parab/parab3-z30.nrrd");
field#1(3)[] F0Z = FZimg ⊛ ctmr;
field#2(3)[] FZ = FZimg ⊛ bspln3;

int imgSize = 300;

strand sample (int xi, int yi) {
    real xx = lerp(-50.0, 50.0, 0.0, real(xi), real(imgSize-1));
    real yy = lerp(-50.0, 50.0, 0.0, real(yi), real(imgSize-1));
    real zz = 25.0;
    vec3 p = [xx,yy,zz];
    real f = xx^2 + yy^2 + zz^2;      // analytic parabola function
    vec3 g = [2.0*xx,2.0*yy,2.0*zz];  // analytic gradient
    tensor[3,3] h = [[2.0,0.0,0.0],   // analytic hessian
                     [0.0,2.0,0.0],
                     [0.0,0.0,2.0]];
    output vec3 val = [0.0,0.0,0.0];
    tensor[3,3] mh = zeros[3,3];
    update {

        // Uncomment one of the following:
    
        // (1) These are the errors in the values
        // This works fine; here as a sanity check
        // val = [|F0X(p)-f|, |F0Y(p)-f|, |F0Z(p)-f|];

        // (2) These are magnitudes of the errors in the gradients
        //val = [|∇FX(p)-g|, |∇FY(p)-g|, |∇FZ(p)-g|];

        // (3) Magnitudes of errors in Hessians
        val = [|∇(∇FX)(p)-h|, |∇(∇FY)(p)-h|, |∇(∇FZ)(p)-h|]/100.0;

        stabilize;
    }
}

initially [ sample(xi, yi) | yi in 0..(imgSize-1), xi in 0..(imgSize-1) ];