// TODO: implement adaptive supersampling
RGBColour World::colourForPixelAt(int i, int j) {
double d = viewport.getViewingDistance();
if (ss_level == 1) {
// no super-sampling
double uValue = viewport.uAmount(i, 1, 0, false);
double vValue = viewport.vAmount(j, 1, 0, false);
vec3 direction = wAxis.scaled(-d) + uAxis.scaled(uValue) + vAxis.scaled(vValue);
Ray theRay(cameraPosition, direction);
return RGBColour(traceRay(theRay, 0.0, 0));
}
// 0.01 => x16, 1.2 => x64
double thresholds[2] = {0.01, 1.2};
double var = 0.0;
int lvl_log = 2;
RGBVec pixelColour;
while (lvl_log <= ss_level) {
pixelColour = RGBVec(0.0,0.0,0.0);
int lvl = int_pow(2, lvl_log - 1);
double scale_factor = 1.0 / static_cast<double>(lvl*lvl);
vec3 sum_x_sq(0.0,0.0,0.0);
for (int a = 0; a < lvl; a++) {
for (int b = 0; b < lvl; b++) {
double uValue = viewport.uAmount(i, ss_level, a, lvl_log > 2);
double vValue = viewport.vAmount(j, ss_level, b, lvl_log > 2);
vec3 direction = wAxis.scaled(-d) + uAxis.scaled(uValue) + vAxis.scaled(vValue);
Ray theRay(cameraPosition, direction);
RGBVec sample = traceRay(theRay, 0.0, 0).scaled(scale_factor);
pixelColour += sample;
if (ss_level > 2) sum_x_sq += sample.getVector().pointwise(sample.getVector());
}
}
if (lvl_log == 2 && ss_level > 2) {
vec3 varvec = sum_x_sq.scaled(scale_factor) - pixelColour.getVector().pointwise(pixelColour.getVector());
var = varvec.magnitude();
if (i % 100 == 0 && j % 100 == 0) std::cout << "var: " << var << std::endl;
}
if (var < thresholds[lvl_log - 2] || lvl_log == ss_level) break;
lvl_log++;
}
if (lvl_log == 2) renderStats.ss_x4++;
else if (lvl_log == 3) renderStats.ss_x16++;
else if (lvl_log == 4) renderStats.ss_x64++;
return RGBColour(pixelColour);
}
void fill_dp_matrix(const std::vector<double> & x,
std::vector< std::vector< double > > & S,
std::vector< std::vector< size_t > > & J)
/*
x: One dimension vector to be clustered, must be sorted (in any order).
S: K x N matrix. S[k][i] is the sum of squares of the distance from
each x[i] to its cluster mean when there are exactly x[i] is the
last point in cluster k
J: K x N backtrack matrix
NOTE: All vector indices in this program start at position 0
*/
{
const int K = S.size();
const int N = S[0].size();
std::vector<double> sum_x(N), sum_x_sq(N);
double shift = x[N/2]; // median. used to shift the values of x to
// improve numerical stability
for(int i = 0; i < N; ++i) {
if(i == 0) {
sum_x[0] = x[0] - shift;
sum_x_sq[0] = (x[0] - shift) * (x[0] - shift);
} else {
sum_x[i] = sum_x[i-1] + x[i] - shift;
sum_x_sq[i] = sum_x_sq[i-1] + (x[i] - shift) * (x[i] - shift);
}
// Initialize for k = 0
S[0][i] = ssq(0, i, sum_x, sum_x_sq);
J[0][i] = 0;
}
for(int k = 1; k < K; ++k) {
int imin;
if(k < K - 1) {
imin = std::max((size_t)1, (size_t)k);
} else {
// No need to compute S[K-1][0] ... S[K-1][N-2]
imin = N-1;
}
#ifdef DEBUG
std::cout << std::endl << "k=" << k << ":";
#endif
fill_row_k(imin, N-1, k, S, J, sum_x, sum_x_sq);
}
}
