+
+/*
+ * NB: This algorithm is not optimal in terms of space complexity. The entire
+ * integer lattice of noise points could be done as 2 lines instead, and for 3D,
+ * 2 lines + 2 planes.
+ * However, this would require the noise calls to be interposed with the
+ * interpolation loops, which may trash the icache, leading to lower overall
+ * performance.
+ * Another optimization that could save half as many noise calls is to carry over
+ * values from the previous noise lattice as midpoints in the new lattice for the
+ * next octave.
+ */
+#define idx(x, y) ((y) * nlx + (x))
+void Noise::gradientMap2D(float x, float y, float step_x, float step_y, int seed) {
+ float v00, v01, v10, v11, u, v, orig_u;
+ int index, i, j, x0, y0, noisex, noisey;
+ int nlx, nly;
+
+ x0 = floor(x);
+ y0 = floor(y);
+ u = x - (float)x0;
+ v = y - (float)y0;
+ orig_u = u;
+
+ //calculate noise point lattice
+ nlx = (int)(u + sx * step_x) + 2;
+ nly = (int)(v + sy * step_y) + 2;
+ index = 0;
+ for (j = 0; j != nly; j++)
+ for (i = 0; i != nlx; i++)
+ noisebuf[index++] = noise2d(x0 + i, y0 + j, seed);
+
+ //calculate interpolations
+ index = 0;
+ noisey = 0;
+ for (j = 0; j != sy; j++) {
+ v00 = noisebuf[idx(0, noisey)];
+ v10 = noisebuf[idx(1, noisey)];
+ v01 = noisebuf[idx(0, noisey + 1)];
+ v11 = noisebuf[idx(1, noisey + 1)];
+
+ u = orig_u;
+ noisex = 0;
+ for (i = 0; i != sx; i++) {
+ buf[index++] = biLinearInterpolation(v00, v10, v01, v11, u, v);
+ u += step_x;
+ if (u >= 1.0) {
+ u -= 1.0;
+ noisex++;
+ v00 = v10;
+ v01 = v11;
+ v10 = noisebuf[idx(noisex + 1, noisey)];
+ v11 = noisebuf[idx(noisex + 1, noisey + 1)];
+ }
+ }
+
+ v += step_y;
+ if (v >= 1.0) {
+ v -= 1.0;
+ noisey++;
+ }
+ }
+}
+#undef idx
+
+
+#define idx(x, y, z) ((z) * nly * nlx + (y) * nlx + (x))
+void Noise::gradientMap3D(float x, float y, float z,
+ float step_x, float step_y, float step_z,
+ int seed) {
+ float v000, v010, v100, v110;
+ float v001, v011, v101, v111;
+ float u, v, w, orig_u, orig_v;
+ int index, i, j, k, x0, y0, z0, noisex, noisey, noisez;
+ int nlx, nly, nlz;
+
+ x0 = floor(x);
+ y0 = floor(y);
+ z0 = floor(z);
+ u = x - (float)x0;
+ v = y - (float)y0;
+ w = z - (float)z0;
+ orig_u = u;
+ orig_v = v;
+
+ //calculate noise point lattice
+ nlx = (int)(u + sx * step_x) + 2;
+ nly = (int)(v + sy * step_y) + 2;
+ nlz = (int)(w + sz * step_z) + 2;
+ index = 0;
+ for (k = 0; k != nlz; k++)
+ for (j = 0; j != nly; j++)
+ for (i = 0; i != nlx; i++)
+ noisebuf[index++] = noise3d(x0 + i, y0 + j, z0 + k, seed);
+
+ //calculate interpolations
+ index = 0;
+ noisey = 0;
+ noisez = 0;
+ for (k = 0; k != sz; k++) {
+ v = orig_v;
+ noisey = 0;
+ for (j = 0; j != sy; j++) {
+ v000 = noisebuf[idx(0, noisey, noisez)];
+ v100 = noisebuf[idx(1, noisey, noisez)];
+ v010 = noisebuf[idx(0, noisey + 1, noisez)];
+ v110 = noisebuf[idx(1, noisey + 1, noisez)];
+ v001 = noisebuf[idx(0, noisey, noisez + 1)];
+ v101 = noisebuf[idx(1, noisey, noisez + 1)];
+ v011 = noisebuf[idx(0, noisey + 1, noisez + 1)];
+ v111 = noisebuf[idx(1, noisey + 1, noisez + 1)];
+
+ u = orig_u;
+ noisex = 0;
+ for (i = 0; i != sx; i++) {
+ buf[index++] = triLinearInterpolation(
+ v000, v100, v010, v110,
+ v001, v101, v011, v111,
+ u, v, w);
+ u += step_x;
+ if (u >= 1.0) {
+ u -= 1.0;
+ noisex++;
+ v000 = v100;
+ v010 = v110;
+ v100 = noisebuf[idx(noisex + 1, noisey, noisez)];
+ v110 = noisebuf[idx(noisex + 1, noisey + 1, noisez)];
+ v001 = v101;
+ v011 = v111;
+ v101 = noisebuf[idx(noisex + 1, noisey, noisez + 1)];
+ v111 = noisebuf[idx(noisex + 1, noisey + 1, noisez + 1)];
+ }
+ }
+
+ v += step_y;
+ if (v >= 1.0) {
+ v -= 1.0;
+ noisey++;
+ }
+ }
+
+ w += step_z;
+ if (w >= 1.0) {
+ w -= 1.0;
+ noisez++;
+ }
+ }