Workbench: Use non-negative lighting evaluation

This makes the lighting a bit more diffuse but don't produce negative
values.

Add a bias of 1.5f to make the lighting a bit more directionnal.

The implementation is based on:
https://github.com/kayru/Probulator/blob/master/Source/Probulator/SphericalHarmonics.h#L136
which is derived from:
http://www.geomerics.com/wp-content/uploads/2015/08/CEDEC_Geomerics_ReconstructingDiffuseLighting1.pdf

The shader implementation is optimized and has the same runtime cost
as previous method:
* no sh eval : 0.13ms
* prev sh eval : 0.14ms
* new sh eval : 0.22ms
* new sh eval opti : 0.14ms

1 files changed, 45 insertions, 0 deletions

diff --git a/source/blender/draw/engines/workbench/workbench_studiolight.c b/source/blender/draw/engines/workbench/workbench_studiolight.c
index c852d7abb90..65732b52471 100644
--- a/source/blender/draw/engines/workbench/workbench_studiolight.c
+++ b/source/blender/draw/engines/workbench/workbench_studiolight.c
@@ -36,10 +36,55 @@ void studiolight_update_world(StudioLight *sl, WORKBENCH_UBO_World *wd)
 {
 	BKE_studiolight_ensure_flag(sl, STUDIOLIGHT_SPHERICAL_HARMONICS_COEFFICIENTS_CALCULATED);
 
+#if STUDIOLIGHT_SH_BANDS == 2
+	/* Use Geomerics non-linear SH. */
+	mul_v3_v3fl(wd->spherical_harmonics_coefs[0], sl->spherical_harmonics_coefs[0], M_1_PI);
+	/* Swizzle to make shader code simpler. */
+	for (int i = 0; i < 3; ++i) {
+		copy_v3_fl3(wd->spherical_harmonics_coefs[i+1], -sl->spherical_harmonics_coefs[3][i],
+		                                                 sl->spherical_harmonics_coefs[2][i],
+		                                                -sl->spherical_harmonics_coefs[1][i]);
+		mul_v3_fl(wd->spherical_harmonics_coefs[i+1], M_1_PI * 1.5f); /* 1.5f is to improve the contrast a bit. */
+	}
+
+	/* Precompute as much as we can. See shader code for derivation. */
+	float len_r1[3], lr1_r0[3], p[3], a[3];
+	for (int i = 0; i < 3; ++i) {
+		mul_v3_fl(wd->spherical_harmonics_coefs[i+1], 0.5f);
+		len_r1[i] = len_v3(wd->spherical_harmonics_coefs[i+1]);
+		mul_v3_fl(wd->spherical_harmonics_coefs[i+1], 1.0f / len_r1[i]);
+	}
+	/* lr1_r0 = lenR1 / R0; */
+	copy_v3_v3(lr1_r0, wd->spherical_harmonics_coefs[0]);
+	invert_v3(lr1_r0);
+	mul_v3_v3(lr1_r0, len_r1);
+	/* p = 1.0 + 2.0 * lr1_r0; */
+	copy_v3_v3(p, lr1_r0);
+	mul_v3_fl(p, 2.0f);
+	add_v3_fl(p, 1.0f);
+	/* a = (1.0 - lr1_r0) / (1.0 + lr1_r0); */
+	copy_v3_v3(a, lr1_r0);
+	add_v3_fl(a, 1.0f);
+	invert_v3(a);
+	negate_v3(lr1_r0);
+	add_v3_fl(lr1_r0, 1.0f);
+	mul_v3_v3(a, lr1_r0);
+	/* sh_coefs[4] = p; */
+	copy_v3_v3(wd->spherical_harmonics_coefs[4], p);
+	/* sh_coefs[5] = R0 * a; */
+	mul_v3_v3v3(wd->spherical_harmonics_coefs[5], wd->spherical_harmonics_coefs[0], a);
+	/* sh_coefs[0] = R0 * (1.0 - a) * (p + 1.0); */
+	negate_v3(a);
+	add_v3_fl(a, 1.0f);
+	add_v3_fl(p, 1.0f);
+	mul_v3_v3(a, p);
+	mul_v3_v3(wd->spherical_harmonics_coefs[0], a);
+#else
 	for (int i = 0; i < STUDIOLIGHT_SH_EFFECTIVE_COEFS_LEN; i++) {
 		/* Can't memcpy because of alignment */
 		copy_v3_v3(wd->spherical_harmonics_coefs[i], sl->spherical_harmonics_coefs[i]);
 	}
+#endif
 }
 
 static void compute_parallel_lines_nor_and_dist(const float v1[2], const float v2[2], const float v3[2], float r_line[2])