Curvalicious is a fast (no raytracing) screen-space curvature OSL shader. It outputs various maps related to curvature, edge detection and concave / convex faces.
It is implemented using Vergne et al. 2009 with additional processes to improve detection at silhouette and for invalid samples (samples perpendicular to camera). These additions make the detection much more stable at different viewing angles.
A red/blue map. Red curves are concave, blue curves are convex, black denotes little curvature.
Same as curvature map, but in grayscale. Ignores concave / convex differentiation.
A typical edge detect algorithm, ran using the screen-space curvature extracted at previous stages.
Marks concave triangles in white (convex in black).
- Doesn't deal well with hard edges / flat surfaces.
- Currently unsupported in Arnold.
- The shader use OSL derivative functionality (
Dx,Dy,filterwidth), which isn't supported in Arnold currently.
- The shader use OSL derivative functionality (
The Vergne et al. technique includes silhouettes as extra curvature. This biases the curvature detection and leads to inconsistent curvature detection at different viewing angles. To correct this, we multiple the gradient (gx, gy) by a correction factor. We use the absolute value of camera space Normal z. Nz is equivalent to the dot product of our current sample with the camera. By doing so, we effectively "flatten" the 3d mesh in screen-space, which allows us to extract its local height information without silhouette bias. The gradient is also normalized to pixel size, to scale with camera distance.
The algorithm cannot divide by zero. When Normal z is below an epsilon threshold, we assign Nz = epsilon. Doing so, and using the new value throughout the evaluation, fixes visual errors for invalid samples (very bright pixels). Without this correction, the edge detection will identify lines at neighboring samples of invalid Nz, which causes visual artifacting. We cannot simply set invalid samples to 0, or use diverging if statements due to Dx and how it works on GPUs. By re-interpreting the below epsilon Nz as epsilon, we create "incorrect" / approximated samples, but this fixes the visual problems.
Romain Vergne, Romain Pacanowski, Pascal Barla, Xavier Granier, Christophe Schlick. Light Warping for Enhanced Surface Depiction. ACM Transactions on Graphics, Association for Computing Machinery, 2009, 28 (3), pp.25:1–25:8. ff10.1145/1531326.1531331ff. ffinria-00400829 https://hal.inria.fr/inria-00400829