testrender: Fix uv derivatives for testrender [AcademySoftwareFoundation#1978] (AcademySoftwareFoundation#2037)

Fix dudx, dudy, dvdx, dvdy, as well as dpdx, dpdy in testrender. Now, bump mapping from both UV-based mapping and 3D-based patterns works well. Mip-Map selection also works fine now. Images in Issue: AcademySoftwareFoundation#1978
This PR is intended to validate math and discuss tests.

Fixes AcademySoftwareFoundation#1978

This fix could potentially affect many other tests since dpdx, dpdy are changed.
I'm going to add tests representing bump and mipmapping in this PR.

---------

Signed-off-by: Alexey Smolenchuk <[email protected]>
Signed-off-by: Larry Gritz <[email protected]>
Co-authored-by: Larry Gritz <[email protected]>

Author: AlexeySmolenchuk

src/testrender/raytracer.h

@@ -279,6 +279,22 @@ struct Scene {
         return ((1 - u - v) * na + u * nb + v * nc).normalize();
     }
 
+    // Project differentials onto surface defined by N
+    OSL_HOSTDEVICE
+    void project(Dual2<Vec3>& p, const Vec3& N, const Vec3& I) const
+    {
+        Vec3 nI    = I.normalized();
+        float cosI = dot(-nI, N);
+
+        if (fabsf(cosI) > 1e-3f) {
+            float deltaX = dot(p.dx(), N) / cosI;
+            float deltaY = dot(p.dy(), N) / cosI;
+
+            p.dx() += nI * deltaX;
+            p.dy() += nI * deltaY;
+        }
+    }
+
     OSL_HOSTDEVICE
     Dual2<Vec2> uv(const Dual2<Vec3>& p, const Vec3& n, Vec3& dPdu, Vec3& dPdv,
                    int primID, float u, float v) const
@@ -304,7 +320,25 @@ struct Scene {
             dPdv         = (-dt12.x * dp02 + dt02.x * dp12) * invdet;
             // TODO: smooth out dPdu and dPdv by storing per vertex tangents
         }
-        return Dual2<Vec2>((1 - u - v) * ta + u * tb + v * tc);
+
+        // L represent planes constructed from opposite points perpendicular
+        // to N and scaled to return 1.0 for scalar product with itself
+        Vec3 La = n.cross(vc - vb);
+        La /= dot(va - vb, La);
+
+        Vec3 Lb = n.cross(va - vc);
+        Lb /= dot(vb - vc, Lb);
+
+        Vec3 Lc = n.cross(vb - va);
+        Lc /= dot(vc - va, Lc);
+
+        Vec2 dTdx = dot(La, p.dx()) * ta + dot(Lb, p.dx()) * tb
+                    + dot(Lc, p.dx()) * tc;
+
+        Vec2 dTdy = dot(La, p.dy()) * ta + dot(Lb, p.dy()) * tb
+                    + dot(Lc, p.dy()) * tc;
+
+        return Dual2<Vec2>((1 - u - v) * ta + u * tb + v * tc, dTdx, dTdy);
     }
 
     OSL_HOSTDEVICE int shaderid(int primID) const { return shaderids[primID]; }

src/testrender/simpleraytracer.cpp

@@ -903,25 +903,26 @@ SimpleRaytracer::globals_from_hit(ShaderGlobalsType& sg, const Ray& r,
     const int meshid = m_meshids[id];
 #endif
 
-    Dual2<Vec3> P = r.point(t);
-    // We are missing the projection onto the surface here
-    sg.P                  = P.val();
-    sg.dPdx               = P.dx();
-    sg.dPdy               = P.dy();
-    sg.N                  = scene.normal(P, sg.Ng, id, u, v);
-    Dual2<Vec2> uv        = scene.uv(P, sg.N, sg.dPdu, sg.dPdv, id, u, v);
-    sg.u                  = uv.val().x;
-    sg.dudx               = uv.dx().x;
-    sg.dudy               = uv.dy().x;
-    sg.v                  = uv.val().y;
-    sg.dvdx               = uv.dx().y;
-    sg.dvdy               = uv.dy().y;
-    sg.surfacearea        = m_mesh_surfacearea[meshid];
     Dual2<Vec3> direction = r.dual_direction();
     sg.I                  = direction.val();
     sg.dIdx               = direction.dx();
     sg.dIdy               = direction.dy();
-    sg.backfacing         = sg.Ng.dot(sg.I) > 0;
+    Dual2<Vec3> P         = r.point(t);
+    sg.P                  = P.val();
+    sg.N                  = scene.normal(P, sg.Ng, id, u, v);
+    // Projecting onto the surface here
+    scene.project(P, sg.N, sg.I);
+    sg.dPdx        = P.dx();
+    sg.dPdy        = P.dy();
+    Dual2<Vec2> uv = scene.uv(P, sg.N, sg.dPdu, sg.dPdv, id, u, v);
+    sg.u           = uv.val().x;
+    sg.dudx        = uv.dx().x;
+    sg.dudy        = uv.dy().x;
+    sg.v           = uv.val().y;
+    sg.dvdx        = uv.dx().y;
+    sg.dvdy        = uv.dy().y;
+    sg.surfacearea = m_mesh_surfacearea[meshid];
+    sg.backfacing  = sg.Ng.dot(sg.I) > 0;
     if (sg.backfacing) {
         sg.N  = -sg.N;
         sg.Ng = -sg.Ng;