hslt: util.h: add boilerplate coordinate derivative function

include/mitsuba/core/util.h

@@ -329,6 +329,14 @@ extern MTS_EXPORT_CORE bool solveLinearSystem2x2(const Float a[2][2], const Floa
  */
 extern MTS_EXPORT_CORE void coordinateSystem(const Vector &a, Vector &b, Vector &c);
 
+/**
+ * \brief Derivatives of a frame formed by coordinateSystem
+ * \param n Source tangent frame that was created with coordinateSystem
+ * \param ds derivative of the frame with respect to s. ds.n should already contain normal derivative along s
+ * \param dt derivative of the frame with respect to t. dt.n should already contain normal derivative along t
+ */
+extern MTS_EXPORT_CORE void coordinateSystemDerivatives(const Frame &frame, Frame &ds, Frame &dt);
+
 /**
  * \brief Generate (optionally jittered) stratified 1D samples
  * \param random Source of random numbers

src/libcore/util.cpp

@@ -21,6 +21,7 @@
 #include <mitsuba/core/random.h>
 #include <mitsuba/core/quad.h>
 #include <mitsuba/core/sse.h>
+#include <mitsuba/core/frame.h>
 #include <boost/bind.hpp>
 #include <stdarg.h>
 #include <iomanip>
@@ -599,6 +600,29 @@ void coordinateSystem(const Vector &a, Vector &b, Vector &c) {
 	b = cross(c, a);
 }
 
+void coordinateSystemDerivatives(const Frame &frame, Frame &ds, Frame &dt) {
+
+	const Vector n = frame.n;
+	const Vector s = frame.s;
+
+	if(std::abs(n.x) > std::abs(n.y)) {
+		const Float invLen = 1 / std::sqrt(n.x * n.x + n.z * n.z);
+		ds.s = Vector(ds.n.z * invLen, 0, -ds.n.x * invLen);
+		ds.s -= s * dot(ds.s, s);
+		dt.s = Vector(dt.n.z * invLen, 0, -dt.n.x * invLen);
+		dt.s -= s * dot(dt.s, s);
+	} else {
+		const Float invLen = 1 / std::sqrt(n.y * n.y + n.z * n.z);
+		ds.s = Vector(0, ds.n.z * invLen, -ds.n.y * invLen);
+		ds.s -= s * dot(ds.s, s);
+		dt.s = Vector(0, dt.n.z * invLen, -dt.n.y * invLen);
+		dt.s -= s * dot(dt.s, s);
+	}
+
+	dt.t = cross(s, ds.n) + cross(dt.s, n);
+	ds.t = cross(s, dt.n) + cross(ds.s, n);
+}
+
 Point2 toSphericalCoordinates(const Vector &v) {
 	Point2 result(
 		std::acos(v.z),

src/librender/trimesh.cpp

@@ -40,7 +40,7 @@ MTS_NAMESPACE_BEGIN
 TriMesh::TriMesh(const std::string &name, size_t triangleCount,
 		size_t vertexCount, bool hasNormals, bool hasTexcoords,
 		bool hasVertexColors, bool flipNormals, bool faceNormals)
- 	: Shape(Properties()), m_triangleCount(triangleCount),
+	: Shape(Properties()), m_triangleCount(triangleCount),
 	  m_vertexCount(vertexCount), m_flipNormals(flipNormals),
 	  m_faceNormals(faceNormals) {
 	m_name = name;
@@ -762,7 +762,7 @@ void TriMesh::getNormalDerivative(const Intersection &its,
 
 		/* Recompute the barycentric coordinates, since 'its.uv' may have been
 		   overwritten with coordinates of the texture "parameterization". */
- 		Vector rel = its.p - p0, du = p1 - p0, dv = p2 - p0;
+		Vector rel = its.p - p0, du = p1 - p0, dv = p2 - p0;
 
 		Float b1  = dot(du, rel), b2 = dot(dv, rel), /* Normal equations */
 			  a11 = dot(du, du), a12 = dot(du, dv),