-GLhandleARB compile_shader(const std::string &shader_src, GLenum type);
-void multiply_3x3_matrices(const Matrix3x3 a, const Matrix3x3 b, Matrix3x3 result);
-void invert_3x3_matrix(const Matrix3x3 m, Matrix3x3 result);
-void print_3x3_matrix(const Matrix3x3 m);
+
+// Compile the given GLSL shader (typically a vertex or fragment shader)
+// and return the object number.
+GLuint compile_shader(const std::string &shader_src, GLenum type);
+
+// Print a 3x3 matrix to standard output. Useful for debugging.
+void print_3x3_matrix(const Eigen::Matrix3d &m);
+
+// Output a GLSL 3x3 matrix declaration.
+std::string output_glsl_mat3(const std::string &name, const Eigen::Matrix3d &m);
+
+// Calculate where to sample, and with what weight, if one wants to use
+// the GPU's bilinear hardware to sample w1 * x[0] + w2 * x[1].
+static inline void combine_two_samples(float w1, float w2, float *offset, float *total_weight)
+{
+ assert(w1 * w2 >= 0.0f); // Should not have differing signs.
+ if (fabs(w1 + w2) < 1e-6) {
+ *offset = 0.5f;
+ *total_weight = 0.0f;
+ } else {
+ *offset = w2 / (w1 + w2);
+ *total_weight = w1 + w2;
+ }
+ assert(*offset >= 0.0f);
+ assert(*offset <= 1.0f);
+}