+// Converts a HSV color to RGB, but keeps luminance constant
+// (ie. color luminance is as if S=0).
+void hsv2rgb_normalized(float h, float s, float v, float *r, float *g, float *b);
+
+// Read a file from disk and return its contents.
+// Dies if the file does not exist.
+std::string read_file(const std::string &filename);
+
+// 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].
+void combine_two_samples(float w1, float w2, float *offset, float *total_weight);
+
+#ifdef NDEBUG
+#define check_error()
+#else
+#define check_error() { int err = glGetError(); if (err != GL_NO_ERROR) { printf("GL error 0x%x at %s:%d\n", err, __FILE__, __LINE__); exit(1); } }
+#endif
+