+
+// 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);
+
+// Compute a * b.
+void multiply_3x3_matrices(const Matrix3x3 a, const Matrix3x3 b, Matrix3x3 result);
+
+// Compute M * [x0 x1 x2]'.
+void multiply_3x3_matrix_float3(const Matrix3x3 M, float x0, float x1, float x2, float *y0, float *y1, float *y2);
+
+// Compute m^-1. Result is undefined if the matrix is singular or near-singular.
+void invert_3x3_matrix(const Matrix3x3 m, Matrix3x3 result);
+
+// Print a 3x3 matrix to standard output. Useful for debugging.
+void print_3x3_matrix(const Matrix3x3 m);