/*
 * Copyright 2012 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */
#if !defined CUBIC_UTILITIES_H
#define CUBIC_UTILITIES_H

#include "DataTypes.h"

double cube_root(double x);
void coefficients(const double* cubic, double& A, double& B, double& C, double& D);
int cubicRoots(double A, double B, double C, double D, double t[3]);
double derivativeAtT(const double* cubic, double t);
// competing version that should produce same results
double derivativeAtT_2(const double* cubic, double t);
void dxdy_at_t(const Cubic& , double t, double& x, double& y);
bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath);
double secondDerivativeAtT(const double* cubic, double t);
void xy_at_t(const Cubic& , double t, double& x, double& y);

#endif