Update README.md

README.md

-spline
-======
+Spline
+===================
 
-Library for creating smooth cubic splines
+
+A template-based Library for creating curves of arbitrary order and dimension, eventually subject to derivative constraints. The main use of the library is the creation of end-effector trajectories for legged robots.
+
+To do so, tools are provided to:
+> - create **exact** splines of arbitrary order (that pass exactly by an arbitrary number waypoints)
+> - constrain initial / end velocities and acceleration for the spline.
+> - constrain take-off and landing phases to follow a straight line along a given normal (to avoid undesired collisions between the effector and the contact surface)
+> automatically handle 3d rotation of the effector.
+
+The library is template-based, thus generic:  the curves can be of any dimension, and can be implemented in double, float  ...
+
+While a Bezier curve implementation is provided (limited to degree 3), the main interest 
+of this library is to create spline curves of arbitrary order
+
+----------
+Example of use for and end-effector trajectory
+-------------
+The library comes with an helper class to automatically generate end-effector trajectories.
+For instance, to create a 2 second long trajectory from the point (0,0,0) to (1,1,0), with a waypoint
+at (0.5,0.5,0.5), one can use the following code:
+
+```
+typedef std::pair<double, Eigen::Vector3d> Waypoint;
+typedef std::vector<Waypoint> T_Waypoint;
+
+// loading helper class namespace
+using namespace spline::helpers;
+
+// Create waypoints
+waypoints.push_back(std::make_pair(0., Eigen::Vector3d(0,0,0)));
+waypoints.push_back(std::make_pair(1., Eigen::Vector3d(0.5,0.5,0.5)));
+waypoints.push_back(std::make_pair(2., Eigen::Vector3d(1,1,0)));
+
+exact_cubic_t* eff_traj = effector_spline(waypoints.begin(),waypoints.end());
+
+effector_spline_rotation traj(waypoints.begin(), waypoints.end());
+
+// evaluate spline
+(*eff_traj)(0.); // (0,0,0)
+(*eff_traj)(2.); // (1,1,0)
+```
+If rotation of the effector must be considered, the code is almost the same:
+
+```
+// initial rotation is 0, end rotation is a rotation by Pi around x axis
+quat_t init_rot(0,0,0,1), end_rot(1,0,0,0);
+effector_spline_rotation eff_traj_rot(waypoints.begin(),waypoints.end(), init_quat, end_quat);
+
+// evaluate spline
+eff_traj_rot(0.); // (0,0,0,0,0,0,1)
+eff_traj_rot(1.); // (0.5,0.5,0.5,0.707107,0,0,0.707107) // Pi/2 around x axis
+eff_traj_rot(2.); // (0,0,0,1,0,0,0)
+```
+
+Additional parameters for the same methods an be used to specify parameters for the take off and
+landing phases: height and duration of the phase, and along which normal.
+Please refer to the Main.cpp files to see all the unit tests and possibilities offered by the library
+
+Installation
+-------------
+The library is header only, so you just need to copy the include folder where you need.
+Eigen is required for the library to work.
+
+To run the tests, there is a CMakeLists.txt:
+```
+	cd $SPLINE_DIR && mkdir build && cd build
+	cmake .. && make 
+	../bin/tests
+```
+
+If everything went fine you should obtain the following output:
+```
+performing tests... 
+no errors found 
+```