[steeringMethod::EndEffectorTrajectory] Improve documentation.

TODO.txt

@@ -17,7 +17,7 @@
     hard-coded optimizer (Graph-RandomShortcut) and then globally with the
     command ps.addPathOptimizer("Graph-RandomShortcut"). Due to how this works,
     this is like doing two times the same thing so the first should be removed.
-    However bugs have been observed when the global optimization is used (Core 
+    However bugs have been observed when the global optimization is used (Core
     dumped). For unknown reasons, in GraphOptimizer::optimize, the dynamic
     cast of current->constraints() may fail on *some* 0-length paths. Ignoring
     empty paths (the "if" I have added) seems to make the problem disappear

doc/Doxyfile.extra.in

@@ -8,3 +8,5 @@ ALIASES   += Link{1}="\ref \1"
 ALIASES   += Link{2}="\ref \1 \"\2\""
 ALIASES   += LHPP{2}="\Link{hpp::\1::\2,\2}"
 ALIASES   += LPinocchio{1}="\LHPP{pinocchio,\1}"
+
+USE_MATHJAX=YES

include/hpp/manipulation/steering-method/end-effector-trajectory.hh

@@ -56,10 +56,36 @@ class HPP_MANIPULATION_DLLAPI EndEffectorTrajectory
     return ptr;
   }
 
-  /// Build a trajectory in SE(3).
-  /// \param points a Nx7 matrix whose rows corresponds to a pose.
-  /// \param weights a 6D vector, weights to be applied when computing
-  ///        the distance between two SE3 points.
+  /** Build a trajectory in SE(3).
+      \param points a Nx7 matrix whose rows corresponds to poses.
+      \param weights a 6D vector, weights to be applied when computing
+             the distance between two SE3 points.
+
+      The trajectory \f$T\f$ is defined as follows. Let \f$N\f$ be the number of
+      lines of matrix \c points, \f$p_i\f$ be the i-th line of \c points and
+      let \f$W\f$ be the
+      diagonal matrix with the coefficients of \c weights:
+      \f[
+      W = \left(\begin{array}{cccccc}
+      w_1 & 0 & 0 & 0 & 0 & 0\\
+      0 & w_2 & 0 & 0 & 0 & 0\\
+      0 & 0 & w_3 & 0 & 0 & 0\\
+      0 & 0 & 0 & w_4 & 0 & 0\\
+      0 & 0 & 0 & 0 & w_5 & 0\\
+      0 & 0 & 0 & 0 & 0 & w_6\\
+      \end{array}\right)
+      \f]
+
+      \f{eqnarray*}{
+        f(t) = \mathbf{p}_i \oplus \frac{t-t_i}{t_{i+1}-t_i} (\mathbf{p}_{i+1}-\mathbf{p}_i) &&
+        \mbox{ for } t \in [t_i,t_{i+1}]
+      \f}
+
+      where \f$t_0 = 0\f$ and
+      \f{eqnarray*}{
+       t_{i+1}-t_i = \|W(\mathbf{p}_{i+1}-\mathbf{p}_i)\| && \mbox{for } i
+       \mbox{ such that } 1 \leq i \leq N-1
+       \f} */
   static PathPtr_t makePiecewiseLinearTrajectory(matrixIn_t points,
                                                  vectorIn_t weights);