Verified Commit 3b53536a authored by Justin Carpentier's avatar Justin Carpentier
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doc: improve documentation of parallel transportation

parent bdfaec54
......@@ -350,6 +350,9 @@ namespace pinocchio
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -375,6 +378,9 @@ namespace pinocchio
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -403,6 +409,9 @@ namespace pinocchio
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -426,6 +435,9 @@ namespace pinocchio
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......
......@@ -161,6 +161,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -185,6 +188,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -205,6 +211,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -227,6 +236,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -247,6 +259,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......@@ -266,6 +281,9 @@ PINOCCHIO_LIE_GROUP_PUBLIC_INTERFACE_GENERIC(Derived,typename)
*
* @details This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \f$ q \oplus v \f$,
* to the tangent space at \f$ q \f$.
* In other words, this functions transforms a tangent vector expressed at \f$ q \oplus v \f$ to a tangent vector expressed at \f$ q \f$, considering that the change of configuration between
* \f$ q \oplus v \f$ and \f$ q \f$ may alter the value of this tangent vector.
* A typical example of parallel transportation is the action operated by a rigid transformation \f$ M \in \text{SE}(3)\f$ on a spatial velocity \f$ v \in \text{se}(3)\f$.
* In the context of configuration spaces assimilated as vectorial spaces, this operation corresponds to Identity.
* For Lie groups, its corresponds to the canonical vector field transportation.
*
......
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