address comments from Monique

This commit is contained in:
Sébastien Loriot 2014-03-04 21:52:27 +01:00
parent a635a22a37
commit efb393b460
2 changed files with 9 additions and 9 deletions

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@ -282,10 +282,10 @@ Given a surface mesh deformation system with a ROI made of \f$ n \f$ vertices an
\f]
where:
- \f$\mathbf{V}\f$ is a \f$n \times 3\f$ matrix denoting the unknowns of the system that represent the vertex coordinates after deformation. The system is built so that the \f$ k \f$ last row correspond to the control vertices.
- \f$\mathbf{L}_f\f$ denotes the Laplacian matrix of the unconstrained vertices. It is a \f$ (n-k) \times n \f$ matrix as defined in Eq. \f$\eqref{eq:lap_system}\f$ with the rows corresponding to the control vertices removed.
- \f$\mathbf{V}\f$ is a \f$n \times 3\f$ matrix denoting the unknowns of the system that represent the vertex coordinates after deformation. The system is built so that the \f$ k \f$ last rows correspond to the control vertices.
- \f$\mathbf{L}_f\f$ denotes the Laplacian matrix of the unconstrained vertices. It is a \f$ (n-k) \times n \f$ matrix as defined in Eq. \f$\eqref{eq:lap_system}\f$ but removing the rows corresponding to the control vertices.
- \f$\mathbf{I}_c\f$ is the \f$k \times k\f$ identity matrix.
- \f${\Delta}_f\f$ denotes the Laplacian representation of the unconstrained vertices as defined in Eq. \f$\eqref{eq:lap_system}\f$ with the rows corresponding to the control vertices removed.
- \f${\Delta}_f\f$ denotes the Laplacian representation of the unconstrained vertices as defined in Eq. \f$\eqref{eq:lap_system}\f$ but removing the rows corresponding to the control vertices.
- \f$\mathbf{V}_c\f$ is a \f$k \times 3\f$ matrix containing the %Cartesian coordinates of the target positions of the control vertices.
The left-hand side matrix of the system of Eq.\f$\eqref{eq:lap_energy_system}\f$ is a square non-symmetric sparse matrix. To
@ -313,9 +313,9 @@ where:
- \f$N(\mathbf{v}'_i)\f$ denotes a new position of the vertex \f$N(\mathbf{v}_i)\f$ after a given deformation
An as-rigid-as possible surface mesh deformation \cgalCite{Sorkine2007AsRigidAs} is defined by minimizing
this energy function under the deformation constraints, that is the assigned position
this energy function under the deformation constraints, i.e. the assigned position
\f$ {v}'_i\f$ for each vertex \f$ \mathbf{v}_i\f$ in the set of control vertices.
Defining the <i>one-ring neighborhood</i> of a vertex as its set of adjacent vertices,s
Defining the <i>one-ring neighborhood</i> of a vertex as its set of adjacent vertices,
the intuitive idea behind this energy function is to allow each one-ring neighborhood of
vertices to have an individual rotation, and at the same time prevents shearing by taking advantage of the
overlapping of one-ring neighborhoods of adjacent vertices (see \cgalFigureRef{Overlapping_cells}).
@ -411,8 +411,8 @@ the set of edges in the link (the <em>rims</em>) of \f$\mathbf{v}_i\f$ in the su
(see \cgalFigureRef{Spoke_and_rim_edges}).
\cgalFigureBegin{Spoke_and_rim_edges, spoke_and_rim_edges_2.png}
The vertices \f$ \mathbf{v}_n\f$ and \f$ \mathbf{v}_m\f$ are the opposite vertices to the edge \f$
\mathbf{v}_i \mathbf{v}_j\f$.
The vertices \f$ \mathbf{v}_n\f$ and \f$ \mathbf{v}_m\f$ are the opposite vertices to the edge
\f$ \mathbf{v}_i \mathbf{v}_j\f$.
\cgalFigureEnd
The method to get the new positions of the unconstrained vertices is similar to the two-step optimization
@ -438,7 +438,7 @@ respect to \f$\mathbf{v}_i\f$ gives the following equation:
\f]
where \f$\mathbf{R}_m\f$ and \f$\mathbf{R}_n\f$ are the rotation matrices of the vertices \f$\mathbf{v}_m\f$,
\f$\mathbf{v}_n\f$ which are the opposite vertices of the edge \f$\mathbf{v}_i, \mathbf{v}_j\f$
\f$\mathbf{v}_n\f$ which are the opposite vertices of the edge \f$\mathbf{v}_i \mathbf{v}_j\f$
(see \cgalFigureRef{Spoke_and_rim_edges}). Note that if the edge \f$ \mathbf{v}_i \mathbf{v}_j \f$ is on
the boundary of the surface mesh, then \f$ w_{ij} \f$ must be 0 and \f$ \mathbf{v}_m
\f$ does not exist.

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@ -108,7 +108,7 @@ class Deform_mesh
//Typedefs
public:
/// \name Public Types
/// \name Types
/// @{
// typedefed template parameters, main reason is doxygen creates autolink to typedefs but not template parameters
///