Merge pull request #136 from jmaleo/meanNormalDer

Mean normal der

CHANGELOG

@@ -11,6 +11,7 @@ Current head (v.1.3 RC)
 
 - Bug-fixes and code improvements
     - [all] Limit explicit use of exceptions and adapt to compilation mode (#135)
+    - [fitting] Fix MeanNormal and MeanNormalDer classes for mean normal vector derivatives computation (#136)
 
 - Docs
     - [spatialPartitioning] Update KdTree docs to reflect the kdtree API refactor (#129)

Ponca/src/Fitting/mean.h

@@ -73,6 +73,15 @@ namespace Ponca {
         PONCA_EXPLICIT_CAST_OPERATORS(MeanNormal,meanNormal)
         PONCA_FITTING_DECLARE_INIT
         PONCA_FITTING_DECLARE_ADDNEIGHBOR
+
+        /// \brief Mean of the normals of the input points
+        ///
+        /// Defined as \f$ n(\mathbf{x}) = \frac{\sum_i w_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i}}{\sum_i w_\mathbf{x}(\mathbf{p_i})} \f$,
+        ///  where \f$\left[\mathbf{p_i}, \mathbf{n_i} \in \text{neighborhood}(\mathbf{x})\right]\f$ are all the point and normal samples in \f$\mathbf{x}\f$'s neighborhood
+        PONCA_MULTIARCH inline VectorType meanNormalVector() const {
+            return (m_sumN / Base::getWeightSum());
+        }
+
     }; //class MeanNormal
 
     template<class DataPoint, class _WFunctor, int DiffType, typename T>
@@ -134,7 +143,6 @@ namespace Ponca {
             PROVIDES_MEAN_NORMAL_DERIVATIVE,  /*!< \brief Provides derivative of the mean normal*/
         };
 
-        private:
         /*! \brief Derivatives of the input normals of the input points vectors*/
         VectorArray m_dSumN {VectorArray::Zero()};
 
@@ -147,27 +155,27 @@ namespace Ponca {
     /// \brief Compute the derivative of the mean normal vector of the input points. 
     /// 
     /// ### Step-by-step derivation of the mean normal : 
-    ///  Given the definition of the mean normal \f$ n(\mathbf{x}) = \frac{\sum_i w_\mathbf{x}(\mathbf{n_i}) \mathbf{n_i}}{\sum_i w_\mathbf{x}(\mathbf{n_i})} \f$, 
-    /// where \f$\left[\mathbf{n_i} \in \text{neighborhood}(\mathbf{x})\right]\f$ are all the normal samples in \f$\mathbf{x}\f$'s neighborhood.
+    ///  Given the definition of the mean normal \f$ n(\mathbf{x}) = \frac{\sum_i w_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i}}{\sum_i w_\mathbf{x}(\mathbf{p_i})} \f$, 
+    /// where \f$\left[\mathbf{p_i}, \mathbf{n_i} \in \text{neighborhood}(\mathbf{x})\right]\f$ are all the point and normal samples in \f$\mathbf{x}\f$'s neighborhood.
     ///
-    /// We denote \f$ t(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{n_i}) \mathbf{n_i} \f$ and \f$ s(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{n_i})\f$, 
+    /// We denote \f$ t(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i} \f$ and \f$ s(\mathbf{x}) = \sum_i w_\mathbf{x}(\mathbf{p_i})\f$, 
     /// such that \f$ n(\mathbf{x}) = \frac{t(\mathbf{x})}{s(\mathbf{x})}\f$.
     ///
     /// By definition, \f$ n'(\mathbf{x}) = \frac{s(\mathbf{x})t'(\mathbf{x}) - t(\mathbf{x})s'(\mathbf{x})}{s(\mathbf{x})^2}\f$.
     ///
-    /// Assuming the weight of each normal is dependent on the position, we have \f$ s'(\mathbf{x}) = \sum_i w'_\mathbf{x}(\mathbf{n_i}) \f$.
+    /// Assuming the weight of each normal is dependent on the position, we have \f$ s'(\mathbf{x}) = \sum_i w'_\mathbf{x}(\mathbf{p_i}) \f$.
     ///
-    /// We rewrite \f$ t(\mathbf{x}) = \sum u(\mathbf{x})v(\mathbf{x}) \f$, with \f$ u(\mathbf{x}) = w_\mathbf{x}(\mathbf{n_i}) \f$ and \f$ v(\mathbf{x}) = \mathbf{n_i} \f$.
+    /// We rewrite \f$ t(\mathbf{x}) = \sum u(\mathbf{x})v(\mathbf{x}) \f$, with \f$ u(\mathbf{x}) = w_\mathbf{x}(\mathbf{p_i}) \f$ and \f$ v(\mathbf{x}) = \mathbf{n_i} \f$.
     ///
     /// Assuming the normal vectors themselves do not change with position, \f$v(\mathbf{x})\f$ is constant, its derivative is null, 
     /// and so \f$ t'(\mathbf{x}) = \sum_i u'(\mathbf{x}) v(\mathbf{x}) = \sum_i w'_\mathbf{x}(\mathbf{n_i}) \mathbf{n_i} \f$.
     ///
-    /// Which leads to \f$ n'(\mathbf{x}) = \frac{\sum_i w'\mathbf{x}(\mathbf{n_i}) \mathbf{n_i} - n(\mathbf{x})\sum w'(\mathbf{x})}{\sum_i w\mathbf{x}(\mathbf{n_i})} \f$.
+    /// Which leads to \f$ n'(\mathbf{x}) = \frac{\sum_i w'_\mathbf{x}(\mathbf{p_i}) \mathbf{n_i} - n(\mathbf{x})\sum_i w'_\mathbf{x}(\mathbf{p_i})}{\sum_i w_\mathbf{x}(\mathbf{p_i})} \f$.
     /// \note This code is not directly tested. 
 
-    PONCA_MULTIARCH inline const VectorArray& dMeanNormal() const
+    PONCA_MULTIARCH VectorArray dMeanNormal() const
     { 
-        return m_dSumN; 
+        return ( m_dSumN - Base::meanNormalVector() * Base::m_dSumW ) / Base::getWeightSum(); 
     }
 
     }; //class MeanNormalDer