# OpenTissue::interpolation Namespace Reference

## Namespaces

namespace  detail

## Classes

class  BaseInterpolator
class  PolynomialInterpolator
class  SplineInterpolator

## Functions

template<typename iterator >
detail::ImplicitFunction
< typename
iterator::value_type >
variational_interpolator (iterator point_begin, iterator point_end, iterator normal_begin, iterator normal_end)

## Function Documentation

template<typename iterator >
 detail::ImplicitFunction OpenTissue::interpolation::variational_interpolator ( iterator point_begin, iterator point_end, iterator normal_begin, iterator normal_end ) ` [inline]`

Variational Interpolation. This implementation is based on the paper:

Greg Turk and James O'Brien, "Shape Transformation Using Variational Implicit Functions," SIGGRAPH 99, August 1999, pp. 335-342.

This can be obtained from: http://www-static.cc.gatech.edu/~turk/my_papers/schange.pdf

Intended usage:

typedef .... vector3_type; typedef ... grid_type;

points[0] = vector3_type( 0.008337971754, -0.393710464239, 0.163935899734 ); ... points[...] = vector3_type( -0.060189183801, -0.305664300919, -0.289155662060 );

normals[0] = vector3_type( 0.121994487941, -0.001839586534, 0.992529094219 ); ... normals[...] = vector3_type( -0.021462006494, 0.442783534527, -0.896371662617 );

grid_type phi;

phi.create( vector3_type(-2,-2,-2), vector3_type(2,2,2), 64,64,64); detail::implicit_function<vector3_type> F = variational_interpolator(m_points.begin(),m_points.end(),m_normals.begin(),m_normals.end()); for(unsigned int k=0;k<64;++k) for(unsigned int j=0;j<64;++j) for(unsigned int i=0;i<64;++i) { vector3_type coord; OpenTissue::grid::idx2coord(m_phi,i,j,k,coord); m_phi(i,j,k) = F(coord); }

This is a bit nitty-griffty, so it may be better to use the variational-interpolator function to create a implicit function functor on the fly. That is create some function like

template<typename grid_type,typename functor_type> void doit(grid_type & phi, functor_type & F) { typedef typename functor_type::return_type vector3_type; for(unsigned int k=0;k<phi.K();++k) for(unsigned int j=0;j<phi.J();++j) for(unsigned int i=0;i<phi.I();++i) { vector3_type coord; OpenTissue::grid::idx2coord(phi,i,j,k,coord); phi(i,j,k) = F(coord); } }

and then simply write

typedef .... vector3_type; typedef ... grid_type; points[0] = vector3_type( 0.008337971754, -0.393710464239, 0.163935899734 ); ... points[...] = vector3_type( -0.060189183801, -0.305664300919, -0.289155662060 ); normals[0] = vector3_type( 0.121994487941, -0.001839586534, 0.992529094219 ); ... normals[...] = vector3_type( -0.021462006494, 0.442783534527, -0.896371662617 ); grid_type phi; phi.create( vector3_type(-2,-2,-2), vector3_type(2,2,2), 64,64,64); doit( phi, variational_interpolator(points.begin(),points.end(),normals.begin(),normals.end()) );

That's it.

Parameters:
 point_begin point_end normal_begin normal_end
Returns:
The resulting variational interpolation function object.