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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2020 Alec Jacobson <alecjacobson@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#include "bezier.h"
#include <cassert>
// Adapted from main.c accompanying
// An Algorithm for Automatically Fitting Digitized Curves
// by Philip J. Schneider
// from "Graphics Gems", Academic Press, 1990
template <typename DerivedV, typename DerivedP>
IGL_INLINE void igl::bezier(
const Eigen::MatrixBase<DerivedV> & V,
const typename DerivedV::Scalar t,
Eigen::PlainObjectBase<DerivedP> & P)
{
// working local copy
DerivedV Vtemp = V;
int degree = Vtemp.rows()-1;
/* Triangle computation */
for (int i = 1; i <= degree; i++)
{
for (int j = 0; j <= degree-i; j++)
{
Vtemp.row(j) = ((1.0 - t) * Vtemp.row(j) + t * Vtemp.row(j+1)).eval();
}
}
P = Vtemp.row(0);
}
template <typename DerivedV, typename DerivedT, typename DerivedP>
IGL_INLINE void igl::bezier(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedT> & T,
Eigen::PlainObjectBase<DerivedP> & P)
{
P.resize(T.size(),V.cols());
for(int i = 0;i<T.size();i++)
{
Eigen::Matrix<typename DerivedV::Scalar,1,DerivedV::ColsAtCompileTime> Pi;
bezier(V,T(i),Pi);
P.row(i) = Pi;
}
}
template <typename VMat, typename DerivedT, typename DerivedP>
IGL_INLINE void igl::bezier(
const std::vector<VMat> & spline,
const Eigen::MatrixBase<DerivedT> & T,
Eigen::PlainObjectBase<DerivedP> & P)
{
if(spline.size() == 0) return;
const int m = T.rows();
const int dim = spline[0].cols();
P.resize(m*spline.size(),dim);
for(int c = 0;c<spline.size();c++)
{
assert(dim == spline[c].cols() && "All curves must have same dimension");
DerivedP Pc;
bezier(spline[c],T,Pc);
P.block(m*c,0,m,dim) = Pc;
}
}
#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
template void igl::bezier<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(std::vector<Eigen::Matrix<double, -1, -1, 0, -1, -1>, std::allocator<Eigen::Matrix<double, -1, -1, 0, -1, -1> > > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
template void igl::bezier<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
template void igl::bezier<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, 1, -1, 1, 1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<double, -1, -1, 0, -1, -1>::Scalar, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, -1, 1, 1, -1> >&);
#endif