Use compile-time cols in point_simplex_squared_distance

[svenpilz]

template <
  int DIM,
  typename Derivedp,
  typename DerivedV,
  typename DerivedEle,
  typename Derivedsqr_d,
  typename Derivedc>
IGL_INLINE void igl::point_simplex_squared_distance(
  const Eigen::MatrixBase<Derivedp> & p,
  const Eigen::MatrixBase<DerivedV> & V,
  const Eigen::MatrixBase<DerivedEle> & Ele,
  const typename DerivedEle::Index primitive,
  Derivedsqr_d & sqr_d,
  Eigen::MatrixBase<Derivedc> & c)
{
  // Use Dynamic because we don't know Ele.cols() at compile time.
  Eigen::Matrix<typename Derivedc::Scalar,1,Eigen::Dynamic> b;
  point_simplex_squared_distance<DIM>( p, V, Ele, primitive, sqr_d, c, b );
}

(From: point_simplex_squared_distance)

Currently it uses Eigen::Matrix<…, Eigen::Dynamic> b;, would it make sense to allow for Eigen::Matrix<…, DerivedEle::ColsAtCompileTime> b;?

From Eigen's documentation

The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

As I read it, it would still fall back to Eigen::Dynamic, but could use ColsAtCompileTime which then would safe a memory allocation in

libigl/include/igl/point_simplex_squared_distance.cpp

Line 132 in 79dc4f6

bary.resize( Derivedb::RowsAtCompileTime == 1 ? 1 : Ele.cols(), Derivedb::ColsAtCompileTime == 1 ? 1 : Ele.cols());

, which could be expensive when used for a large number of query points from AABB.

I found this while profiling an Emscripten build with enabled multi-threading: emscripten-core/emscripten#15914.

[alecjacobson]

I think this is a good idea. I wonder if this should be excised and re-written though. The templating on dimension for AABB has been a real pain and particularly when hitting this code point.

[svenpilz]

We made some further testing and may found an additional bottleneck.

So far we have: https://github.com/libigl/libigl/compare/main...svenpilz:reduceDynamicAllocations?expand=1

Would this be interesting as a pull-request for you?

Edit: Added as #2001.