implicit_curve_2d.cpp

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// -*- Mode:C++; Coding:us-ascii-unix; fill-column:158 -*-
/*******************************************************************************************************************************************************.H.S.**/
/**
 @file      implicit_curve_2d.cpp
 @author    Mitch Richling http://www.mitchr.me/
 @date      2024-07-13
 @brief     Sampleing on a 2D grid to extract an implicit curve.@EOL
 @std       C++23
 @copyright 
  @parblock
  Copyright (c) 2024, Mitchell Jay Richling <http://www.mitchr.me/> All rights reserved.
 
  Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
 
  1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
 
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
     and/or other materials provided with the distribution.
 
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
     without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  DAMAGE.
  @endparblock
 @filedetails   
 
  For many of us our first exposure to an implicit curve was the unit circle in high school algebra, @f$x^2+y^2=1@f$, where we were ask to graph @f$y@f$ with
  respect to @f$x@f$ only to discover that @f$y@f$ didn't appear to be a function of @f$x@f$ because @f$y@f$ had TWO values for some values of @f$x@f$!  But
  we soon discovered that a great many interesting curves could be defined this way, and that we could represent them all by thinking of the equations as a
  functions of two variables and the curves as sets of zeros.  That is to say, we can always write an implicit equation in two variables in the form
  @f$F(x,y)=0@f$, and think of the implicit curve as the set of roots, or zeros, of the function @f$F@f$.  We can then generalize this
  idea to "level sets" as solutions to @f$F(x,y)=L@f$ -- i.e. the set of points where the function is equal to some "level" @f$L@f$.
 
  Many visualization tools can extract a "level set" from a mesh.  For 2D meshes (surfaces), the level sets are frequently 1D sets (curves). The trick to
  obtaining high quality results is to make sure the triangulation has a high enough resolution.  Of course we could simply sample the 2D grid uniformly
  with a very fine mesh.  A better way is to detect where the curve is, and to sample at higher resolution near the curve.
 
  Currently we demonstrate a couple ways to refine the mesh near the curve:
   - Using cell_cross_range_level() to find cells that cross a particular level (zero in this case)
   - Using cell_cross_sdf() instead -- which generally works just like cell_cross_range_level() with a level of zero.
 
  Today we extract the curve with Paraview, but I hope to extend MR_rt_to_cc to extract level sets in the future:
   - Extract "standard" midpoint level sets (TBD)
   - Solve for accurate edge/function level intersections, and construct high quality level sets. (TBD)
*/
/*******************************************************************************************************************************************************.H.E.**/
/** @cond exj */
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#include "MR_rect_tree.hpp"
#include "MR_cell_cplx.hpp"
#include "MR_rt_to_cc.hpp"
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
typedef mjr::tree15b2d1rT            tt_t;
typedef mjr::MRccT5                  cc_t;
typedef mjr::MR_rt_to_cc<tt_t, cc_t> tc_t;
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// This function is a classic "difficult case" for implicit curve algorithms.
tt_t::rrpt_t f(tt_t::drpt_t xvec) {
  double x = xvec[0];
  double y = xvec[1];
  double z = ((2*x*x*y - 2*x*x - 3*x + y*y*y - 33*y + 32) * ((x-2)*(x-2) + y*y + 3))/3000;
  if (z>1.0)
    z=1.0;
  if (z<-1.0)
    z=-1.0;
  return z;
}
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
int main() {
  tt_t tree({-10.0, -6.5},
            { 10.0,  6.5});
  cc_t ccplx;
 
  // First we sample the top cell.  Just one cell!
  tree.sample_cell(f);
 
  // Now we recursively refine cells that seem to cross over the curve
  tree.refine_leaves_recursive_cell_pred(7, f, [&tree](tt_t::diti_t i) { return (tree.cell_cross_range_level(i, 0, 0.0)); });
 
  // We could have used the function f as an SDF, and achieved the same result with the following:
  // tree.refine_leaves_recursive_cell_pred(7, f, [&tree](tt_t::diti_t i) { return (tree.cell_cross_sdf(i, f)); });
 
  tree.dump_tree(20);
 
  // Convert the geometry into a 3D dataset so we can see the contour on the surface
  tc_t::construct_geometry_fans(ccplx,
                                tree,
                                2,
                                {{tc_t::val_src_spc_t::FDOMAIN, 0},
                                 {tc_t::val_src_spc_t::FDOMAIN, 1},
                                 {tc_t::val_src_spc_t::FRANGE,  0}});
 
  ccplx.create_named_datasets({"x", "y", "f(x,y)"});
 
  ccplx.write_xml_vtk("implicit_curve_2d.vtu", "implicit_curve_2d");
}
/** @endcond */