surface_plot_edge.cpp

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// -*- Mode:C++; Coding:us-ascii-unix; fill-column:158 -*-
/*******************************************************************************************************************************************************.H.S.**/
/**
 @file      surface_plot_edge.cpp
 @author    Mitch Richling http://www.mitchr.me/
 @date      2024-07-16
 @brief     Surface with an undefined regions.@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   
 
  Surface plots are frequently complicated by regions upon which the function singular or undefined.  These functions often behave quite poorly on the
  boundaries of such regions.  For this example we consider @f$f(x, y)=\sqrt{1-x^2-y^2}@f$ -- the upper half of the unit sphere.  Outside the unit circle this
  function is complex.  As we approach the unit circle from the center, the derivative approaches infinity.
 
  Right now this example illustrates two things:
 
    - How to drive up the sample rate near NaNs.
    - How to repair triangles containing NaNs.
*/
/*******************************************************************************************************************************************************.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;
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
tt_t::rrpt_t half_sphere(tt_t::drpt_t xvec) {
  double m = xvec[0] * xvec[0] + xvec[1] * xvec[1];
  if (m > 1) {
    return std::numeric_limits<double>::quiet_NaN();
  } else {
    return std::sqrt(1-m);
  }
}
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
int main() {
  tt_t tree({-1.1, -1.1}, 
            { 1.1,  1.1});
  cc_t ccplx;
 
  // Sample a uniform grid across the domain
  tree.refine_grid(5, half_sphere);
 
  /* half_sphere produces NaNs outside the unit circle.  
     We can refine cells that cross the unit circle using refine_recursive_if_cell_vertex_is_nan */
  tree.refine_recursive_if_cell_vertex_is_nan(7, half_sphere);
 
  /* We can acheive the same result via refine_leaves_recursive_cell_pred & cell_vertex_is_nan. */
  // tree.refine_leaves_recursive_cell_pred(6, half_sphere, [&tree](int i) { return (tree.cell_vertex_is_nan(i)); });
 
  /* We can acheive similar results by refining on the unit curcle via an SDF -- See surface_plot_corner.cpp */
 
  /* Balance the three to the traditional level of 1 (no cell borders a cell more than half it's size) */
  tree.balance_tree(1, half_sphere);
 
  tree.dump_tree(10);
 
  /* By passing half_sphere() to the construct_geometry_fans() we enable broken edges (an edge with one good point and one NaN) to be repaired. */
  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}},
                                half_sphere
                               );
 
  ccplx.create_named_datasets({"x", "y", "f(x,y)"},
                              {{"NORMALS", {0, 1, 2}}});
 
  ccplx.dump_cplx(10);
 
  ccplx.write_xml_vtk("surface_plot_edge.vtu", "surface_plot_edge");
}
/** @endcond */