test-cube.cc

Construct a topological cube using Euler operators.

Geometrically, the constructed cube collapses to a single point, because All vertices are assigned to the same coords(1,1,1); to form a real cube, assign different pnt apropriately at each operation.

See conclass-cube.jpg for an illustration of the conclassion process

Author:

Xianming Chen
Computer Science Department
University of Utah

Date:

16 Aug 2006
Copyright (c) 2006, University of Utah

/**
 *\file         test-cube.cc
 *
 *\brief        Construct a topological cube directly using Euler operators
 *. 
 *\example      test-cube.cc
 *
 *              Construct a topological cube using Euler operators. 
 *
 *              Geometrically, the constructed cube collapses to a single point, because 
 *              All vertices are assigned to the same coords(1,1,1);
 *              to form a real cube, assign different pnt apropriately at each operation.
 *
 *              See conclass-cube.jpg for an illustration of the conclassion process
 *
 *\image        html construct-cube.jpg
 *
 *\author       Xianming Chen\n
 *              Computer Science Department\n
 *              University of Utah
 *
 *\date          16 Aug 2006\n
 *              Copyright (c) 2006, University of Utah
 */


#include "print.h"
using namespace std;
using namespace euler;


int main()
{
  point_t p(1.,1.,1.);  // geometrically collapsed to one pnt.

  /* 
   * intialize to skeletal cube: 
   * topology = 1 0d-cell + 1 2d-cells
   */
  solid_t *s = solid_t :: mvfs(p);
  loop_t *l = s->f->l;   // singular loop: 0
  cerr << s << endl;
  
  /* 
   * add 3 consecutive dangling edges to form an open square:
   * topology = 4 0d-cell + 3 1d-cells + 1 2d-cell          
   */
  l->mev( l->mev( l->mev( l->f->l->e, p ), p ), p );
  l->del_single_vertex_edge_pair();      // loop = 0 1 2 3 2 1
  cerr << l << endl;   
  

  /*
   * close the open square by splitting the loop
   * topology = 2 2d-cells (faces) + 4 1d-cells (edges) + 4 0d-cells (vertices)
   */
  s->mef(l->e, l->e->nxt->nxt->nxt);    // new loop: 3 0 1 2  (top cube face), old loop l= 0 3 2 1
  cerr << s << endl;                   
  cerr << l << endl;                   

  
  /*
   * next, add a dangling edge to each vertex of the square
   */
  edge_t
    *e03 = l->e,
    *e10 = e03->pre,
    *e21 = e10->pre,
    *e32 = e21->pre;

  l->mev(e03, p);

  l->mev(e10, p);

  l->mev(e21, p);
  l->mev(e32, p);   // now: 0 3 7 3 2 6 2 1 5 1 0 4
  cerr << s << endl;
  cerr << l << endl;

  /*
   * close the 4 opening squares to form the cube
   */
  edge_t
    *e40 = l->e->pre,
    *e73 = l->e->nxt->nxt,
    *e62 = e73->nxt->nxt->nxt,
    *e51 = e62->nxt->nxt->nxt;
    
  s->mef(e40, e73);
  s->mef(e73, e62);
  s->mef(e62, e51);
  s->mef(e51, e51->nxt->nxt->nxt);

  cerr << s << endl;
}

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