# Last edited on 2005-02-12 02:07:41 by stolfi

  To do:
  ??? tent --> finel (finite element)?
  ??? dg_tent_domain_cell = CellIndex of the kth cell in the domain of a tent.
  ??? dg_basic -> dg_grid
  
  
  Status of modules on 2003-10-13:
  
  -- OK ----------------------------------------------------------------

    dg_basic.h, dg_basic.c
      
      Dimensions, axes, sets of axes. Boxes and faces. The infinite
      dyadic multigrid {G*}. Cell indices and ranks. Cell-relative
      coordinates. Cell positions and grid walking. Locus in {G*}.
      Star of a locus.  Canonical geometry for {G*}.
      Text formatting for face index, cell index, and locus.
      Vectors of cell index and locus.

    dg_tree.h, dg_tree.c
    
      Finite dyadic trees and their interpretation as finite,
      non-uniform dyadic grids.  Tree node enclosing a cell.
      Node stars. Shrinking and splitting node stars.
      Vectors of node pointers.
      
    dg_spline.h, dg_spline.c
    
      Univariate Bézier polynomials. Univariate splines (mother
      splines) with two-cell support: B-spline-type and Hermite-type.
      Multidimensional tensor-style elements (/tents/). Tent
      evaluation. Enumeration of tent bases for the splines on a
      finite grid {G}.

        TO DO: (1) Trimming of elements associated with a locus
        so as to imitate total-degree behavior instead 
        of tensor-style behavior.
        
        (2) Efficient update of a tent basis after node split/join.
  
        (3) Extend the whole theory to the case {g < 2*c +
        1}. The support of the univariate mother splines
        then covers {2*c-g+3} unit intervals, namely {[-1..2*c-g+2]}.
        Note that there will be wrap-around whenever the grid
        size {sz} is less than {2*c-g+3}.
        
        (4) Rename:
        
          DG_HER --> DG_PK_H, DG_TK_H 
          DG_BSP --> DG_PK_B, DG_TK_B 
          dg_SplineKind --> dg_pulse_kind_t, dg_tent_kind_t
          dg_mother_spline --> dg_pulse_mother
          

    dg_plot.h, dg_plot.c
    
      Plotting color bands and isolines of a multivariate multiaffine
      function on a quadrilateral. Ditto for a multivariate affine
      function on a triangle. Plotting of a subtree of a finite dyadic
      grid, whose shape is defined by a tensort-style Bézier patch.
      
  -- not OK ------------------------------------------------------------

    bz_basic.h, bz_basic.c
    
      Bézier patch (a tensor-style polynomial mapping from {R^m} to
      {R^n}). Degree vector of a Bézier patch (one degree per axis).
      Index of a control point or coeff for a univariate Bézier
      polynomial. Index vector for a coeff of a Bézier patch. Patch
      allocation and delocation. Locating a coeff in a patch.
      Evaluating at a point (De Casteljau algorithm). Trimming and
      reparametrizing a patch to a given box. Splitting a patch.
      Bounding the range. Extracting, modifying, and flattening a
      face. Rasing the degree. Approximating a general patch by a
      multiaffine patch or affine function. Compting the gradient of a
      patch. Finding the inverse image of a point.  Printing a patch.
    
    dg_makegrid.h, dg_makegrid.c
    
      Creating a finite grid with client-defined spatially variable
      resolution.
    
    dg_spline-old.c
    dg_plotextra.h
    dg_plotextra.c
    dg_plot-claudio.h
    dg_plot-claudio.c
    dg_itemmap.h
    dg_itemmap.c
    junk1.c
    junk.c
    
      Junk and work-in-progress.