INTERFACE Squared;

(*
   This interface contain procedures to build several faces such as: n-gons,
   triangles and squares, and complexes : cube, ball, bigcube (3D array  of
   cube) with procedures for the glueing of two such complexes.

   Created by L. Lozada (see the copyright and authorship futher down).

   Revisions:

   30-08-2000 : Nice version of the "MakeOctahedron" procedure.
   19-09-2000 : Added the procedure "MakeDodecahedronTriang".
   27-10-2000 : Modified "SetCubePropiertes" procedure.
   04-11-2000 : Added the "CubeNegVertices" and "CubeBarycenter" procedures.

*)

IMPORT Triangulation, LR4;

FROM Triangulation IMPORT Pair, Topology, Vertex, Coords;

TYPE 
  TriPair =  ARRAY OF ARRAY OF ARRAY [0..1] OF Pair;

PROCEDURE MakeTriangle(): Pair;
  (* Make one triangular face and set the three pairs facetedges with the
     same face component. *)

PROCEDURE MakeSquare(): Pair;
  (* Builds one squared face. The four "pairs" have the same face component. *)

PROCEDURE MakeOctahedron(): ARRAY [0..7] OF Pair;
  (* Builds a Octahedron. *)

PROCEDURE MakeOctahedronTriang(Original: BOOLEAN): ARRAY [0..7] OF Pair;
  (* Builds a triangulated Octahedron. If Original=TRUE the procedure empha-
     size the original elements. *)

PROCEDURE MakeIcosahedronTriang(Original: BOOLEAN): ARRAY [0..19] OF Pair;
  (* Builds a triangulated Icosahedron. If Original=TRUE the procedure empha-
     size the original elements. *)

PROCEDURE MakeDodecahedronTriang(
  Original: BOOLEAN;
  ) : ARRAY[0..11] OF ARRAY [0..4] OF Pair;
  (* Builds a triangulated Dodecahedron, trough the automatic gluing of
     tetrahedra. If Original=TRUE the procedure emphasize the original
     elements. *)

PROCEDURE MakeGon(n: CARDINAL): Pair;
  (* Builds one "n-gon" face. The "n-pairs" have the same face component. *)

PROCEDURE MakeGonFull(n: CARDINAL): REF ARRAY OF Pair;
  (* Builds one "n-gon" face. The "n-pairs" have the same face component and
     this procedure return one pair facet-edge by side. *)
  
PROCEDURE MakeCube(): ARRAY [0..5] OF Pair;
  (*
    Builds a cube from six squared faces. Returns one pair from each face.    
    Face 0 is the bottom, faces 1..4 are the sides, face 5 is the
    top, as shown below.
    
  |      +------+
  |      |      |
  |      |      |
  |      |5     |
  |      +------+------+------+------+
  |      |      |      |      |      |
  |      |      |      |      |      |
  |      |1     |2     |3     |4     |
  |      +------+------+------+------+
  |      |      |
  |      |      |
  |      |0     |
  |      +------+
  *)               

PROCEDURE MakeBall() : ARRAY [0..3] OF Pair;
  (* Buils one polyhedron with American football shape. This polyhedron
     is the gluing scheme for obtain the "pseudomanifold" complex. *)

PROCEDURE MakeTetrahedron() : ARRAY [0..3] OF Pair;
  (* Builds one tetrahedron such that the facetedges pairs have "Ppos=NIL".
     Use in Baricentric Subdivision. *)

PROCEDURE MakePyramid(n: CARDINAL) : REF ARRAY OF Pair;
  (* Builds a pyramid with base as a n-gon face. *)

PROCEDURE MakeColumnCube(order: CARDINAL) : REF TriPair;
  (* Build one bidimensional array of cubes of order: "order x order". *)

PROCEDURE MakeBigCube(order: CARDINAL) : REF TriPair;         
  (* Build one tridimensional array of cubic cellulas. Return two arrays of
     pairs of order: "order x order", not eliminated by gluing procedure of
     columns of cubes. *)

PROCEDURE CubeNegVertices(a: Pair): ARRAY [0..7] OF Vertex;
  (* The vertices of the negative cube of "a" ("PnegP(a)"). *)

PROCEDURE CubeBarycenter(a: Pair; READONLY c: Coords): LR4.T;
  (* The barycenter of the negative cube of pair "a". *)

PROCEDURE SetCubeProperties(a: REF TriPair; o: CARDINAL; READONLY tp:Topology);
  (* Set the propiertes of a tridimensional array of cubic cells, such that
     it emphasis the elements of the external big cube. *)

PROCEDURE GlueCube(a,b : Pair) : Pair;
  (* Make the glueing of two simples cubes around of one squared face common.
     The pair "a" and their adjacentes on the same face component is killed. *)

PROCEDURE GlueBall(a,b: Pair) : Pair;
  (* Make the glueing of two simples 2-gon faces around of one common face.
     The pair "a" and their adjacentes on the same face component is killed. *)

PROCEDURE GlueBigCube(a,b : Pair; n: CARDINAL) : Pair;
  (* Make the glueing of two simples "bigcubes" around of one squared grid
     common face. The pair "a" and their adjacentes on the same squared grid
     face component is killed. *)

END Squared.

(**************************************************************************)
(*                                                                        *)
(* Copyright (C) 2000 Universidade Estadual de Campinas (UNICAMP)         *)
(*                                                                        *)
(* Authors:                                                               *)
(*   L. Lozada & J. Stolfi      - UNICAMP <lozada@dcc.unicamp.br>         *)
(*                                                                        *)
(* This file can be freely used, distributed, and modified, provided that *)
(* this copyright and authorship notice is included in every copy or      *)
(* derived version.                                                       *)
(*                                                                        *)
(* DISCLAIMER: This software is offered ``as is'', without any guarantee  *)
(*   as to fitness for any particular purpose.  Neither the copyright     *)
(*   holder nor the authors or their employers can be held responsible    *)
(*   for any damages that may result from its use.                        *)
(*                                                                        *)
(**************************************************************************)