# This file computes the coefficients of the derivatives of the 4-sided
# patch with respect to a given direction 
#
#         d0d0--------d00d
#          |           |
#          |           | ^ 1
#          |           | |
#          |           |
#         0dd0--------0d0d
#               <-- 2

# bb is the input table of coefficients and d is the degree of patch.
# The two directions are shown in the figure.
# A minus sign will take care of negative directions

bb4D := proc(bb,du:integer, dv:integer,dir:integer)

local new,i,j,k,h:

    if dir = 2 then
       for i from 0 to du do
	    for j from 0 to dv-1 do
		k := dv-1-j:
		h := dv*(bb[i,du-i][j+1,k] - bb[i,du-i][j,k+1]):
		new[i,du-i][j,k] := simplify(h):
	    od:
       od:
       RETURN(new);
    fi:
    if dir = -2 then
       for i from 0 to du do
	    for j from 0 to dv-1 do
		k := dv-1-j:
		h  := dv*(bb[i,du-i][j,k+1] - bb[i,du-i][j+1,k]):
		new[i,du-i][j,k] := simplify(h):
	    od:
       od:
       RETURN(new);
    fi:

    if dir = 1 then
       for i from 0 to du-1 do
	    k := du-1-i:
	    for j from 0 to dv do
		h := du*(bb[i+1,k][j,dv-j] - bb[i,k+1][j,dv-j]):
		new[i,k][j,dv-j] := simplify(h):
	    od:
       od:
       RETURN(new);
    fi:
    if dir = -1 then
       for i from 0 to du-1 do
	    k := du-1-i:
	    for j from 0 to dv do
		h := du*(bb[i,k+1][j,dv-j] - bb[i+1,k][j,dv-j]):
		new[i,k][j,dv-j] := simplify(h):
	    od:
       od:
       RETURN(new);
    fi:

new:
end:

#-----------------------------------------------------------------------------

test := 0:
if test = 1 then
    bbd := bb4D(bb,1,1,1):
    print(bbd):
    mylibname := `/.arthur/u22/jorg/TEX/CURRENT/MLIB`;
    read ``.mylibname.`/`.bb4x1:
    b1 := bb4x1(bbd,0,1,-2,0):
    print(b1);
fi:
if test = 2 then
    bbd := bb4D(bb,3,3,2):
    #print(bbd):
    read bb4_x1:
    b1 := bb4_x1(bbd,3,2,1):
    print(b1);
fi: