# Maple code to define Lagrange interpolating functions/coords/coeffs
# $Header$

################################################################################

#
# 1-D interpolating functions
#

fn_1d_order1 :=
proc(x)
+ c0 + c1*x
end proc;

fn_1d_order2 :=
proc(x)
+ c0 + c1*x + c2*x^2
end proc;

fn_1d_order3 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3
end proc;

fn_1d_order4 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4
end;

fn_1d_order5 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5
end;

fn_1d_order6 :=
proc(x)
+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6
end;

########################################

# coordinates for 1-D interpolating functions
coords_list_1d := [x];

########################################

#
# coefficients in 1-D interpolating functions
#

coeffs_list_1d_order1 := [c0, c1];
coeffs_list_1d_order2 := [c0, c1, c2];
coeffs_list_1d_order3 := [c0, c1, c2, c3];
coeffs_list_1d_order4 := [c0, c1, c2, c3, c4];
coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5];
coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6];

################################################################################

#
# 2-D interpolating functions (maximum degree)
#

fn_2d_order1 :=
proc(x,y)
+ c01*y
+ c00   + c10*x
end proc;

fn_2d_order2 :=
proc(x,y)
+ c02*y^2
+ c01*y   + c11*x*y
+ c00     + c10*x   + c20*x^2
end proc;

fn_2d_order3 :=
proc(x,y)
+ c03*y^3
+ c02*y^2 + c12*x*y^2
+ c01*y   + c11*x*y   + c21*x^2*y
+ c00     + c10*x     + c20*x^2   + c30*x^3
end proc;

fn_2d_order4 :=
proc(x,y)
+ c04*y^4
+ c03*y^3 + c13*x*y^3
+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2
+ c01*y   + c11*x*y   + c21*x^2*y   + c31*x^3*y
+ c00     + c10*x     + c20*x^2     + c30*x^3   + c40*x^4
end;

########################################

# coordinates for 2-D interpolating functions
coords_list_2d := [x,y];

########################################

#
# coefficients in 2-D interpolating functions (maximum degree)
#

coeffs_list_2d_order1 := [
			 c01,
			 c00, c10
			 ];
coeffs_list_2d_order2 := [
			 c02,
			 c01, c11,
			 c00, c10, c20
			 ];
coeffs_list_2d_order3 := [
			 c03,
			 c02, c12,
			 c01, c11, c21,
			 c00, c10, c20, c30
			 ];
coeffs_list_2d_order4 := [
			 c04,
			 c03, c13,
			 c02, c12, c22,
			 c01, c11, c21, c31,
			 c00, c10, c20, c30, c40
			 ];

################################################################################

#
# 3-D interpolating functions (maximum degree)
#

fn_3d_order1 :=
proc(x,y,z)
# z^0 -----------
+ c010*y
+ c000   + c100*x
# z^1 -----------
+ c001*z
end proc;

fn_3d_order2 :=
proc(x,y,z)
# z^0 --------------------------
+ c020*y^2
+ c010*y   + c110*x*y
+ c000     + c100*x   + c200*x^2
# z^1 --------------------------
+ c011*y*z
+ c001*z   + c101*x*z
# z^2 --------------------------
+ c002*z^2
end proc;

fn_3d_order3 :=
proc(x,y,z)
# z^0 -------------------------------------------
+ c030*y^3
+ c020*y^2   + c120*x*y^2
+ c010*y     + c110*x*y   + c210*x^2*y
+ c000       + c100*x     + c200*x^2   + c300*x^3
# z^1 -------------------------------------------
+ c021*y^2*z
+ c011*y  *z + c111*x*y*z
+ c001    *z + c101*x  *z + c201*x^2*z
# z^2 -------------------------------------------
+ c012*y*z^2
+ c002  *z^2 + c102*x*z^2
# z^3 -------------------------------------------
+ c003  *z^3
end proc;

fn_3d_order4 :=
proc(x,y,z)
# z^0 --------------------------------------------------------
+ c040*y^4
+ c030*y^3     + c130*x*y^3
+ c020*y^2     + c120*x*y^2   + c220*x^2*y^2
+ c010*y       + c110*x*y     + c210*x^2*y   + c310*x^3*y
+ c000         + c100*x       + c200*x^2     + c300*x^3   + c400*x^4
# z^1 -------------------------------------------
+ c031*y^3*z
+ c021*y^2*z   + c121*x*y^2*z
+ c011*y  *z   + c111*x*y  *z + c211*x^2*y*z
+ c001    *z   + c101*x    *z + c201*x^2  *z + c301*x^3*z
# z^2 -------------------------------------------
+ c022*y^2*z^2
+ c012*y  *z^2 + c112*x*y*z^2
+ c002    *z^2 + c102*x  *z^2 + c202*x^2*z^2
# z^3 -------------------------------------------
+ c013*y  *z^3
+ c003    *z^3 + c103*x  *z^3
# z^4 -------------------------------------------
+ c004    *z^4
end;

########################################

# coordinates for 3-D interpolating functions
coords_list_3d := [x,y,z];

########################################

#
# coefficients in 3-D interpolating functions (maximum degree)
#

coeffs_list_3d_order1 := [
			 # z^0 -----
			 c010,
			 c000, c100,
			 # z^1 -----
			 c001
			 ];
coeffs_list_3d_order2 := [
			 # z^0 -----------
			 c020,
			 c010, c110,
			 c000, c100, c200,
			 # z^1 -----------
			 c011,
			 c001, c101,
			 # z^2 -----------
			 c002
			 ];
coeffs_list_3d_order3 := [
			 # z^0 ----------------
			 c030,
			 c020, c120,
			 c010, c110, c210,
			 c000, c100, c200, c300,
			 # z^1 ----------------
			 c021,
			 c011, c111,
			 c001, c101, c201,
			 # z^2 ----------------
			 c012,
			 c002, c102,
			 # z^3 ----------------
			 c003
			 ];
coeffs_list_3d_order4 := [
			 # z^0 -----------------------
			 c040,
			 c030, c130,
			 c020, c120, c220,
			 c010, c110, c210, c310,
			 c000, c100, c200, c300, c400,
			 # z^1 -----------------------
			 c031,
			 c021, c121,
			 c011, c111, c211,
			 c001, c101, c201, c301,
			 # z^2 -----------------------
			 c022,
			 c012, c112,
			 c002, c102, c202,
			 # z^3 -----------------------
			 c013,
			 c003, c103,
			 # z^4 -----------------------
			 c004
			 ];

################################################################################