How to make a function that calculates many coefficients (>100) and reclaim them on many functions without having to return all these values?

I have a surface, and I have to calculate A LOT of different coefficients for a point on this surface.

This is the function wich calculates the coeficientes on the point x=[u v] of a surface:

function the_coeficients_of_a_point_on_surface(x)
    u = x(1)
    v = x(2)

    %% Defines surface
    %Surface from Cazals article
    U = [0 0 0 0 0 1 1 1 1 1];
    V = [0 0 0 0 0 1 1 1 1 1];
    k = 4;
    l = 4;
    P        = [0 1/4 2/4 3/4 1;   0  1/4 2/4 3/4 4/4;   0  1/4 2/4 3/4 4/4;   0  1/4 2/4 3/4 4/4;  0 1/4 2/4 3/4 1];
    P(:,:,2) = [0  0   0   0  0;  1/4 1/4 1/4 1/4 1/4;  2/4 2/4 2/4 2/4 2/4;  3/4 3/4 3/4 3/4 3/4;  1  1   1   1  1];
    P(:,:,3) = [0  0   0   0  0;   0   1  -1  -1   0 ;   0  -1   1   1   0 ;   0   1  -1   1   0 ;  0  0   0   0  0];
    P(:,:,4) = [1  1   1   1  1;   1   1   1   1   1 ;   1   1   1   1   1 ;   1   1   1   1   1 ;  1  1   1   1  1];
    %corrects parameters
    P(:,:,1) = transpose(P(:,:,1));
    P(:,:,2) = transpose(P(:,:,2));
    P(:,:,3) = transpose(P(:,:,3));
    P(:,:,4) = transpose(P(:,:,4));
    %Puts everything on homogenous coordinates
    PW(:,:,1)   = P(:,:,4).*P(:,:,1);
    PW(:,:,2)   = P(:,:,4).*P(:,:,2);
    PW(:,:,3)   = P(:,:,4).*P(:,:,3);
    PW(:,:,4)   = P(:,:,4);

    %% Surface operations
    %- partial derivatives of the surface (order 1 to 4)
    %- Use squeeze(DS(c,d,:))' to get vector of partial derivative values
    DS = derivative_order_cd_NURBS_surface(u,v,U,V,PW,k+1,l+1,5,5);

    %% First fundamental form and its partial derivatives
    [E,Eu,Ev,Euu,Euv,Evv,...
     F,Fu,Fv,Fuu,Fuv,Fvv,...
     G,Gu,Gv,Guu,Guv,Gvv] = first_fundamental_form(squeeze(DS(2,1,:))',squeeze(DS(1,2,:))',...
                                                   squeeze(DS(3,1,:))',squeeze(DS(2,2,:))',squeeze(DS(1,2,:))',...
                                                   squeeze(DS(4,1,:))',squeeze(DS(3,2,:))',squeeze(DS(2,3,:))',squeeze(DS(1,4,:))');

    %% Surface normal, Rational Surface Normal (bar) and its partial derivatives
    [N,barN,...
     barNu,barNv,...
     barNuu,barNuv,barNvv] = surface_normal(squeeze(DS(2,1,:))',squeeze(DS(1,2,:))',...
                                            squeeze(DS(3,1,:))',squeeze(DS(2,2,:))',squeeze(DS(1,2,:))',...
                                            squeeze(DS(4,1,:))',squeeze(DS(3,2,:))',squeeze(DS(2,3,:))',squeeze(DS(1,4,:))');

    %% Second fundamental form, rational Second fundamental form (bar) and its partial derivatives
    [e,bare,...
     bareu,barev,bareuu,bareuv,barevv,...
     f,barf,...
     barfu,barfv,barfuu,barfuv,barfvv,...
     g,barg,...
     bargu,bargv,barguu,barguv,bargvv] = second_fundamental_form(squeeze(DS(3,1,:))',squeeze(DS(2,2,:))',squeeze(DS(1,2,:))',...
                                                                 squeeze(DS(4,1,:))',squeeze(DS(3,2,:))',squeeze(DS(2,3,:))',squeeze(DS(1,4,:))',...
                                                                 squeeze(DS(5,1,:))',squeeze(DS(4,2,:))',squeeze(DS(3,3,:))',squeeze(DS(2,4,:))',squeeze(DS(1,5,:))',...
                                                                 N,barN,barNu,barNv,barNuu,barNuv,barNvv);

    %% Principal curvatures coefficients and its partial derivatives
    [A,Au,Av,Auu,Auv,Avv,...
     B,barB,barBu,barBv,barBuu,barBuv,barBvv,...
     C,barC,barCu,barCv,barCuu,barCuv,barCvv] = auxiliary_ABC(E,Eu,Ev,Euu,Euv,Evv,...
                                                              F,Fu,Fv,Fuu,Fuv,Fvv,...
                                                              G,Gu,Gv,Guu,Guv,Gvv,...
                                                              e,bare,bareu,barev,bareuu,bareuv,barevv,...
                                                              f,barf,barfu,barfv,barfuu,barfuv,barfvv,...
                                                              g,barg,bargu,bargv,barguu,barguv,bargvv);

    %% Rational coefficients for ridges and umbilics
    [Pu,Puu,Puv,Pv,Pvu,Pvv,...
     Ru,Ruu,Ruv,Rv,Rvu,Rvv,...
     Q,Qu,Qv] = auxiliary_PRQ(A,Au,Av,Auu,Auv,Avv,...
                              barB,barBu,barBv,barBuu,barBuv,barBvv,...
                              barC,barCu,barCv,barCuu,barCuv,barCvv);
end

I have all these coefficients and I wanted them to work like the code below on many functions:

function [y] = critical_points(x)
    the_coeficients_of_a_point_on_surface(x)
    %% Algorithm description
    %--Generates curvature critical points system of equations
    y(1) = Q.*(Pu.^2) - Ru.^2;
    y(2) = Q.*(Pv.^2) - Rv.^2;
end

The reason behind this is because I'll have to use these smaller functions in a lot of other functions, and I really want these smaller functions to have only "x" as input. The smaller function doesn't work. Is there a way to define the function "the_coeficients_of_a_point_on_surface(x)" so the "critical_points(x)" function works?

I'll have lots of other smaller functions that will use all the coefficients, not only the coefficients "critical_points(x)" is using. The point is: I don't want to make "the_coeficients_of_a_point_on_surface(x)" to return ALL its coefficients. I just want to be able to calculate and use them on functions that look like "critical_points(x)"

Answer 1

[John D'Errico]

Return a single struct that contains all of these variables as fields.