Generating line equation describing an axisymetric body (blunt sphere-cone)

I am attempting to generate a script file which will generate the equation of a line in 2d for an axisymetric body. I am wishing to create a radially-nosed frustrum wich then has a shoulder radius at the widest point. The symetry is taken about the X axis, with (0,0) denoting the origin of the co-ordinate scheme.

I have user definable variables of nose radius, body radius, cone semiangle, shoulder radius.

I can extrapolate the points of tangency between the nose radius and frustrum, and shoulder radius and frustrum.

code extract following:

%This script will generate the forebody heatshield geometry of a generic %aeroshell

%state the known input variables

%Rb Body radius

%Rs Shoulder radius

%Rn Nose radius

%THETA frustrum semi-angle

%define the co-ordinates of the sphere-frustrum and frustrum-shoulder line %segments

% x and y co-ordinates of nose-frustrum tangent: xtn=Rn*[1-sin(THETA)]; ytn=Rn*cos(THETA);

% x and y co-ordinates of frustrum-shoulder tangent

xts=Rn*[1-sin(THETA)]+[Rb-Rn*cos(THETA)-Rs*(1-cos(THETA))]*cot(THETA); yts=(Rb-Rn)*[1-cos(THETA)];

%Rl Forebody depth = (xts+Rs) Rl=(xts+Rs);

%define origin and end points of the line x1=0; y1=0;

x2=Rl; y2=0;

%define the length of the line for the aeroshell x axis

%x=linspace(x1,R1,x2);

%create the function describing the line %interim equation for frustrum XF=linspace(254.7,1754.1,1499);

YF=0.994*(XF); plot(XF,YF)

% plot the graph of the function.

figure(1) plot(XF,YF,'r+-') axis square

% plot a surface plot of the function above to create 3D body % use the cylinder command to obtain the desired geometry.

figure(2) [X,Y,Z] = cylinder(YF); surf(Z,Y,X); axis square colorbar

%plot surface normal vectors

figure(3) [X,Y,Z] = cylinder(YF); surfnorm(-Z,-Y,-X,'FaceColor','green','EdgeColor','none'); axis square, grid on,camlight left; lighting phong

%rotate the line function around axis of symetry

%create a surface plot of the line

I would like to create the line equation describing this curve which can then be plotted against an x axis x axis linespace command. The cylinder plot commander and surface normal vectors will be used to generate the plot form the data produced

Given my available data variables, how can i either interpolate all of the line points, or create an equation describing the entire line? If further clarification or images are required I can upload them.