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# Advanced Mathematics and Mechanics Applications Using MATLAB, 3rd Edition

### Howard Wilson (view profile)

14 Oct 2002 (Updated )

Companion Software (amamhlib)

...
```function [x1,y1,x2,y2,x3,y3,xf,yf,zf]= ...
srfex(da,na,df,nf)
% [x1,y1,x2,y2,x3,y3,xf,yf,zf]= ...
%                            srfex(da,na,df,nf)
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%
% This graphics example draws three toruses
% intersecting a spike.
%
% User m functions called: frus, surfmany

if nargin==0
da=[4.0,.45]; na=[42,15];
df=[2.2,0,15]; nf=[43,4];
end

% Create a torus with polygonal cross section.
% Data for the torus is stored in da and na

r0=da(1); r1=da(2); nfaces=na(1); nlat=na(2);
t=linspace(0,2*pi,nlat)';
xz=[r0+r1*cos(t),r1*sin(t)];
z1=xz(:,2); z1=z1(:,ones(1,nfaces+1));
th=linspace(0,2*pi,nfaces+1);
x1=xz(:,1)*cos(th); y1=xz(:,1)*sin(th);
y2=x1; z2=y1; x2=z1; y3=x2; z3=y2; x3=z2;

% Create a frustum of a pyramid. Data for the
% frustum is stored in df and nf
rb=df(1); rt=df(2); h=df(3);
[xf,yf,zf]=frus(rb,rt,h,nf); zf=zf-.35*h;

% Plot four figures combined together
hold off; clf; close;
surfmany(x1,y1,z1,x2,y2,z2,x3,y3,z3,xf,yf,zf)
xlabel('x axis'); ylabel('y axis');
zlabel('z axis');
title('Spike and Intersecting Toruses');
axis equal; axis('off');
colormap([1 1 1]); figure(gcf); hold off;
% print -deps srfex

%=============================================

function [X,Y,Z]=frus(rb,rt,h,n,noplot)
%
% [X,Y,Z]=frus(rb,rt,h,n,noplot)
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%
% This function computes points on the surface
% of a conical frustum which has its axis along
% the z axis.
%
% rb,rt,h - the base radius,top radius and
%           height
% n       - vector of two integers defining the
%           axial and circumferential grid
%           increments on the surface
% noplot  - parameter input when no plot is
%           desired
%
% X,Y,Z   - points on the surface
%
% User m functions called: none

if nargin==0
rb=2; rt=1; h=3; n=[23, 35];
end

th=linspace(0,2*pi,n(2)+1)'-pi/n(2);
sl=sqrt(h^2+(rb-rt)^2); s=sl+rb+rt;
m=ceil(n(1)/s*[rb,sl,rt]);
rbot=linspace(0,rb,m(1));
rside=linspace(rb,rt,m(2));
rtop=linspace(rt,0,m(3));
r=[rbot,rside(2:end),rtop(2:end)];
hbot=zeros(1,m(1));
hside=linspace(0,h,m(2));
htop=h*ones(1,m(3));
H=[hbot,hside(2:end),htop(2:end)];
Z=repmat(H,n(2)+1,1);
xy=exp(i*th)*r; X=real(xy); Y=imag(xy);
if nargin<5
surf(X,Y,Z); title('Frustum'); xlabel('x axis')
ylabel('y axis'), zlabel('z axis')
grid on, colormap([1 1 1]);
figure(gcf);
end

%=============================================

function surfmany(varargin)
%function surfmany(x1,y1,z1,x2,y2,z2,...
%                x3,y3,z3,..,xn,yn,zn)
% This function plots any number of surfaces
% on the same set of axes without shape
% distortion. When no input is given then a
% six-legged solid composed of spheres and
% cylinders is shown.
%
% User m functions called: none
%----------------------------------------------

if nargin==0
% Default data for a six-legged solid
n=10; rs=.25; d=7; rs=2; rc=.75;
[xs,ys,zs]=sphere;  [xc,yc,zc]=cylinder;
xs=rs*xs; ys=rs*ys; zs=rs*zs;
xc=rc*xc; yc=rc*yc; zc=2*d*zc-d;
x1=xs; y1=ys; z1=zs;
x2=zs+d; y2=ys; z2=xs;
x3=zs-d; y3=ys; z3=xs;
x4=xs; y4=zs-d; z4=ys;
x5=xs; y5=zs+d; z5=ys;
x6=xs; y6=ys; z6=zs+d;
x7=xs; y7=ys; z7=zs-d;
x8=xc; y8=yc; z8=zc;
x9=zc; y9=xc; z9=yc;
x10=yc; y10=zc; z10=xc;
varargin={x1,y1,z1,x2,y2,z2,x3,y3,z3,...
x4,y4,z4,x5,y5,z5,x6,y6,z6,x7,y7,z7,...
x8,y8,z8,x9,y9,z9,x10,y10,z10};
end

% Find the data range
n=length(varargin);
r=realmax*[1,-1,1,-1,1,-1];
s=inline('min([a;b])','a','b');
b=inline('max([a;b])','a','b');
for k=1:3:n
x=varargin{k}; y=varargin{k+1};
z=varargin{k+2};
x=x(:); y=y(:); z=z(:);
r(1)=s(r(1),x); r(2)=b(r(2),x);
r(3)=s(r(3),y); r(4)=b(r(4),y);
r(5)=s(r(5),z); r(6)=b(r(6),z);
end

% Plot each surface
hold off, newplot
for k=1:3:n
x=varargin{k}; y=varargin{k+1};
z=varargin{k+2};
surf(x,y,z); axis(r), hold on
end

% Set axes and display the combined plot
axis equal, axis(r), grid on
xlabel('x axis'), ylabel('y axis')
zlabel('z axis')
title('SEVERAL SURFACES COMBINED')
% colormap([127/255 1 212/255]); % aquamarine
colormap([1 1 1]);, figure(gcf), hold off ```

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