# Construction of complex geometry using command lines

### Hongxue Cai (view profile)

09 Jan 2006 (Updated )

complex geometry using command lines

cgeometry.m
```%   ------    These codes show you how to construct and mesh complex geometry
%   ------    using command lines, very useful for solving
%   ------    PDEs in continous domains
%   ------           by Hongxue Cai @ Northwestern University   -------------->

% These code need MATLAB PDE Toolbox

%x, y-coordinates of the geometrical elements which dfining the geometrical
%domain. These values come from an application which models the tectorial
%membrane in the inner ear. These should be different for different
%applications, therefore readers should not pay much attention to the
%individual numbers.
xy = [
-0.01430000000000   0.00255766422613
-0.00954483106568   0.00776466551413
-0.00411900762330   0.00903776158615
0.00152629824713   0.00978098020364
0.00236820179834   0.00774844523211
-0.01760000000000   0.00187878393617
-0.01760000000000  -0.00013871129459
-0.01474101729286   0.00047264657699
-0.01122101729286   0.00031358294595
];

% x, y- coordinates and radius of the center point for circular arcs
xycR = [
-0.01760000000000   0.01023878393617   0.00836000000000
-0.00605407636840   0.00508611522649   0.00440000000000
-0.00268321950888   0.01994365506126   0.01100000000000
0.00194725002273   0.00876471271787   0.00110000000000
-0.01354587812765  -0.01210697797173   0.01263626967942
];

x = xy(:, 1);
y = xy(:, 2);
xc = xycR(:, 1);
yc = xycR(:, 2);
Rc = xycR(:, 3);

%geometry matrix, in which, each colum defines a geometrical element that
%can be either a line or a circular arc. (Note that any complex geometry can
%be composed by line and circular arts.) In each colum, the number in row#1
%indicates the type of the geometrica element, 2 for line element, 2 for
%circular arts. Then, row#2 is the x-coordinate of the starting point;
%row#3, that of the ending point; Row #4 and #5 are, respectively the
%y-coordinates of the the starting and ending point. The number in the 6th
%anf 7th
%rows indicate the location of geometric domain, (0,1) on the left side of this
%geometric element, (1,0) on th right. The rows 8, 9, 10 are zero for line,
%and repesent the x, y-coordinates and the radius of the center point for a
%circular arc.
gTM = [
2       1       1	    1 	    2  	    2 	    1	    1	    1
x(1)    x(3)    x(3)	x(5)  	x(9)  	x(7)	x(6)	x(9)	x(8)
x(2)    x(2)    x(4)	x(4)  	x(5)	x(6)	x(1)	x(8)	x(7)
y(1)    y(3)    y(3)	y(5)	y(9)	y(7)	y(6)	y(9)	y(8)
y(2)    y(2)    y(4)	y(4)	y(5)	y(6)	y(1)	y(8)	y(7)
0       1       0	    1	    1	    0	    0	    0	    0
1       0       1	    0	    0	    1	    1	    1	    1
0       xc(2)   xc(3)   xc(4)	0	    0	    xc(1)	xc(5)	xc(5)
0       yc(2)   yc(3)   yc(4)	0	    0	    yc(1)	yc(5)	yc(5)
0       Rc(2)   Rc(3)	Rc(4)	0	    0	    Rc(1)	Rc(5)	Rc(5)
];

%plotting geometry
figure
pdegplot(gTM)

%meshing
[pTM,eTM,tTM] = initmesh(gTM);
[pTM,eTM,tTM] = refinemesh(gTM,pTM,eTM,tTM);

%plotting mesh
figure
pdemesh(pTM,eTM,tTM);```