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function seashell (a, b, c, n, azimuth, elevation, res)
% SEASHELL draws a pretty seashell, using a 3D parametric surface.
%
% Usage:
%
% seashell (a, b, c, n, azimuth, elevation, res)
% seashell ('spin') ;
%
% All arguments are optional. The first four control the coefficients of
% the parametric surface (u and v are the surface parameters):
%
% x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ;
% y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ;
% z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ;
%
% a,b: these determine how pointy or flat the shell is (informally...)
% c: determines how much the shell overlaps with itself
% n: the number of spirals in the shell
%
% azimuth, elevation: determines the viewing angle (see the 'view' function)
% res: the mesh size (res-by-res). A larger number gives a smoother surface.
%
% If the azimuth is Inf, then the seashell view is spun dynamically.
% Also try seashell ('spin') ;
%
% References:
% T. Davis & K. Sigmon, MATLAB Primer, 7th edition, CRC Press, 2005, pp. 80.
% von Seggern, CRC Standard Curves and Surfaces, 2nd edition, CRC Press,
% 1993, pp. 306-307.
%
% Example:
% seashell ; % draws the front cover of the MATLAB Primer
% seashell (-0.5) ; % draws the back cover
% seashell (a,b,c,n,az,el,res) ; % all options, defaults:
% % a=-0.2, b=0.5, c=0.1, n=2, az=-150, el=10, res=128
%
% for a = -1:.1:1
% seashell (a) ;
% drawnow ;
% end
% for b = -1:.1:1
% seashell (-.2, b) ;
% drawnow
% end
%
% See also SHELLGUI, SURF, VIEW, LINSPACE, MESHGRID, SHADING, LIGHTING,
% LIGHTANGLE, COLORMAP, AXIS, MATERIAL, SIN, COS, PI.
% SHELLGUI, Copyright (c) 2006, Timothy A Davis. All Rights Reserved.
% SPDX-License-Identifier: BSD-3-clause
% use default input parameters, if not present
if (nargin == 1 && ischar (a))
in = -1 ;
else
in = nargin ;
end
if (in < 1)
a = -0.2 ;
end
if (in < 2)
b = 0.5 ;
end
if (in < 3)
c = 0.1 ;
end
if (in < 4)
n = 2 ;
end
if (in < 5)
azimuth = -150 ;
end
if (in < 6)
elevation = 10 ;
end
if (in < 7)
res = 128 ;
end
if (in == -1)
azimuth = Inf ;
end
% sanity checks
if (a == 0)
a = 0.01 ;
end
if (n <= 0)
n = 0.1 ;
end
% construct the res-by-res mesh
t = linspace(0, 2*pi, res) ;
[u,v] = meshgrid(t) ;
% define the surface
x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ;
y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ;
z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ;
% plot the surface
surf(x,y,z,y)
shading interp
axis off
axis equal
colormap(hsv(1024))
material shiny
lighting gouraud
lightangle(80, -40)
lightangle(-90, 60)
% fix the view, or spin the seashell
if (isfinite (azimuth))
view([azimuth elevation])
else
for az = -180:10:180
view ([az elevation])
drawnow
end
end
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