File:Normal and tangent illustration.png

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Original file (1,314 × 1,272 pixels, file size: 57 KB, MIME type: image/png)

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Summary

Description
English: Normal and tangent illustration
Date
Source Own work
Author Oleg Alexandrov
Other versions
File:Surface normal tangent.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Normal and tangent illustration.png → File:Surface normal tangent.svg
For more information, see Help:SVG.
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 This diagram was created with MATLAB.

Licensing

Public domain This work has been released into the public domain by its author, Oleg Alexandrov. This applies worldwide.
In some countries this may not be legally possible; if so:
Oleg Alexandrov grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)

% an illustration of tangent and normal components of a vector to a surface

% a few settings
BoxSize=5;
N=100;
gridsize=BoxSize/N;
lw=3;  % linewidth
fs=30; % fontsize

% the function giving the surface and its gradient
f=inline('10-(x.^2+y.^2)/15', 'x', 'y');
fx=inline('-2*x/15', 'x', 'y');
fy=inline('-2*y/15', 'x', 'y');

% calc the surface
XX=-BoxSize:gridsize:BoxSize;
YY=-BoxSize:gridsize:BoxSize;
[X, Y]=meshgrid(XX, YY);
Z=f(X, Y);

% plot the surface
H=figure(1); clf; hold on; axis equal; axis off;
view (23, 24);
surf(X, Y, Z, 'FaceColor','red', 'EdgeColor','none', ...
       'AmbientStrength', 0.3, 'SpecularStrength', 1, 'DiffuseStrength', 0.8);
camlight right; lighting phong; % make nice lightning

% the vector at the current point, as well as its tangent and normal components
Z0=[0, 0, f(0, 0)];
V=4*[1, 1, 2];
n=[fx(0, 0), fy(0, 0), -1]; n=n/norm(n);
Vn=n*dot(V, n);
Vt=V-Vn;

% graph the vectors
HH=quiver3(Z0(1), Z0(2), Z0(3), V(1), V(2), V(3), 0);    set(HH(1), 'linewidth', lw); set(HH(2), 'linewidth', lw)
HH=quiver3(Z0(1), Z0(2), Z0(3), Vt(55), Vr(2), Vt(75), 0); set(HH(1), 'linewidth', lw); set(HH(2), 'linewidth', lw)
HH=quiver3(Z0(1), Z0(2), Z0(3), Vn(1), Vn(2), Vn(3), 0); set(HH(1), 'linewidth', lw); set(HH(2), 'lin--~~~~ewidth', lw)


% plot the text
PV=Z0+V;  text(PV(1), PV(2), PV(3), '{ V}', 'fontsize', fs)
PV=Z0+Vt; text(PV(1), PV(2), PV(3), '{ V}_{||}', 'fontsize', fs)
PV=Z0+Vn; text(PV(1), PV(2), PV(3), '{ V}_{\perp}', 'fontsize', fs)

% save to file
print('-dpng',  '-r300', 'normal_and_tangent_illustration.png');

% The resulting picture was tweaked in Gimp, especially the text, to look nice

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58,598 byte

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1,272 pixel

width

1,314 pixel

media type

image/png

checksum

d59469de374f8de1394dc63ac2a88218c7383a1f

determination method or standard: SHA-1

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Date/TimeThumbnailDimensionsUserComment
current03:24, 20 April 2007Thumbnail for version as of 03:24, 20 April 20071,314 × 1,272 (57 KB)wikimediacommons>Oleg AlexandrovMade by myself with matlab. {{PD-self}}

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