File:Surface integral illustration.svg
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![File:Surface integral illustration.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Surface_integral_illustration.svg/512px-Surface_integral_illustration.svg.png)
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Summary
DescriptionSurface integral illustration.svg |
English: The definition of surface integral relies on splitting the surface into small surface elements. Figure 1: The definition of surface integral relies on splitting the surface into small surface elements. Each element is associated with a vector dS of magnitude equal to the area of the element and with direction normal to the element and pointing outward. |
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Date | 11 December 2014 | |||
Source | Own work based on: Surface integral illustration.png & SVG - Export of figures | |||
Author | McMetrox | |||
Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following license:
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Other versions |
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SVG development InfoField | ||||
Source code InfoField | MATLAB code% An illustration of the surface integral.
% It shows how a surface is split into surface elements.
function main()
% the function giving the surface and its gradient
f=inline('10-(x.^2+y.^2)/15', 'x', 'y');
BoxSize=5; % surface dimensions are 2*BoxSize x 2*BoxSize
M = 10; % M x M = the number of surface elements into which to split the surface
N=10; % N x N = number of points in each surface element
spacing = 0.1; % spacing between surface elements
H=2*BoxSize/(M-1); % size of each surface element
gridsize=H/N; % distance between points on a surface element
figure(1); clf; hold on; axis equal; axis off;
for i=1:(M-1)
for j=1:(M-1)
Lx = -BoxSize + (i-1)*H+spacing; Ux = -BoxSize + (i )*H-spacing;
Ly = -BoxSize + (j-1)*H+spacing; Uy = -BoxSize + (j )*H-spacing;
% calc the surface element
XX=Lx:gridsize:Ux;
YY=Ly:gridsize:Uy;
[X, Y]=meshgrid(XX, YY);
Z=f(X, Y);
% plot the surface element
surf(X, Y, Z, 'FaceColor','red', 'EdgeColor','none', ...
'AmbientStrength', 0.3, 'SpecularStrength', 1, 'DiffuseStrength', 0.8);
end
end
view (-18, 40); % viewing angle
%camlight headlight; lighting phong; % make nice lightning
% save to file
plot2svg('Surface_integral_illustration.svg');
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Captions
surface integral
Items portrayed in this file
depicts
11 December 2014
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:36, 12 December 2014 | ![]() | 512 × 348 (20 KB) | wikimediacommons>McMetrox | Reduced file size |
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Image title | Matlab Figure Converted by PLOT2SVG written by Juerg Schwizer |
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Width | 100% |
Height | 100% |