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| Keywords: Surface integral illustration.svg en 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 own based Surface integral illustration png http //www mathworks com/matlabcentral/fileexchange/7401-scalable-vector-graphics--svg--export-of-figures SVG - Export of figures McMetrox 2014-12-11 see below SVG Created with MATLAB v none Surface integral illustration png png Cc-zero Source code MATLAB <source lang matlab > 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' ; </source> Images with Matlab source code Surface plots Grids | ||||
