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| View Original: | Normal and tangent illustration.png (1314x1272) | |||
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| Keywords: Normal and tangent illustration.png Made by myself with matlab Surface normal tangent svg Source code MATLAB <source lang 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 </source> Tangent vectors Surface plots Files by User Oleg Alexandrov from en wikipedia Images with Matlab source code math | ||||
