球体同胚表面准各向同性采样附matlab代码

%% sphere_homeo_sfc_isotropic_splg%% Function to isotropically sample a given sphere-homeomorphic surface.%% Author & support : nicolas.douillet (at) free.fr, 2017-2020.%%% Syntax%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z);%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v);%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v, option_random_sampling);%%% Description%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z)% generates a tricolon vector / [60*120 3] matrix of X, Y, and Z coordinates% of points sampling the -sphere-homeomorphic- surface defined by% function handles fctn_x, fctn_y, and fctn_z.%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v)% generates range_u(1,3)*range_v(1,3) samples located in the area% [min(u), max(u)] x [min(v) max(v)] = [range_u(1,1), range_u(1,2)] x [range_v(1,1) range_v(1,2)]%% sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v, option_random_sampling)% randoms the sampling if option_random_sampling = 1,% else -option_random_sampling = 0- sampling is uniform.%%% See also%% <https://fr.mathworks.com/matlabcentral/fileexchange/64307-torus-homeomorphic-surface-quasi-isotropic-sampling?s_tid=prof_contriblnk torus_homeo_sfc_isotropic_splg>|% <https://fr.mathworks.com/matlabcentral/fileexchange/69212-geoid geoid> |% <https://fr.mathworks.com/help/matlab/ref/rand.html rand> | % <https://fr.mathworks.com/help/matlab/ref/mesh.html mesh> | % <https://fr.mathworks.com/help/matlab/ref/trimesh.html trimesh>%%% Input arguments%% - fctn_x : function handle in x direction, in spherical coordinates, assumed overloaded for vectors and matrices.%% - fctn_y : function handle in y direction, in spherical coordinates, assumed overloaded for vectors and matrices.%% - fctn_z : function handle in z direction, in spherical coordinates, assumed overloaded for vectors and matrices.%% - range_u : real row vector double, u parameter vector of type : [min(u), max(u), nb_samples_u].%% - range_v : real row vector double, v parameter vector of type : [min(v), max(v), nb_samples_v].%% - option_random_sampling : logical, *true (1) /false (0).%%% Output arguments%%        [| | |]% - M = [X Y Z], real matrix double, the point set. Size(M) = [nb_samples_u*nb_samples_v 3].%        [| | |]%% - u : real matrix double, the sampling matrix / grid in u direction. Size(u) = [nb_samples_u,nb_samples_v].%% - v : real matrix double, the sampling matrix / grid in v direction. Size(v) = [nb_samples_u,nb_samples_v].%%        [ |  |  |] % - T = [i1 i2 i3], positive integer matrix double, the triangulation. Size(T) = [nb_triangles,3].%        [ |  |  |] %%       with nb_triangles = nb_samples_u*(nb_samples_v-2).%       T is relevant only in the case option_random_sampling = false/0.%%% Example #1% Isotropic random samplingfctn_x = @(u,v)sin(u).*cos(v);fctn_y = @(u,v)sin(u).*sin(v);fctn_z = @(u,v)cos(u);range_u = [0 pi 20];    % latitude angle for a sphererange_v = [0 2*pi 40]; % longitude angle for a sphere[M1, u1, v1] = sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v);figure;plot3(M1(:,1), M1(:,2), M1(:,3), 'b.'), hold on;axis equal, axis square, axis tight;colormap([0 0 1]);%% Example #2% Isotropic regular sampling[M2, u2, v2, T] = sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v, 0);TRI = triangulation(T, M2(:,1), M2(:,2), M2(:,3));figure;trimesh(TRI), hold on;axis equal, axis square, axis tight;colormap([0 0 1]);