球体同胚表面准各向同性采样附matlab代码.zip

function [M, u, v, T] = sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v, option_random_sampling) %% 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 = true/1, % else -option_random_sampling = false/0- sampling is uniform. % % % See also : RAND, MESH, 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 % % Unit sphere sampling % fctn_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 sphere % range_v = [0 2*pi 40]; % longitude angle for a sphere % % [M1, u, v] = sphere_homeo_sfc_isotropic_splg(fctn_x, fctn_y, fctn_z, range_u, range_v); % [M2, u, v, 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; % subplot(1,2,1); % plot3(M1(:,1), M1(:,2), M1(:,3), 'b.'), hold on; % axis equal, axis square, axis tight; % colormap([0 0 1]); % subplot(1,2,2); % trimesh(TRI), hold on; % axis equal, axis square, axis tight; % colormap([0 0 1]); %% Input parsing assert(nargin >= 3, 'Not enough input arguments.'); assert(nargin < 7, 'Too many input arguments.'); if nargin < 6 option_random_sampling = 1; disp('Random sampling option selected by default.'); if nargin < 5 range_v = [0 2*pi 120]; disp('range_v missing ; default vector is [0 pi 120]'); if nargin < 4 range_u = [0 pi 60]; disp('range_u missing ; default vector is [0 pi 60]'); end end end % Check function handles assert(isa(fctn_x,'function_handle'), 'fctn_x is not a function handle'); assert(isa(fctn_y,'function_handle'), 'fctn_y is not a function handle'); assert(isa(fctn_z,'function_handle'), 'fctn_z is not a function handle'); % Check (u, v) parameter ranges assert(numel(range_u) >= 2, 'No range_u max value ; range_u must contain at least two elements.'); if size(range_u,2) < 2 range_u = range_u'; end if (size(range_u,2) < 3 || range_u(1,3) < 1) range_u = cat(2, range_u, 60); warning('range_u : missing or incorrect value for the number of samples ; set to 60 by default'); else assert(isreal(range_u(1,3)) && range_u(1,3) >= 1 && rem(range_u(1,3),1) == 0, 'range_u number of elements must be an integer.'); end u_min = range_u(1,1); u_max = range_u(1,2); nb_samples_u = range_u(1,3); assert(u_max >= u_min, 'range_u : must be u_min <= u_max.'); assert(numel(range_v) >= 2, 'no range_v max value ; range_v must contain at least two elements.'); if size(range_v,2) < 2 range_v = range_v'; end if(size(range_v,2) < 3 || range_v(1,3) < 1) range_v = cat(2, range_v, 120); disp('range_v number of samples missing or incorrect value ; set to 120 by default'); else assert(isreal(range_v(1,3)) && range_v(1,3) >= 1 && rem(range_v(1,3),1) == 0, 'range_v number of elements must be an integer.'); end %% Body v_min = range_v(1,1); v_max = range_v(1,2); nb_samples_v = range_v(1,3); assert(v_max >= v_min, 'range_v : must be v_min <= v_max.'); % Surface sampling [~, u_step] = meshgrid(linspace(-1,1,nb_samples_v), linspace(-1,1,nb_samples_u)); u_rand = 2*(rand(nb_samples_u, nb_samples_v) - 0.5); u = option_random_sampling * u_rand + (1-option_random_sampling) * u_step; u = acos(u)/pi; u = u_min + u_max * u; v_step = meshgrid(linspace(0,1,nb_samples_v), linspace(0,1,nb_samples_u)); v_rand = rand(nb_samples_u, nb_samples_v); v = option_random_sampling * v_rand + (1-option_random_sampling) * v_step; v = v_min + v_max * v; X = fctn_x(u,v); Y = fctn_y(u,v); Z = fctn_z(u,v); % Triplet indices for mesh facets T = zeros(nb_samples_u*nb_samples_v, 3); row_idx = 1; i = 1; while(i < nb_samples_v) j = 1; while(j < nb_samples_u) T(row_idx, :) = [(i-1)*nb_samples_u+j (i-1)*nb_samples_u+j+1 i*nb_samples_u+j]; row_idx = row_idx + 1; T(row_idx, :) = [i*nb_samples_u+j i*nb_samples_u+j+1 (i-1)*nb_samples_u+j+1]; row_idx = row_idx + 1; j = j + 1; end % begin-end loop junction T(row_idx, :) = [(i-1)*nb_samples_u+j (i-1)*nb_samples_u+1 i*nb_samples_u+j]; row_idx = row_idx + 1; T(row_idx, :) = [i*nb_samples_u+j i*nb_samples_u (i-1)*nb_samples_u+1]; row_idx = row_idx + 1; i = i + 1; end % Format X, Y, Z data into M matrix assert(numel(X) == numel(Y) && numel(X) == numel(Z) && numel(Y) == numel(Z), 'X, Y, and Z numbers of elements mismatch.'); assert(size(X,1) == size(Y,1) && size(X,1) == size(Z,1) && size(Y,1) == size(Z,1), 'X, Y, and Z dimensions mismatch.'); if size(X,2) > 1 X = X(:); Y = Y(:); Z = Z(:); end M = [X Y Z]; end % sphere_homeo_sfc_isotropic_splg