Mercurial > octave
view scripts/plot/draw/ostreamtube.m @ 31706:597f3ee61a48 stable
update Octave Project Developers copyright for the new year
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 06 Jan 2023 13:11:27 -0500 |
parents | 796f54d4ddbf |
children | 2e484f9f1f18 |
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######################################################################## ## ## Copyright (C) 2019-2023 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} ostreamtube (@var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) ## @deftypefnx {} {} ostreamtube (@var{u}, @var{v}, @var{w}, @var{sx}, @var{sy}, @var{sz}) ## @deftypefnx {} {} ostreamtube (@var{xyz}, @var{x}, @var{y}, @var{z}, @var{u}, @var{v}, @var{w}) ## @deftypefnx {} {} ostreamtube (@dots{}, @var{options}) ## @deftypefnx {} {} ostreamtube (@var{hax}, @dots{}) ## @deftypefnx {} {@var{h} =} ostreamtube (@dots{}) ## Calculate and display streamtubes. ## ## Streamtubes are approximated by connecting circular crossflow areas ## along a streamline. The expansion of the flow is determined by the local ## crossflow divergence. ## ## The vector field is given by @code{[@var{u}, @var{v}, @var{w}]} and is ## defined over a rectangular grid given by @code{[@var{x}, @var{y}, @var{z}]}. ## The streamtubes start at the seed points ## @code{[@var{sx}, @var{sy}, @var{sz}]}. ## ## The tubes are colored based on the local vector field strength. ## ## The input parameter @var{options} is a 2-D vector of the form ## @code{[@var{scale}, @var{n}]}. The first parameter scales the start radius ## of the streamtubes (default 1). The second parameter specifies the number ## of vertices that are used to construct the tube circumference (default 20). ## ## @code{ostreamtube} can be called with a cell array containing pre-computed ## streamline data. To do this, @var{xyz} must be created with the ## @code{stream3} function. This option is useful if you need to alter the ## integrator step size or the maximum number of vertices of the streamline. ## ## If the first argument @var{hax} is an axes handle, then plot into this axes, ## rather than the current axes returned by @code{gca}. ## ## The optional return value @var{h} is a graphics handle to the plot ## objects created for each streamtube. ## ## Example: ## ## @example ## @group ## [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3:0.1:0); ## u = -x / 10 - y; ## v = x - y / 10; ## w = - ones (size (x)) / 10; ## ostreamtube (x, y, z, u, v, w, 1, 0, 0); ## @end group ## @end example ## ## @seealso{stream3, streamline, streamribbon, streamtube} ## @end deftypefn ## References: ## ## @inproceedings{ ## title = {Visualization of 3-D vector fields - Variations on a stream}, ## author = {Dave Darmofal and Robert Haimes}, ## year = {1992} ## } ## ## @article{ ## title = {Efficient streamline, streamribbon, and streamtube constructions on unstructured grids}, ## author = {Ueng, Shyh-Kuang and Sikorski, C. and Ma, Kwan-Liu}, ## year = {1996}, ## month = {June}, ## publisher = {IEEE Transactions on Visualization and Computer Graphics}, ## } function h = ostreamtube (varargin) [hax, varargin, nargin] = __plt_get_axis_arg__ ("ostreamtube", varargin{:}); options = []; xyz = []; switch (nargin) case 6 [u, v, w, spx, spy, spz] = varargin{:}; [m, n, p] = size (u); [x, y, z] = meshgrid (1:n, 1:m, 1:p); case 7 if (iscell (varargin{1})) [xyz, x, y, z, u, v, w] = varargin{:}; else [u, v, w, spx, spy, spz, options] = varargin{:}; [m, n, p] = size (u); [x, y, z] = meshgrid (1:n, 1:m, 1:p); endif case 8 [xyz, x, y, z, u, v, w, options] = varargin{:}; case 9 [x, y, z, u, v, w, spx, spy, spz] = varargin{:}; case 10 [x, y, z, u, v, w, spx, spy, spz, options] = varargin{:}; otherwise print_usage (); endswitch scale = 1; num_circum = 20; if (! isempty (options)) switch (numel (options)) case 1 scale = options(1); case 2 scale = options(1); num_circum = options(2); otherwise error ("ostreamtube: OPTIONS must be a 1- or 2-element vector"); endswitch if (! isreal (scale) || scale <= 0) error ("ostreamtube: SCALE must be a real scalar > 0"); endif if (! isreal (num_circum) || num_circum < 3) error ("ostreamtube: number of tube vertices N must be greater than 2"); endif num_circum = fix (num_circum); endif if (isempty (hax)) hax = gca (); else hax = hax(1); endif if (isempty (xyz)) xyz = stream3 (x, y, z, u, v, w, spx, spy, spz, 0.2); endif div = divergence (x, y, z, u, v, w); ## Use the bounding box diagonal to determine the starting radius mxx = mnx = mxy = mny = mxz = mnz = []; j = 1; for i = 1 : length (xyz) sl = xyz{i}; if (! isempty (sl)) slx = sl(:,1); sly = sl(:,2); slz = sl(:,3); mxx(j) = max (slx); mnx(j) = min (slx); mxy(j) = max (sly); mny(j) = min (sly); mxz(j) = max (slz); mnz(j) = min (slz); j += 1; endif endfor dx = max (mxx) - min (mnx); dy = max (mxy) - min (mny); dz = max (mxz) - min (mnz); rstart = scale * sqrt (dx*dx + dy*dy + dz*dz) / 25; h = []; for i = 1 : length (xyz) sl = xyz{i}; num_vertices = rows (sl); if (! isempty (sl) && num_vertices > 2) usl = interp3 (x, y, z, u, sl(:,1), sl(:,2), sl(:,3)); vsl = interp3 (x, y, z, v, sl(:,1), sl(:,2), sl(:,3)); wsl = interp3 (x, y, z, w, sl(:,1), sl(:,2), sl(:,3)); vv = sqrt (usl.*usl + vsl.*vsl + wsl.*wsl); div_sl = interp3 (x, y, z, div, sl(:,1), sl(:,2), sl(:,3)); is_singular_div = find (isnan (div_sl), 1, "first"); if (! isempty (is_singular_div)) max_vertices = is_singular_div - 1; else max_vertices = num_vertices; endif if (max_vertices > 2) htmp = plottube (hax, sl, div_sl, vv, max_vertices, ... rstart, num_circum); h = [h; htmp]; endif endif endfor endfunction function h = plottube (hax, sl, div_sl, vv, max_vertices, rstart, num_circum) phi = linspace (0, 2*pi, num_circum); cp = cos (phi); sp = sin (phi); ## 1st streamline segment X0 = sl(1,:); X1 = sl(2,:); R = X1 - X0; RE = R / norm (R); ## Guide point and its rotation to create a segment KE = get_normal1 (RE); K = rstart * KE; XS0 = rotation (K, RE, cp, sp) + repmat (X0.', 1, num_circum); ## End of first segment ract = rstart * exp (0.5 * div_sl(2) * norm (R) / vv(2)) * ... sqrt (vv(1) / vv(2)); rold = ract; K = ract * KE; XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); px = zeros (num_circum, max_vertices); py = zeros (num_circum, max_vertices); pz = zeros (num_circum, max_vertices); pc = zeros (num_circum, max_vertices); px(:,1) = XS0(1,:).'; py(:,1) = XS0(2,:).'; pz(:,1) = XS0(3,:).'; pc(:,1) = vv(1) * ones (num_circum, 1); px(:,2) = XS(1,:).'; py(:,2) = XS(2,:).'; pz(:,2) = XS(3,:).'; pc(:,2) = vv(2) * ones (num_circum, 1); for i = 3 : max_vertices ## Next streamline segment X0 = X1; X1 = sl(i,:); R = X1 - X0; RE = R / norm (R); ## Tube radius ract = rold * exp (0.5 * div_sl(i) * norm (R) / vv(i)) * ... sqrt (vv(i-1) / vv(i)); rold = ract; ## Project KE onto RE and get the difference in order to transport ## the normal vector KE along the vertex array Kp = KE - RE * dot (KE, RE); KE = Kp / norm (Kp); K = ract * KE; ## Rotate around RE and collect surface patches XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); px(:,i) = XS(1,:).'; py(:,i) = XS(2,:).'; pz(:,i) = XS(3,:).'; pc(:,i) = vv(i) * ones (num_circum, 1); endfor h = surface (hax, px, py, pz, pc); endfunction ## Arbitrary N normal to X function N = get_normal1 (X) if ((X(3) == 0) && (X(1) == -X(2))) N = [(- X(2) - X(3)), X(1), X(1)]; else N = [X(3), X(3), (- X(1) - X(2))]; endif N /= norm (N); endfunction ## Rotate X around U where |U| = 1 ## cp = cos (angle), sp = sin (angle) function Y = rotation (X, U, cp, sp) ux = U(1); uy = U(2); uz = U(3); Y(1,:) = X(1) * (cp + ux * ux * (1 - cp)) + ... X(2) * (ux * uy * (1 - cp) - uz * sp) + ... X(3) * (ux * uz * (1 - cp) + uy * sp); Y(2,:) = X(1) * (uy * ux * (1 - cp) + uz * sp) + ... X(2) * (cp + uy * uy * (1 - cp)) + ... X(3) * (uy * uz * (1 - cp) - ux * sp); Y(3,:) = X(1) * (uz * ux * (1 - cp) - uy * sp) + ... X(2) * (uz * uy * (1 - cp) + ux * sp) + ... X(3) * (cp + uz * uz * (1 - cp)); endfunction %!demo %! clf; %! [x, y, z] = meshgrid (-1:0.1:1, -1:0.1:1, -3.5:0.1:0); %! a = 0.1; %! b = 0.1; %! u = - a * x - y; %! v = x - a * y; %! w = - b * ones (size (x)); %! sx = 1.0; %! sy = 0.0; %! sz = 0.0; %! ostreamtube (x, y, z, u, v, w, sx, sy, sz, [1.2, 30]); %! colormap (jet); %! shading interp; %! view ([-47, 24]); %! camlight (); %! lighting gouraud; %! grid on; %! view (3); %! axis equal; %! set (gca, "cameraviewanglemode", "manual"); %! title ("Spiral Sink"); %!demo %! clf; %! [x, y, z] = meshgrid (-2:0.5:2); %! t = sqrt (1.0./(x.^2 + y.^2 + z.^2)).^3; %! u = - x.*t; %! v = - y.*t; %! w = - z.*t; %! [sx, sy, sz] = meshgrid (-2:4:2); %! xyz = stream3 (x, y, z, u, v, w, sx, sy, sz, [0.1, 60]); %! ostreamtube (xyz, x, y, z, u, v, w, [2, 50]); %! colormap (jet); %! shading interp; %! view ([-47, 24]); %! camlight (); %! lighting gouraud; %! grid on; %! view (3); %! axis equal; %! set (gca, "cameraviewanglemode", "manual"); %! title ("Integration Towards Sink"); ## Test input validation %!error <Invalid call> ostreamtube () %!error <Invalid call> ostreamtube (1) %!error <Invalid call> ostreamtube (1,2) %!error <Invalid call> ostreamtube (1,2,3) %!error <Invalid call> ostreamtube (1,2,3,4) %!error <Invalid call> ostreamtube (1,2,3,4,5) %!error <OPTIONS must be a 1- or 2-element> ostreamtube (1,2,3,4,5,6,[1,2,3]) %!error <SCALE must be a real scalar . 0> ostreamtube (1,2,3,4,5,6,[1i]) %!error <SCALE must be a real scalar . 0> ostreamtube (1,2,3,4,5,6,[0]) %!error <N must be greater than 2> ostreamtube (1,2,3,4,5,6,[1,1i]) %!error <N must be greater than 2> ostreamtube (1,2,3,4,5,6,[1,2])