Mercurial > jwe > octave
view scripts/plot/draw/ostreamtube.m @ 28141:23f667483fab stable
Add Matlab compatible "streamtube" function (bug #57471).
* streamtube.m: Add new function "streamtube" based on "ostreamtube" that is
Matlab compatible.
* ostreamtube.m, stream3.m, streamline.m, module.mk, plot.txi, NEWS: Add
references.
author | Markus Meisinger <chloros2@gmx.de> |
---|---|
date | Wed, 19 Feb 2020 07:50:04 +0100 |
parents | 695bb31e565b |
children | 23e6c897526a 0a5b15007766 |
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######################################################################## ## ## Copyright (C) 2019-2020 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, 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 0 print_usage (); 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 error ("ostreamtube: invalid number of inputs"); 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: invalid number of OPTIONS elements"); 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); X0 = sl(1, :); X1 = sl(2, :); ## 1st rotation axis R = X1 - X0; RE = R / norm (R); ## Initial radius vold = vv(1); vact = vv(2); ract = rstart * exp (0.5 * div_sl(2) * norm (R) / vact) * sqrt (vold / vact); vold = vact; rold = ract; ## Guide point and its rotation to create a segment N = get_normal1 (R); K = ract * N; XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); px = zeros (num_circum, max_vertices - 1); py = zeros (num_circum, max_vertices - 1); pz = zeros (num_circum, max_vertices - 1); pc = zeros (num_circum, max_vertices - 1); px(:, 1) = XS(1, :).'; py(:, 1) = XS(2, :).'; pz(:, 1) = XS(3, :).'; pc(:, 1) = vact * ones (num_circum, 1); for i = 3 : max_vertices KK = K; X0 = X1; X1 = sl(i, :); R = X1 - X0; RE = R / norm (R); ## Tube radius vact = vv(i); ract = rold * exp (0.5 * div_sl(i) * norm (R) / vact) * sqrt (vold / vact); vold = vact; rold = ract; ## Project KK onto RE and get the difference in order to calculate the next ## guiding point Kp = KK - RE * dot (KK, RE); K = ract * Kp / norm (Kp); ## Rotate around RE and collect surface patches XS = rotation (K, RE, cp, sp) + repmat (X1.', 1, num_circum); px(:, i - 1) = XS(1, :).'; py(:, i - 1) = XS(2, :).'; pz(:, i - 1) = XS(3, :).'; pc(:, i - 1) = vact * 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 ostreamtube () %!error <invalid number of inputs> ostreamtube (1) %!error <invalid number of inputs> ostreamtube (1,2) %!error <invalid number of inputs> ostreamtube (1,2,3) %!error <invalid number of inputs> ostreamtube (1,2,3,4) %!error <invalid number of inputs> ostreamtube (1,2,3,4,5) %!error <invalid number of OPTIONS> 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])