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meshgen.m
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meshgen.m
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classdef meshgen
% MESHGEN: Mesh generation class
% Handles input parameters to create a meshgen class object that can be
% used to build a msh class.
% Copyright (C) 2018 Keith Roberts & William Pringle
%
% This program 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.
%
% This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
%
% Available options:
% ef % edgefx class
% bou % geodata class
% h0 % minimum edge length (optional if bou exists)
% bbox % bounding box [xmin,ymin; xmax,ymax] (manual specification, no bou)
% proj % structure containing the m_map projection info
% plot_on % flag to plot (def: 1) or not (0)
% nscreen % how many it to plot and write temp files (def: 5)
% itmax % maximum number of iterations.
% pfix % fixed node positions (nfix x 2 )
% egfix % edge constraints
% outer % meshing boundary (manual specification, no bou)
% inner % island boundaries (manual specification, no bou)
% mainland % the shoreline boundary (manual specification, no bou)
% fixboxes % a flag that indicates which boxes will use fixed constraints
% memory_gb % memory in GB allowed to use for initial rejector
% cleanup % logical flag or string to trigger cleaning of topology (default is on).
% direc_smooth % logical flag to trigger direct smoothing of mesh in the cleanup
% dj_cutoff % the cutoff area fraction for disjoint portions to delete
% qual_tol % tolerance for the accepted negligible change in quality
% enforceWeirs % whether or not to enforce weirs in meshgen
% enforceMin % whether or not to enfore minimum edgelength for all edgefxs
% big_mesh % set to 1 to remove the bou data from memory
properties
fd % handle to distance function
fh % handle to edge function
h0 % minimum edge length
edgefx % edgefx class
bbox % bounding box [xmin,ymin; xmax,ymax]
pfix % fixed node positions (nfix x 2 )
egfix % edge constraints
fixboxes % a flag that indicates which boxes will use fixed constraints
plot_on % flag to plot (def: 1) or not (0)
nscreen % how many it to plot and write temp files (def: 5)
bou % geodata class
ef % edgefx class
itmax % maximum number of iterations.
outer % meshing boundary (manual specification, no bou)
inner % island boundaries (manual specification, no bou)
mainland % the shoreline boundary (manual specification, no bou)
boubox % the bbox as a polygon 2-tuple
inpoly_flip % used to flip the inpoly test to determine the signed distance.
memory_gb % memory in GB allowed to use for initial rejector
cleanup % logical flag or string to trigger cleaning of topology (default is on).
direc_smooth % logical flag to trigger direct smoothing of mesh in the cleanup
dj_cutoff % the cutoff area fraction for disjoint portions to delete
grd = msh(); % create empty mesh class to return p and t in.
big_mesh % release bou data from memory
qual % mean, lower 3rd sigma, and the minimum element quality.
qual_tol % tolerance for the accepted negligible change in quality
proj % structure containing the m_map projection info
anno % Approx. Nearest Neighbor search object.
annData % datat contained with KD-tree in anno
Fb % bathymetry data interpolant
enforceWeirs % whether or not to enforce weirs in meshgen
enforceMin % whether or not to enfore minimum edgelength for all edgefxs
end
methods
% class constructor/default grd generation options
function obj = meshgen(varargin)
% Check for m_map dir
M_MAP_EXISTS=0;
if exist('m_proj','file')==2
M_MAP_EXISTS=1 ;
end
if M_MAP_EXISTS~=1
error('Where''s m_map? Chief, you need to read the user guide')
end
% Check for utilties dir
UTIL_DIR_EXISTS=0 ;
if exist('inpoly.m','file')
UTIL_DIR_EXISTS=1;
end
if UTIL_DIR_EXISTS~=1
error('Where''s the utilities directory? Chief, you need to read the user guide')
end
p = inputParser;
% unpack options and set default ones, catch errors.
defval = 0; % placeholder value if arg is not passed.
% add name/value pairs
addOptional(p,'h0',defval);
addOptional(p,'bbox',defval);
addOptional(p,'fh',defval);
addOptional(p,'pfix',defval);
addOptional(p,'egfix',defval);
addOptional(p,'fixboxes',defval);
addOptional(p,'inner',defval);
addOptional(p,'outer',defval);
addOptional(p,'mainland',defval);
addOptional(p,'bou',defval);
addOptional(p,'ef',defval);
addOptional(p,'plot_on',defval);
addOptional(p,'nscreen',defval);
addOptional(p,'itmax',defval);
addOptional(p,'memory_gb',1);
addOptional(p,'cleanup',1);
addOptional(p,'direc_smooth',1);
addOptional(p,'dj_cutoff',0.25);
addOptional(p,'big_mesh',defval);
addOptional(p,'proj',defval);
addOptional(p,'qual_tol',defval);
addOptional(p,'enforceWeirs',1);
addOptional(p,'enforceMin',1);
% parse the inputs
parse(p,varargin{:});
%if isempty(varargin); return; end
% store the inputs as a struct
inp = p.Results;
% kjr...order these argument so they are processed in a predictable
% manner. Process the general opts first, then the OceanMesh
% classes...then basic non-critical options.
inp = orderfields(inp,{'h0','bbox','enforceWeirs','enforceMin','fh',...
'inner','outer','mainland',...
'bou','ef',... %<--OceanMesh classes come after
'egfix','pfix','fixboxes',...
'plot_on','nscreen','itmax',...
'memory_gb','qual_tol','cleanup',...
'direc_smooth','dj_cutoff',...
'big_mesh','proj'});
% get the fieldnames of the edge functions
fields = fieldnames(inp);
% loop through and determine which args were passed.
% also, assign reasonable default values if some options were
% not assigned.
for i = 1 : numel(fields)
type = fields{i};
switch type
% parse aux options first
case('h0')
% Provide in meters
obj.h0 = inp.(fields{i});
case('fh')
if isa(inp.(fields{i}),'function_handle')
obj.fh = inp.(fields{i});
end
% can't check for errors here yet.
case('bbox')
obj.bbox= inp.(fields{i});
if iscell(obj.bbox)
% checking bbox extents
ob_min = obj.bbox{1}(:,1);
ob_max = obj.bbox{1}(:,2);
for ii = 2:length(obj.bbox)
if any(obj.bbox{ii}(:,1) < ob_min) || ...
any(obj.bbox{ii}(:,2) > ob_max)
error(['Outer bbox must contain all ' ...
'inner bboxes: inner box #' ...
num2str(ii) ' violates this'])
end
end
end
% if user didn't pass anything explicitly for
% bounding box make it empty so it can be populated
% from ef as a cell-array
if obj.bbox(1)==0
obj.bbox = [];
end
case('pfix')
obj.pfix= inp.(fields{i});
if obj.pfix(1)~=0
obj.pfix(:,:) = inp.(fields{i});
else
obj.pfix = [];
end
if obj.enforceWeirs
for j = 1 : length(obj.bou)
if ~isempty(obj.bou{j}.weirPfix)
obj.pfix = [obj.pfix ; obj.bou{j}.weirPfix];
end
end
end
case('egfix')
obj.egfix= inp.(fields{i});
if ~isempty(obj.egfix) && obj.egfix(1)~=0
obj.egfix = inp.(fields{i});
else
obj.egfix = [];
end
if obj.enforceWeirs
for j = 1 : length(obj.bou)
if ~isempty(obj.bou{j}.weirEgfix) && ~isempty(obj.egfix)
obj.egfix = [obj.egfix ; obj.bou{j}.weirEgfix+max(obj.egfix(:))];
else
obj.egfix = obj.bou{j}.weirEgfix;
end
end
end
obj.egfix = renumberEdges(obj.egfix);
case('fixboxes')
obj.fixboxes= inp.(fields{i});
case('bou')
% got it from user arg
if obj.outer~=0, continue; end
obj.outer = {} ;
obj.inner = {} ;
obj.mainland = {} ;
obj.bou = inp.(fields{i});
% handle when not a cell
if ~iscell(obj.bou)
boutemp = obj.bou;
obj.bou = cell(1);
obj.bou{1} = boutemp;
end
% then the geodata class was provide, unpack
for ee = 1:length(obj.bou)
try
arg = obj.bou{ee} ;
catch
arg = obj.bou;
end
if isa(arg,'geodata')
obj.outer{ee} = obj.bou{ee}.outer;
obj.inner{ee} = obj.bou{ee}.inner;
% save bathy interpolant to meshgen
if ~isempty(obj.bou{ee}.Fb)
obj.Fb{ee} = obj.bou{ee}.Fb ;
end
if ~isempty(obj.inner{ee}) && ...
obj.inner{ee}(1)~= 0
obj.outer{ee} = [obj.outer{ee};
obj.inner{ee}];
end
obj.mainland{ee} = obj.bou{ee}.mainland;
obj.boubox{ee} = obj.bou{ee}.boubox;
obj.inpoly_flip{ee} = obj.bou{ee}.inpoly_flip;
if obj.big_mesh
% release gdat's
obj.bou{ee}.mainland= [];
obj.bou{ee}.outer= [];
if ~isempty(obj.bou{ee}.inner)
obj.bou{ee}.inner= [];
end
end
end
end
case('ef')
tmp = inp.(fields{i});
if isa(tmp, 'function_handle')
error('Please specify your edge function handle through the name/value pair fh');
end
obj.ef = tmp;
% handle when not a cell
if ~iscell(obj.ef)
eftemp = obj.ef;
obj.ef = cell(1);
obj.ef{1} = eftemp;
end
% Gather boxes from ef class.
for ee = 1 : length(obj.ef)
if isa(obj.ef{ee},'edgefx')
obj.bbox{ee} = obj.ef{ee}.bbox;
end
end
% checking bbox extents
if iscell(obj.bbox)
ob_min = obj.bbox{1}(:,1);
ob_max = obj.bbox{1}(:,2);
for ii = 2:length(obj.bbox)
if any(obj.bbox{ii}(:,1) < ob_min) || ...
any(obj.bbox{ii}(:,2) > ob_max)
error(['Outer bbox must contain all ' ...
'inner bboxes: inner box #' ...
num2str(ii) ' violates this'])
end
end
end
% kjr 2018 June: get h0 from edge functions
for ee = 1:length(obj.ef)
if isa(obj.ef{ee},'edgefx')
obj.h0(ee) = obj.ef{ee}.h0;
end
end
% kjr 2018 smooth the outer automatically
if length(obj.ef) > 1
% kjr 2020, ensure the min. sizing func is
% used
if obj.enforceMin
obj.ef = enforce_min_ef(obj.ef);
end
obj.ef = smooth_outer(obj.ef,obj.Fb);
end
% Save the ef interpolants into the edgefx
for ee = 1:length(obj.ef)
if isa(obj.ef{ee},'edgefx')
obj.fh{ee} = @(p)obj.ef{ee}.F(p);
end
end
case('plot_on')
obj.plot_on= inp.(fields{i});
case('big_mesh')
obj.big_mesh = inp.(fields{i});
case('nscreen')
obj.nscreen= inp.(fields{i});
if obj.nscreen ~=0
obj.nscreen = inp.(fields{i});
obj.plot_on = 1;
else
obj.nscreen = 5; % default
end
case('itmax')
obj.itmax= inp.(fields{i});
if obj.itmax ~=0
obj.itmax = inp.(fields{i});
else
obj.itmax = 100;
warning('No itmax specified, itmax set to 100');
end
case('qual_tol')
obj.qual_tol = inp.(fields{i});
if obj.qual_tol ~=0
obj.qual_tol = inp.(fields{i});
else
obj.qual_tol = 0.01;
end
case('inner')
if ~isa(obj.bou,'geodata')
obj.inner = inp.(fields{i});
end
case('outer')
if ~isa(obj.bou,'geodata')
obj.outer = inp.(fields{i});
if obj.inner(1)~=0
obj.outer = [obj.outer; obj.inner];
end
end
case('mainland')
if ~isa(obj.bou,'geodata')
obj.mainland = inp.(fields{i});
end
case('memory_gb')
if ~isa(obj.bou,'memory_gb')
obj.memory_gb = inp.(fields{i});
end
case('cleanup')
obj.cleanup = inp.(fields{i});
if isempty(obj.cleanup) || obj.cleanup == 0
obj.cleanup = 'none';
elseif obj.cleanup == 1
obj.cleanup = 'default';
end
case('dj_cutoff')
obj.dj_cutoff = inp.(fields{i});
case('direc_smooth')
obj.direc_smooth = inp.(fields{i});
case('proj')
obj.proj = inp.(fields{i});
% default CPP
if obj.proj == 0; obj.proj = 'equi'; end
if ~isempty(obj.bbox)
% kjr Oct 2018 use outer coarsest box for
% multiscale meshing
lon_mi = obj.bbox{1}(1,1)-obj.h0(1)/1110;
lon_ma = obj.bbox{1}(1,2)+obj.h0(1)/1110;
lat_mi = obj.bbox{1}(2,1)-obj.h0(1)/1110;
lat_ma = obj.bbox{1}(2,2)+obj.h0(1)/1110;
else
lon_mi = -180; lon_ma = 180;
lat_mi = -90; lat_ma = 90;
end
% Set up projected space
dmy = msh() ;
dmy.p(:,1) = [lon_mi; lon_ma];
dmy.p(:,2) = [lat_mi; lat_ma];
del = setProj(dmy,1,obj.proj) ;
case('enforceWeirs')
obj.enforceWeirs = inp.(fields{i});
case('enforceMin')
obj.enforceMin = inp.(fields{i});
end
end
if isempty(varargin); return; end
% error checking
if isempty(obj.boubox) && ~isempty(obj.bbox)
% Make the bounding box 5 x 2 matrix in clockwise order if
% it isn't present. This case must be when the user is
% manually specifying the PSLG.
obj.boubox{1} = [obj.bbox(1,1) obj.bbox(2,1);
obj.bbox(1,1) obj.bbox(2,2); ...
obj.bbox(1,2) obj.bbox(2,2);
obj.bbox(1,2) obj.bbox(2,1); ...
obj.bbox(1,1) obj.bbox(2,1); NaN NaN];
end
if any(obj.h0==0), error('h0 was not correctly specified!'), end
if isempty(obj.outer), error('no outer boundary specified!'), end
if isempty(obj.bbox), error('no bounding box specified!'), end
obj.fd = @dpoly; % <-default distance fx accepts p and pv (outer polygon).
% kjr build ANN object into meshgen
obj = createANN(obj) ;
global MAP_PROJECTION MAP_COORDS MAP_VAR_LIST
obj.grd.proj = MAP_PROJECTION ;
obj.grd.coord = MAP_COORDS ;
obj.grd.mapvar = MAP_VAR_LIST ;
end
% Creates Approximate nearest neighbor objects on start-up
function obj = createANN(obj)
box_vec = 1:length(obj.bbox);
for box_num = box_vec
if ~iscell(obj.outer)
dataset = obj.outer;
dataset(isnan(obj.outer(:,1)),:) = [];
else
dataset = obj.outer{box_num};
dataset(isnan(obj.outer{box_num}(:,1)),:) = [];
end
if all(abs(obj.bbox{box_num}(1,:)) == 180)
% This line removes the line that can appear in the
% center for a global mesh
dataset(abs(dataset(:,1)) > 180-1e-6,:) = [];
dataset(abs(dataset(:,1)) < 1e-6,:) = [];
end
[dataset(:,1),dataset(:,2)] = m_ll2xy(dataset(:,1),dataset(:,2));
dataset(isnan(dataset(:,1)),:) = [];
dmy = ann(dataset');
obj.anno{box_num} = dmy;
obj.annData{box_num}=dataset;
end
end
function obj = build(obj)
%DISTMESH2D 2-D Mesh Generator using Distance Functions.
% Checking existence of major inputs
%%
warning('off','all')
%%
tic
it = 1 ;
Re = 6378.137e3;
geps = 1e-3*min(obj.h0)/Re;
deps = sqrt(eps);
ttol=0.1; Fscale = 1.2; deltat = 0.1;
delIT = 0 ; delImp = 2;
imp = 10; % number of iterations to do mesh improvements (delete/add)
% unpack initial points.
p = obj.grd.p;
if isempty(p)
disp('Forming initial point distribution...');
% loop over number of boxes
for box_num = 1:length(obj.h0)
disp([' for box #' num2str(box_num)]);
% checking if cell or not and applying local values
h0_l = obj.h0(box_num);
max_r0 = 1/h0_l^2;
if ~iscell(obj.bbox)
bbox_l = obj.bbox'; % <--we must tranpose this!
else
bbox_l = obj.bbox{box_num}'; % <--tranpose!
end
if ~iscell(obj.fh)
fh_l = obj.fh;
else
fh_l = obj.fh{box_num};
end
% Lets estimate the num_points the distribution will be
num_points = ceil(2/sqrt(3)*prod(abs(diff(bbox_l)))...
/(h0_l/111e3)^2);
noblks = ceil(num_points*2*8/obj.memory_gb*1e-9);
len = abs(bbox_l(1,1)-bbox_l(2,1));
blklen = len/noblks;
st = bbox_l(1,1) ; ed = st + blklen; ns = 1;
%% 1. Create initial distribution in bounding box
%% (equilateral triangles)
for blk = 1 : noblks
if blk == noblks
ed = bbox_l(2,1);
end
ys = bbox_l(1,2);
ny = floor(1e3*m_lldist(repmat(0.5*(st+ed),2,1),...
[ys;bbox_l(2,2)])/h0_l);
dy = diff(bbox_l(:,2))/ny;
ns = 1;
% start at lower left and make grid going up to
% north latitude
for ii = 1:ny
if st*ed < 0
nx = floor(1e3*m_lldist([st;0],...
[ys;ys])/(2/sqrt(3)*h0_l)) + ...
floor(1e3*m_lldist([0;ed],...
[ys;ys])/(2/sqrt(3)*h0_l));
else
nx = floor(1e3*m_lldist([st;ed],...
[ys;ys])/(2/sqrt(3)*h0_l));
end
ne = ns+nx-1;
if mod(ii,2) == 0
% no offset
x(ns:ne) = linspace(st,ed,nx);
else
% offset
dx = (ed-st)/nx;
x(ns:ne) = linspace(st+0.5*dx,ed,nx);
end
y(ns:ne) = ys;
ns = ne+1; ys = ys + dy;
end
st = ed;
ed = st + blklen;
p1 = [x(:) y(:)]; clear x y
%% 2. Remove points outside the region, apply the rejection method
p1 = p1(feval(obj.fd,p1,obj,box_num) < geps,:); % Keep only d<0 points
r0 = 1./feval(fh_l,p1).^2; % Probability to keep point
p1 = p1(rand(size(p1,1),1) < r0/max_r0,:); % Rejection method
p = [p; p1]; % Adding p1 to p
end
if box_num == 1
% add points along the outermost polygon to fill
% outer extent more quickly.
outer_temp = obj.outer{1};
Inan = find(isnan(outer_temp(:,1)),1,'first');
p1 = outer_temp(1:Inan-1,:);
p1 = p1(feval(obj.fd,p1,obj,box_num) < geps,:); % Keep only d<0 points
r0 = 1./feval(fh_l, p1).^2; % Probability to keep point
p1 = p1(rand(size(p1,1),1) < r0/max_r0,:); % Rejection method
p = [p; p1]; % Adding p1 to p
end
end
else
disp('User-supplied initial points!');
obj.grd.b = [];
h0_l = obj.h0(end); % finest h0 (in case of a restart of meshgen.build).
end
% remove pfix/egfix outside of desired subdomain
nfix = size(obj.pfix,1); % Number of fixed points
negfix = size(obj.egfix,1); % Number of edge constraints
if negfix > 0
if length(obj.fixboxes)==1 && obj.fixboxes(1)==0
obj.fixboxes(1)=1 ;
end
pfixkeep = setdiff([1:nfix]',unique(obj.egfix(:)));
% remove bars if midpoint is outside domain
egfix_mid = (obj.pfix(obj.egfix(:,1),:) + ...
obj.pfix(obj.egfix(:,2),:))/2;
for jj = 1 : length(obj.fixboxes)
if obj.fixboxes(jj)
iboubox = obj.boubox{jj};
inbar(:,jj) = inpoly(egfix_mid,iboubox(1:end-1,:));
end
end
inbar = sum(inbar,2) ;
obj.egfix(~inbar,:) = [];
tmppfix = obj.pfix([unique(obj.egfix(:)); pfixkeep],:);
obj.pfix = tmppfix;
obj.egfix = renumberEdges(obj.egfix);
negfix = size(obj.egfix,1); % Number of edge constraints.
end
if nfix > 0
if length(obj.fixboxes)==1 && obj.fixboxes(1)==0
obj.fixboxes(1)=1 ;
end
% remove pfix if outside domain
for jj = 1 : length(obj.fixboxes)
if obj.fixboxes(jj)
inbox(:,jj) = inpoly(obj.pfix,obj.boubox{jj}(1:end-1,:));
end
end
inbox = sum(inbox,2) ;
inbox(unique(obj.egfix(:))) = 1;
obj.pfix(~inbox,:) = [];
nfix = size(obj.pfix,1); % Number of fixed points
end
if nfix >= 0, disp(['Using ',num2str(nfix),' fixed points.']);end
if negfix > 0
if max(obj.egfix(:)) > length(obj.pfix)
error('FATAL: egfix does index correcty into pfix.');
end
disp(['Using ',num2str(negfix),' fixed edges.']);
end
if ~isempty(obj.pfix); p = [obj.pfix; p]; end
N = size(p,1); % Number of points N
disp(['Number of initial points after rejection is ',num2str(N)]);
%% Iterate
pold = inf; % For first iteration
if obj.plot_on >= 1
clf,view(2),axis equal;
end
toc
fprintf(1,' ------------------------------------------------------->\n') ;
disp('Begin iterating...');
while 1
tic
if ~mod(it,obj.nscreen) && delIT == 0
disp(['Iteration =' num2str(it)]) ;
end
% 3. Retriangulation by the Delaunay algorithm
if max(sqrt(sum((p(1:size(pold,1),:)-pold).^2,2))/h0_l*111e3) > ttol % Any large movement?
p = fixmesh(p); % Ensure only unique points.
N = size(p,1); pold = p; % Save current positions
[t,p] = delaunay_elim(p,obj.fd,geps,0); % Delaunay with elimination
if isempty(t)
disp('Exiting')
return
end
% Getting element quality and check "goodness"
if exist('pt','var'); clear pt; end
[pt(:,1),pt(:,2)] = m_ll2xy(p(:,1),p(:,2));
tq = gettrimeshquan( pt, t);
mq_m = mean(tq.qm);
mq_l = min(tq.qm);
mq_s = std(tq.qm);
mq_l3sig = mq_m - 3*mq_s;
obj.qual(it,:) = [mq_m,mq_l3sig,mq_l];
% If mesh quality went down "significantly" since last iteration
% which was a mesh improvement iteration, then rewind.
if ~mod(it,imp+1) && obj.qual(it,1) - obj.qual(it-1,1) < -0.10 || ...
~mod(it,imp+1) && (N - length(p_before_improve))/length(p_before_improve) < -0.10
disp('Mesh improvement was unsuccessful...rewinding...');
p = p_before_improve;
N = size(p,1); % Number of points changed
pold = inf;
it = it + 1;
continue
else
N = size(p,1); pold = p; % Assign number of points and save current positions
end
% 4. Describe each bar by a unique pair of nodes.
bars = [t(:,[1,2]); t(:,[1,3]); t(:,[2,3])]; % Interior bars duplicated
bars = unique(sort(bars,2),'rows'); % Bars as node pairs
% 5. Graphical output of the current mesh
if obj.plot_on >= 1 && (mod(it,obj.nscreen)==0 || it == 1)
cla,m_triplot(p(:,1),p(:,2),t)
m_grid
title(['Iteration = ',num2str(it)]);
if negfix > 0
m_plot(reshape(obj.pfix(obj.egfix,1),[],2)',...
reshape(obj.pfix(obj.egfix,2),[],2)','r-')
end
if nfix > 0
m_plot(obj.pfix(:,1),obj.pfix(:,2),'b.')
end
plt = cell2mat(obj.boubox');
% reduce point spacing for asecthics
[plt2(:,2),plt2(:,1)] = my_interpm(plt(:,2),plt(:,1),0.1) ;
hold on ; axis manual
m_plot(plt2(:,1),plt2(:,2),'g','linewi',2)
drawnow
end
end
% Getting element quality and check goodness
if exist('pt','var'); clear pt; end
[pt(:,1),pt(:,2)] = m_ll2xy(p(:,1),p(:,2));
tq = gettrimeshquan( pt, t);
mq_m = mean(tq.qm);
mq_l = min(tq.qm);
mq_s = std(tq.qm);
mq_l3sig = mq_m - 3*mq_s;
obj.qual(it,:) = [mq_m,mq_l3sig,mq_l];
% Improve the quality of triangles next to fixed edges by
% deleting the point part of thin triangles without the fixed
% point in it. Thin triangles have poor geometric quality <
% 10%.
if ~isempty(obj.egfix) && ~mod(it,delImp)
del = heal_fixed_edges(p,t,obj.egfix) ;
if ~isempty(del)
delIT = delIT + 1 ;
if delIT < 5
p(del,:)= [];
pold = inf;
disp(['Deleting ',num2str(length(del)),...
' points close to fixed edges']);
continue;
else
% Abandon strategy..if it will not terminate
disp('Moving to next iteration');
end
end
delIT = 0 ;
end
% Termination quality, mesh quality reached is copacetic.
qual_diff = mq_l3sig - obj.qual(max(1,it-imp),2);
if ~mod(it,imp)
if abs(qual_diff) < obj.qual_tol
% Do the final elimination of small connectivity
[t,p] = delaunay_elim(p,obj.fd,geps,1);
disp('Quality of mesh is good enough, exit')
close all;
break;
end
end
% Saving a temp mesh
if ~mod(it,obj.nscreen) && delIT == 0
disp(['Number of nodes is ' num2str(length(p))])
disp(['Mean mesh quality is ' num2str(mq_m)])
disp(['Min mesh quality is ' num2str(mq_l)])
disp(['3rd sigma lower mesh quality is ' num2str(mq_l3sig)])
tempp = p; tempt = t;
save('Temp_grid.mat','it','tempp','tempt');
clearvars tempp tempt
end
% 6. Move mesh points based on bar lengths L and forces F
barvec = pt(bars(:,1),:)- pt(bars(:,2),:); % List of bar vectors
if strcmp(obj.grd.proj.name,'UTM')
% UTM is already in meters (useful for small domains)
L = sqrt(sum(barvec.^2,2))*Re;
else
% Get spherical earth distances
long = zeros(length(bars)*2,1);
lat = zeros(length(bars)*2,1);
long(1:2:end) = p(bars(:,1),1);
long(2:2:end) = p(bars(:,2),1);
lat(1:2:end) = p(bars(:,1),2);
lat(2:2:end) = p(bars(:,2),2);
L = m_lldist(long,lat); L = L(1:2:end)*1e3; % L = Bar lengths in meters
end
ideal_bars = 0.5*(pt(bars(:,1),:) + pt(bars(:,2),:)); % Used to determine what bars are in bbox
[ideal_bars(:,1),ideal_bars(:,2)] = ... % needs to be in non-projected
m_xy2ll(ideal_bars(:,1),ideal_bars(:,2)); % coordinates
hbars = 0*ideal_bars(:,1);
for box_num = 1:length(obj.h0) % For each bbox, find the bars that are in and calculate
if ~iscell(obj.fh) % their ideal lengths.
fh_l = obj.fh;
else
fh_l = obj.fh{box_num};
end
h0_l = obj.h0(box_num);
if box_num > 1
h0_l = h0_l/111e3; % create buffer to evalulate fh between nests
iboubox = obj.boubox{box_num}(1:end-1,:) ;
inside = inpoly(ideal_bars,iboubox) ;
else
inside = true(size(hbars));
end
hbars(inside) = feval(fh_l,ideal_bars(inside,:)); % Ideal lengths
end
L0 = hbars*Fscale*median(L)/median(hbars); % L0 = Desired lengths using ratio of medians scale factor
LN = L./L0; % LN = Normalized bar lengths
% Mesh improvements (deleting and addition)
if ~mod(it,imp)
p_before_improve = p;
nn = []; pst = [];
if qual_diff < imp*obj.qual_tol && qual_diff > 0
% Remove elements with small connectivity
nn = get_small_connectivity(p,t);
disp(['Deleting ' num2str(length(nn)) ' due to small connectivity'])
% Remove points that are too close (< LN = 0.5)
if any(LN < 0.5)
% Do not delete pfix too close.
nn1 = setdiff(reshape(bars(LN < 0.5,:),[],1),[(1:nfix)']);
disp(['Deleting ' num2str(length(nn1)) ' points too close together'])
nn = unique([nn; nn1]);
end
% Split long edges however many times to
% better lead to LN of 1
if any(LN > 2)
nsplit = floor(LN);
nsplit(nsplit < 1) = 1;
adding = 0;
% Probably we can just split once?
for jj = 2:2
il = find(nsplit >= jj);
xadd = zeros(length(il),jj-1);
yadd = zeros(length(il),jj-1);
for jjj = 1 : length(il)
deltax = (p(bars(il(jjj),2),1)- p(bars(il(jjj),1),1))/jj;
deltay = (p(bars(il(jjj),2),2)- p(bars(il(jjj),1),2))/jj;
xadd(jjj,:) = p(bars(il(jjj),1),1) + (1:jj-1)*deltax;
yadd(jjj,:) = p(bars(il(jjj),1),2) + (1:jj-1)*deltay;
end
pst = [pst; xadd(:) yadd(:)];
adding = numel(xadd) + adding;
end
disp(['Adding ',num2str(adding) ,' points.'])
end
end
if ~isempty(nn) || ~isempty(pst)
% Doing the actual subtracting and add
p(nn,:)= [];
p = [p; pst];
pold = inf;
it = it + 1;
continue;
end
end
F = (1-LN.^4).*exp(-LN.^4)./LN; % Bessens-Heckbert edge force
Fvec = F*[1,1].*barvec;
Ftot = full(sparse(bars(:,[1,1,2,2]),ones(size(F))*[1,2,1,2],[Fvec,-Fvec],N,2));
Ftot(1:nfix,:) = 0; % Force = 0 at fixed points
pt = pt + deltat*Ftot; % Update node positions
[p(:,1),p(:,2)] = m_xy2ll(pt(:,1),pt(:,2));
%7. Bring outside points back to the boundary
d = feval(obj.fd,p,obj,[],1); ix = d > 0; % Find points outside (d>0)
ix(1:nfix) = 0;
if sum(ix) > 0
pn = p(ix,:) + deps;
dgradx = (feval(obj.fd,[pn(:,1),p(ix,2)],obj,[])...%,1)...
-d(ix))/deps; % Numerical
dgrady = (feval(obj.fd,[p(ix,1),pn(:,2)],obj,[])...%,1)...
-d(ix))/deps; % gradient
dgrad2 = dgradx.^+2 + dgrady.^+2;
p(ix,:) = p(ix,:) - [d(ix).*dgradx./dgrad2,...
d(ix).*dgrady./dgrad2];
end
% 8. Termination criterion: Exceed itmax
it = it + 1 ;
if ( it > obj.itmax )
% Do the final deletion of small connectivity
[t,p] = delaunay_elim(p,obj.fd,geps,1);
disp('too many iterations, exit')
close all;
break ;
end
toc
end
%%
warning('on','all')
%%
disp('Finished iterating...');
fprintf(1,' ------------------------------------------------------->\n') ;
%% Doing the final cleaning and fixing to the mesh...
% Clean up the mesh if specified
if ~strcmp(obj.cleanup,'none')
% Put the mesh class into the grd part of meshgen and clean
obj.grd.p = p; obj.grd.t = t;
[obj.grd,qout] = clean(obj.grd,obj.cleanup,...
'nscreen',obj.nscreen,'djc',obj.dj_cutoff,...
'pfix',obj.pfix);
obj.grd.pfix = obj.pfix ;
obj.grd.egfix= obj.egfix ;
obj.qual(end+1,:) = qout;
else
% Fix mesh on the projected space
[p(:,1),p(:,2)] = m_ll2xy(p(:,1),p(:,2));
[p,t] = fixmesh(p,t);
[p(:,1),p(:,2)] = m_xy2ll(p(:,1),p(:,2));
% Put the mesh class into the grd part of meshgen
obj.grd.p = p; obj.grd.t = t;
obj.grd.pfix = obj.pfix ;
obj.grd.egfix= obj.egfix ;
end
% Check element order, important for the global meshes crossing
% -180/180 boundary
obj.grd = CheckElementOrder(obj.grd);
if obj.plot_on
figure; plot(obj.qual,'linewi',2);
hold on
% plot the line dividing cleanup and distmesh
plot([it it],[0 1],'--k')
xticks(1:5:obj.itmax);
xlabel('Iterations'); ylabel('Geometric element quality');
title('Geometric element quality with iterations');
set(gca,'FontSize',14);
legend('q_{mean}','q_{mean}-q_{3\sigma}', 'q_{min}','Location','best');
grid minor
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%
% Auxiliary subfunctions %
%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t,p] = delaunay_elim(p,fd,geps,final)
% Removing mean to reduce the magnitude of the points to
% help the convex calc
if exist('pt1','var'); clear pt1; end
[pt1(:,1),pt1(:,2)] = m_ll2xy(p(:,1),p(:,2));
if isempty(obj.egfix)
p_s = pt1 - repmat(mean(pt1),[N,1]);
TR = delaunayTriangulation(p_s);
else
TR = delaunayTriangulation(pt1(:,1),pt1(:,2),obj.egfix);
pt1 = TR.Points;
end
for kk = 1:final+1
if kk > 1
% Perform the following below upon exit from the mesh
% generation algorithm
nn = get_small_connectivity(pt1,t);
nn1 = heal_fixed_edges(pt1,t,obj.egfix) ;
nn = unique([nn; nn1]) ;
TR.Points(nn,:) = [];
pt1(nn,:) = [];
end
t = TR.ConnectivityList;
pmid = squeeze(mean(reshape(pt1(t,:),[],3,2),2)); % Compute centroids
[pmid(:,1),pmid(:,2)] = m_xy2ll(pmid(:,1),pmid(:,2)); % Change back to lat lon
t = t(feval(fd,pmid,obj,[]) < -geps,:); % Keep interior triangles
if kk == 1
% Deleting very straight triangles
tq_n = gettrimeshquan( pt1, t);
bad_ele = any(tq_n.vang < 1*pi/180 | ...
tq_n.vang > 179*pi/180,2);
t(bad_ele,:) = [];
end
end
if length(pt1) ~= length(p)
clear p
[p(:,1),p(:,2)] = m_xy2ll(pt1(:,1),pt1(:,2));
end
end
function nn = get_small_connectivity(p,t)
% Get node connectivity (look for 4)
[~, enum] = VertToEle(t);
% Make sure they are not boundary nodes
bdbars = extdom_edges2(t, p);
bdnodes = unique(bdbars(:));
I = find(enum <= 4);
nn = setdiff(I',[(1:nfix)';bdnodes]); % and don't destroy pfix or egfix!
return;
end
function del = heal_fixed_edges(p,t,egfix)
% kjr april2019
% if there's a triangle with a low geometric quality that
% contains a fixed edge, remove the non-fixed vertex
% perform this on every other iteration to allow non-fixed
% points to create equilateral triangles nearby the locked
% edge.
% returns points IDs that should be deleted.
TR = triangulation(t,p) ;
elock = edgeAttachments(TR,egfix) ;
tq = gettrimeshquan(p,t);
elock = unique(cell2mat(elock'));
dmy = elock(tq.qm(elock) < 0.25);
badtria = t(dmy,:);
del = badtria(badtria > nfix) ;
end
end % end distmesh2d_plus