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tricost.m
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tricost.m
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function tricost(varargin)
%TRICOST draw quality-metrics for a 2-simplex triangulation
%embedded in the two-dimensional plane.
% TRICOST(VERT,EDGE,TRIA,TNUM) draws histograms of quality
% metrics for the triangulation.
% VERT is a V-by-2 array of XY coordinates in the triangu-
% lation, EDGE is an array of constrained edges, TRIA is a
% T-by-3 array of triangles, and TNUM is a T-by-1 array of
% part indices. Each row of TRIA and EDGE define an eleme-
% nt. VERT(TRIA(II,1),:), VERT(TRIA(II,2),:) and VERT(TRIA
% (II,3),:) are the coordinates of the II-TH triangle. The
% edges in EDGE are defined in a similar manner. NUM is an
% array of part indexing, such that TNUM(II) is the index
% of the part in which the II-TH triangle resides.
%
% TRICOST(...,HVRT) additionally draws histograms of rela-
% tive edge-length, indicating conformance to the spacing
% constraints. HVRT is a V-by-1 array of spacing informat-
% ion, per an evaluation of the mesh-size function at the
% mesh vertices VERT.
%
% See also REFINE2, SMOOTH2
%-----------------------------------------------------------
% Darren Engwirda : 2017 --
% Email : d.engwirda@gmail.com
% Last updated : 09/07/2018
%-----------------------------------------------------------
vert = [] ; conn = [] ; tria = [] ;
tnum = [] ; hvrt = [] ;
%---------------------------------------------- extract args
if (nargin>=+1), vert = varargin{1}; end
if (nargin>=+2), conn = varargin{2}; end
if (nargin>=+3), tria = varargin{3}; end
if (nargin>=+4), tnum = varargin{4}; end
if (nargin>=+5), hvrt = varargin{5}; end
%---------------------------------------------- basic checks
if ( ~isnumeric(vert) || ...
~isnumeric(conn) || ...
~isnumeric(tria) || ...
~isnumeric(tnum) || ...
~isnumeric(hvrt) )
error('tricost:incorrectInputClass' , ...
'Incorrect input class.') ;
end
%---------------------------------------------- basic checks
if (ndims(vert) ~= +2 || ...
ndims(conn) ~= +2 || ...
ndims(tria) ~= +2 )
error('tricost:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
if (size(vert,2)~= +2 || ...
size(conn,2) < +2 || ...
size(tria,2) < +3 )
error('tricost:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
nvrt = size(vert,1) ;
ntri = size(tria,1) ;
%---------------------------------------------- basic checks
if (min(min(conn(:,1:2))) < +1 || ...
max(max(conn(:,1:2))) > nvrt )
error('tricost:invalidInputs', ...
'Invalid EDGE input array.') ;
end
if (min(min(tria(:,1:3))) < +1 || ...
max(max(tria(:,1:3))) > nvrt )
error('tricost:invalidInputs', ...
'Invalid TRIA input array.') ;
end
%-- borrowed from the JIGSAW library!
%-- draw sub-axes directly -- sub-plot gives
%-- silly inconsistent ax spacing...!
axpos31 = [.125,.750,.800,.150] ;
axpos32 = [.125,.450,.800,.150] ;
axpos33 = [.125,.150,.800,.150] ;
axpos41 = [.125,.835,.800,.135] ;
axpos42 = [.125,.590,.800,.135] ;
axpos43 = [.125,.345,.800,.135] ;
axpos44 = [.125,.100,.800,.135] ;
%-- draw cost histograms for 2-tria elements
figure;
set(gcf,'color','w','units','normalized', ...
'position',[.05,.10,.30,.30]);
if (~isempty(hvrt))
%-- have size-func data
axes('position',axpos41); hold on;
scrhist(triscr2(vert,tria),'tria3');
axes('position',axpos42); hold on;
anghist(triang2(vert,tria),'tria3');
axes('position',axpos43); hold on;
hfnhist(relhfn2(vert, ...
tria,hvrt),'tria3');
axes('position',axpos44); hold on;
deghist(trideg2(vert,tria),'tria3');
else
%-- null size-func data
axes('position',axpos31); hold on;
scrhist(triscr2(vert,tria),'tria3');
axes('position',axpos32); hold on;
anghist(triang2(vert,tria),'tria3');
axes('position',axpos33); hold on;
deghist(trideg2(vert,tria),'tria3');
end
end
function [mf] = mad(ff)
%MAD return mean absolute deviation (from the mean).
mf = mean(abs(ff-mean(ff))) ;
end
function deghist(dd,ty)
%DEGHIST draw histogram for "degree" quality-metric.
dd = dd(:);
be = 1:max(dd);
hc = histc(dd,be);
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(be,hc,1.05,'facecolor',k,'edgecolor',k);
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',2:2:12,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0,12]);
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.225,0,'$|d|_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.225,0, '|d|_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.225,0,'$|d|_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.225,0, '|d|_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function anghist(ad,ty)
%ANGHIST draw histogram for "angle" quality-metric.
ad = ad(:);
be = linspace(0.,180.,91);
bm =(be(1:end-1)+be(2:end))/2.;
hc = histc(ad,be);
switch (ty)
case 'tria4'
poor = bm < 10. | bm >= 160. ;
okay =(bm >= 10. & bm < 20. )| ...
(bm >= 140. & bm < 160.);
good =(bm >= 20. & bm < 30. )| ...
(bm >= 120. & bm < 140.);
best = bm >= 30. & bm < 120. ;
case 'tria3'
poor = bm < 15. | bm >= 150. ;
okay =(bm >= 15. & bm < 30. )| ...
(bm >= 120. & bm < 150.);
good =(bm >= 30. & bm < 45. )| ...
(bm >= 90. & bm < 120.);
best = bm >= 45. & bm < 90. ;
end
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',0:30:180,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,180.]) ;
mina = max(1.000,min(ad)); %%!! so that axes don't obscure!
maxa = min(179.0,max(ad));
bara = mean(ad(:));
mada = mad (ad(:));
line([ mina, mina],...
[0,max(hc)],'color','r','linewidth',1.5);
line([ maxa, maxa],...
[0,max(hc)],'color','r','linewidth',1.5);
if ( mina > 25.0)
text(mina-1.8,.90*max(hc),num2str(min(ad),'%16.1f'),...
'horizontalalignment',...
'right','fontsize',15) ;
else
text(mina+1.8,.90*max(hc),num2str(min(ad),'%16.1f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
if ( maxa < 140.)
text(maxa+1.8,.90*max(hc),num2str(max(ad),'%16.1f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
else
text(maxa-1.8,.90*max(hc),num2str(max(ad),'%16.1f'),...
'horizontalalignment',...
'right','fontsize',15) ;
end
if ( maxa < 100.)
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(maxa-16.,.45*max(hc),...
'$\bar{\sigma}_{\theta}\!= $',...
'horizontalalignment', 'left',...
'fontsize',16,'interpreter','latex') ;
text(maxa+1.8,.45*max(hc),num2str(mad(ad),'%16.2f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
else
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(maxa-16.,.45*max(hc),...
'$\bar{\sigma}_{\theta}\!= $',...
'horizontalalignment', 'left',...
'fontsize',16,'interpreter','latex') ;
text(maxa+1.8,.45*max(hc),num2str(mad(ad),'%16.3f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
end
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-9.0,0.0,'$\theta_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-9.0,0.0, '\theta_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-9.0,0.0,'$\theta_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-9.0,0.0, '\theta_{f}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function scrhist(sc,ty)
%SCRHIST draw histogram for "score" quality-metric.
sc = sc(:);
be = linspace(0.,1.,101);
bm = (be(1:end-1)+be(2:end)) / 2.;
hc = histc(sc,be);
switch (ty)
case{'tria4','dual4'}
poor = bm < .25 ;
okay = bm >= .25 & bm < .50 ;
good = bm >= .50 & bm < .75 ;
best = bm >= .75 ;
case{'tria3','dual3'}
poor = bm < .30 ;
okay = bm >= .30 & bm < .60 ;
good = bm >= .60 & bm < .90 ;
best = bm >= .90 ;
end
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',.0:.2:1.,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,1.]) ;
mins = max(0.010,min(sc)); %%!! so that axes don't obscure!
maxs = min(0.990,max(sc));
line([ mins, mins],...
[0,max(hc)],'color','r','linewidth',1.5);
line([mean(sc),mean(sc)],...
[0,max(hc)],'color','r','linewidth',1.5);
if ( mins > .4)
text(mins-.01,.9*max(hc),num2str(min(sc),'%16.3f'),...
'horizontalalignment',...
'right','fontsize',15) ;
else
text(mins+.01,.9*max(hc),num2str(min(sc),'%16.3f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
if ( mean(sc) > mins + .150)
text(mean(sc)-.01,.9*max(hc),num2str(mean(sc),'%16.3f'),...
'horizontalalignment','right','fontsize',15) ;
end
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{T}}_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{t}_{\tau}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{T}}_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{t}_{f}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'dual4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{D}}_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{d}_{\tau}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'dual3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{D}}_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{d}_{f}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function hfnhist(hf,ty)
%HFNHIST draw histogram for "hfunc" quality-metric.
be = linspace(0.,2.,101);
bm = (be(1:end-1)+be(2:end)) / 2.;
hc = histc(hf,be);
poor = bm < .40 | bm >= 1.6 ;
okay =(bm >= .40 & bm < .60 )| ...
(bm >= 1.4 & bm < 1.6 );
good =(bm >= .60 & bm < .80 )| ...
(bm >= 1.2 & bm < 1.4 );
best = bm >= .80 & bm < 1.2 ;
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',.0:.5:2.,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,2.]);
line([max(hf),max(hf)],...
[0,max(hc)],'color','r','linewidth',1.5);
text(max(hf)+.02,.90*max(hc),num2str(max(hf),'%16.2f'),...
'horizontalalignment','left','fontsize',15) ;
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(max(hf)-.18,.45*max(hc),'$\bar{\sigma}_{h}\! = $',...
'horizontalalignment','left',...
'fontsize',16,'interpreter','latex') ;
text(max(hf)+.02,.45*max(hc),num2str(mad(hf),'%16.2f'),...
'horizontalalignment','left','fontsize',15) ;
end
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-0.10,0.0,'$h_{r}$','horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-0.10,0.0, 'h_{r}' ,'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end