function?[rectxrectyareaperimeter]?=?minboundrect（xymetric）
%?minboundrect:?Compute?the?minimal?bounding?rectangle?of?points?in?the?plane
%?usage:?[rectxrectyareaperimeter]?=?minboundrect（xymetric）
%
%?arguments:?（input）
%??xy?-?vectors?of?points?describing?points?in?the?plane?as
%????????（xy）?pairs.?x?and?y?must?be?the?same?lengths.
%
%??metric?-?（OPTIONAL）?-?single?letter?character?flag?which
%????????denotes?the?use?of?minimal?area?or?perimeter?as?the
%????????metric?to?be?minimized.?metric?may?be?either?‘a‘?or?‘p‘
%????????capitalization?is?ignored.?Any?other?contraction?of?‘area‘
%????????or?‘perimeter‘?is?also?accepted.
%
%????????DEFAULT:?‘a‘????（‘area‘）
%
%?arguments:?（output）
%??rectxrecty?-?5x1?vectors?of?points?that?define?the?minimal
%????????bounding?rectangle.
%
%??area?-?（scalar）?area?of?the?minimal?rect?itself.
%
%??perimeter?-?（scalar）?perimeter?of?the?minimal?rect?as?found
%
%
%?Note:?For?those?individuals?who?would?prefer?the?rect?with?minimum
%?perimeter?or?area?careful?testing?convinces?me?that?the?minimum?area
%?rect?was?generally?also?the?minimum?perimeter?rect?on?most?problems
%?（with?one?class?of?exceptions）.?This?same?testing?appeared?to?verify?my
%?assumption?that?the?minimum?area?rect?must?always?contain?at?least
%?one?edge?of?the?convex?hull.?The?exception?I?refer?to?above?is?for
%?problems?when?the?convex?hull?is?composed?of?only?a?few?points
%?most?likely?exactly?3.?Here?one?may?see?differences?between?the
%?two?metrics.?My?thanks?to?Roger?Stafford?for?pointing?out?this
%?class?of?counter-examples.
%
%?Thanks?are?also?due?to?Roger?for?pointing?out?a?proof?that?the
%?bounding?rect?must?always?contain?an?edge?of?the?convex?hull?in
%?both?the?minimal?perimeter?and?area?cases.
%
%
%?See?also:?minboundcircle?minboundtri?minboundsphere
%
%
%?default?for?metric
if?（nargin<3）?||?isempty（metric）
??metric?=?‘a‘;
elseif?~ischar（metric）
??error?‘metric?must?be?a?character?flag?if?it?is?supplied.‘
else
??%?check?for?‘a‘?or?‘p‘
??metric?=?lower（metric（:）‘）;????????????????????
??ind?=?strmatch（metric{‘area‘‘perimeter‘}）;?????????????
??if?isempty（ind）????????????????
????error?‘metric?does?not?match?either?‘‘area‘‘?or?‘‘perimeter‘‘‘
??end

??%?just?keep?the?first?letter.
??metric?=?metric（1）;
end

%?preprocess?data
x=x（:）;
y=y（:）;

%?not?many?error?checks?to?worry?about
n?=?length（x）;????????????????????????????????????
if?n~=length（y）???????????????????????????????
??error?‘x?and?y?must?be?the?same?sizes‘
end

%?start?out?with?the?convex?hull?of?the?points?to
%?reduce?the?problem?dramatically.?Note?that?any
%?points?in?the?interior?of?the?convex?hull?are
%?never?needed?so?we?drop?them.
if?n>3
%???edges?=?convhull（xy{‘Qt‘}）;??%?‘Pp‘?will?silence?the?warnings
try
edges?=?convhull（xy）;
catch
end
??%?exclude?those?points?inside?the?hull?as?not?relevant
??%?also?sorts?the?points?into?their?convex?hull?as?a
??%?closed?polygon

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????5260??2019-11-21?15:09??minboundrect.m

?????文件???????2841??2019-12-23?17:46??yidongpingjunfa.m

-----------?---------??----------?-----??----

?????????????????8101????????????????????2