function?B?=?basisfun?（iv?uv?p?U）

%?BASISFUN:??Basis?function?for?B-Spline
%
%?Calling?Sequence:
%?
%???N?=?basisfun（ivuvpU）
%???
%????INPUT:
%???
%??????iv?-?knot?span??（?from?FindSpan（）?）
%??????uv?-?parametric?points
%??????p??-?spline?degree
%??????U??-?knot?sequence
%???
%????OUTPUT:
%???
%??????N?-?Basis?functions?vector（numel（uv）*（p+1））
%???
%????Adapted?from?Algorithm?A2.2?from?‘The?NURBS?BOOK‘?pg70.
%
%?See?also:?
%
%????numbasisfun?basisfunder?findspan
%
%?Copyright?（C）?2000?Mark?Spink
%?Copyright?（C）?2007?Daniel?Claxton
%?Copyright?（C）?2009?Carlo?de?Falco
%
%????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?.

B?=?zeros（numel（uv）?p+1）;
???????????????????????????????????????????????
for?jj?=?1:numel（uv）?

??i?=?iv（jj）?+?1;?%%?findspan?uses?0-based?numbering
??u?=?uv（jj）;

??left?=?zeros（p+11）;
??right?=?zeros（p+11）;

??N（1）?=?1;
??for?j=1:p
????left（j+1）?=?u?-?U（i+1-j）;
????right（j+1）?=?U（i+j）?-?u;
????saved?=?0;

????for?r=0:j-1
??????temp?=?N（r+1）/（right（r+2）?+?left（j-r+1））;
??????N（r+1）?=?saved?+?right（r+2）*temp;
??????saved?=?left（j-r+1）*temp;
????end
????
????N（j+1）?=?saved;
??end

??B?（jj?:）?=?N;

end

end

%!test
%!??n?=?3;?
%!??U?=?[0?0?0?1/2?1?1?1];?
%!??p?=?2;?
%!??u?=?linspace?（0?1?10）;??
%!??s?=?findspan?（n?p?u?U）;??
%!??Bref?=?[1.00000???0.00000???0.00000
%!??????????0.60494???0.37037???0.02469
%!??????????0.30864???0.59259???0.09877
%!??????????0.11111???0.66667???0.22222
%!??????????0.01235???0.59259???0.39506
%!??????????0.39506???0.59259???0.01235
%!??????????0.22222???0.66667???0.11111
%!??????????0.09877???0.59259???0.30864
%!??????????0.02469???0.37037???0.60494
%!??????????0.00000???0.00000???1.00000];
%!??B?=?basisfun?（s?u?p?U）;
%!??assert?（B?Bref?1e-5）;