function?alpha?=?anglePoints3d（varargin）
%ANGLEPOINTS3D?Compute?angle?between?three?3D?points
%
%???ALPHA?=?anglePoints3d（P1?P2）
%???Computes?angle?（P1?O?P2）?in?radians?between?0?and?PI.
%
%???ALPHA?=?anglePoints3d（P1?P2?P3）
%???Computes?angle?（P1?P2?P3）?in?radians?between?0?and?PI.
%
%???ALPHA?=?anglePoints3d（PTS）
%???PTS?is?a?3x3?or?2x3?array?containing?coordinate?of?points.
%
%???See?also
%???points3d?angles3d
%
%???---------
%???author?:?David?Legland?
%???INRA?-?TPV?URPOI?-?BIA?IMASTE
%???created?the?21/02/2005.
%

%???HISTORY
%???20/09/2005?:?add?case?of?single?argument?for?all?points
%???04/01/2007:?check?typo

p2?=?[0?0?0];
if?length（varargin）==1
????pts?=?varargin{1};
????if?size（pts?1）==2
????????p1?=?pts（1:）;
????????p0?=?[0?0?0];
????????p2?=?pts（2:）;
????else
????????p1?=?pts（1:）;
????????p0?=?pts（2:）;
????????p2?=?pts（3:）;
????end
elseif?length（varargin）==2
????p1?=?varargin{1};
????p0?=?[0?0?0];
????p2?=?varargin{2};
elseif?length（varargin）==3
????p1?=?varargin{1};
????p0?=?varargin{2};
????p2?=?varargin{3};
end

%?ensure?all?data?have?same?size
n1?=?size（p1?1）;
n2?=?size（p2?1）;
n0?=?size（p0?1）;
if?n1~=n2
????if?n1==1
????????p1?=?repmat（p1?[n2?1]）;
????elseif?n2==1
????????p2?=?repmat（p2?[n1?1]）;
????else
????????error（‘Arguments?P1?and?P2?must?have?the?same?size‘）;
????end
end
if?n1~=n0
????if?n1==1
????????p1?=?repmat（p1?[n0?1]）;
????elseif?n0==1
????????p0?=?repmat（p0?[n1?1]）;
????else
????????error（‘Arguments?P1?and?P0?must?have?the?same?size‘）;
????end
end

%?normalized?vectors
p1?=?normalizeVector3d（p1-p0）;
p2?=?normalizeVector3d（p2-p0）;

%?compute?angle
alpha?=?acos（dot（p1?p2?2））;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2011-06-30?15:51??geom3d\
?????目錄???????????0??2011-06-30?15:51??geom3d\geom3d\
?????文件????????1734??2010-08-11?22:13??geom3d\geom3d\anglePoints3d.m
?????文件????????1710??2011-06-29?17:57??geom3d\geom3d\angles3d.m
?????文件????????2035??2011-03-21?03:07??geom3d\geom3d\angleSort3d.m
?????文件?????????621??2010-07-26?22:00??geom3d\geom3d\box3dVolume.m
?????文件?????????671??2011-06-27?14:53??geom3d\geom3d\boxes3d.m
?????文件????????1505??2008-10-13?22:15??geom3d\geom3d\cart2cyl.m
?????文件????????1631??2011-06-29?17:57??geom3d\geom3d\cart2sph2.m
?????文件????????1791??2011-06-29?17:57??geom3d\geom3d\cart2sph2d.m
?????文件????????3400??2011-06-30?13:40??geom3d\geom3d\changelog.txt
?????文件?????????629??2010-07-29?18:07??geom3d\geom3d\changes.txt
?????文件????????1013??2011-06-21?18:36??geom3d\geom3d\circle3dOrigin.m
?????文件????????1307??2011-06-21?20:41??geom3d\geom3d\circle3dPoint.m
?????文件????????1423??2011-06-29?17:57??geom3d\geom3d\circle3dPosition.m
?????文件?????????913??2011-06-22?14:51??geom3d\geom3d\circles3d.m
?????文件????????2957??2011-03-21?03:07??geom3d\geom3d\clipLine3d.m
?????文件????????1061??2011-03-21?03:07??geom3d\geom3d\clipPoints3d.m
?????文件????????2567??2008-10-13?22:15??geom3d\geom3d\clipPolygon3dHP.m
?????文件?????????931??2011-03-21?03:07??geom3d\geom3d\composeTransforms3d.m
?????文件???????11470??2011-06-29?21:57??geom3d\geom3d\Contents.m
?????文件????????1785??2011-01-11?18:57??geom3d\geom3d\createBasisTransform3d.m
?????文件????????1921??2011-06-20?19:30??geom3d\geom3d\createEulerAnglesRotation.m
?????文件????????4579??2011-03-21?03:07??geom3d\geom3d\createLine3d.m
?????文件????????3360??2011-05-27?21:16??geom3d\geom3d\createPlane.m
?????文件????????1311??2010-08-11?22:13??geom3d\geom3d\createRotation3dLineAngle.m
?????文件????????1865??2011-03-21?03:07??geom3d\geom3d\createRotationOx.m
?????文件????????1969??2011-03-21?03:07??geom3d\geom3d\createRotationOy.m
?????文件????????1878??2011-03-21?03:07??geom3d\geom3d\createRotationOz.m
?????文件????????1869??2011-03-21?03:07??geom3d\geom3d\createScaling3d.m
?????文件?????????990??2011-03-21?03:07??geom3d\geom3d\createSphere.m
............此處省略174個文件信息