%?Bezier?interpolation?for?given?four?control?points.
%?Each?control?point?can?be?in?N-Dimensional?vector?space.
%?Input:
%?P0P1P2P3:?four?control?points?of?bezier?curve
%??????????????control?points?can?have?any?number?of?coordinates
%?t（optional?arg）:vector?that?holds?paramter?t?values?b/w?0?and?1?at?which?
%?????????????????bezier?curve?is?evaluated?（default?101?values?between?0
%?????????????????and?1.）

%?Output:
%?Q?evaluated?values?of?bezier?curves.?Number?of?columns?of?Q?are?equal?to
%?number?of?coordinates?in?control?point.?For?example?for?2-D?Q?has?two
%?columns.?Column?1?for?x?value?and?column?2?for?y?values.?Similarly?for
%?3-D?Q?will?have?three?columns

function?Q=bezierInterp（P0P1P2P3varargin）

%%%?Default?Values?%%%
t=linspace（01101）;?%?uniform?parameterization?
defaultValues?=?{t};
%%%?Assign?Valus?%%%
nonemptyIdx?=?~cellfun（‘isempty‘varargin）;
defaultValues（nonemptyIdx）?=?varargin（nonemptyIdx）;
[t]?=?deal（defaultValues{:}）;
%?%?--------------------------------
M=[-1??3?-3?1;
????3?-6??3?0;
???-3??3??0?0;
????1??0??0?0];
for?k=1:length（t）
????Q（k:）=[t（k）^3?t（k）^2?t（k）?1]*M*[P0;P1;P2;P3];
end
%?%?Ref:?Mathematical?Elements?of?Computer?Graphics?by
%?%??????David?F.?Rogers?and?J.?Alan?Adams?（pg.?296）
%?%?--------------------------------
%?%?OR
%?%?Equation?of?Bezier?Curve?utilizes?Horner‘s?rule?for?efficient?computation.
%?%?Q（t）=（-P0?+?3*（P1-P2）?+?P3）*t^3?+?3*（P0-2*P1+P2）*t^2?+?3*（P1-P0）*t?+?Px0
%?c3?=?-P0?+?3*（P1-P2）?+?P3;
%?c2?=?3*（P0?-?（2*P1）+P2）;?
%?c1?=?3*（P1?-?P0）;
%?c0?=?P0;
%?for?k=1:length（t）
%?????Q（k:）=（（c3*t（k）+c2）*t（k）+c1）*t（k）?+?c0;????
%?end

%?%?%?--------------------------------
%?%?%?Author:?Dr.?Murtaza?Khan
%?%?%?Email?:?drkhanmurtaza@gmail.com
%?%?%?--------------------------------

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

?????文件???????1811??2009-07-09?17:00??cubicbezierlsufit\cubicbezierlsufit\bezierInterp.m

?????文件???????2214??2009-07-09?16:59??cubicbezierlsufit\cubicbezierlsufit\BezierInterpCPMatSegVec.m

?????文件???????6137??2009-07-09?17:00??cubicbezierlsufit\cubicbezierlsufit\bzapproxu.m

?????文件??????45518??2007-07-10?13:22??cubicbezierlsufit\cubicbezierlsufit\cubicbezierleastsquarefit.pdf

?????文件???????3107??2009-07-09?17:00??cubicbezierlsufit\cubicbezierlsufit\FindBezierControlPointsND.m

?????文件???????1622??2009-07-09?17:00??cubicbezierlsufit\cubicbezierlsufit\FindBzCP4AllSeg.m

?????文件???????1984??2009-07-09?17:01??cubicbezierlsufit\cubicbezierlsufit\FindGivenRangeMatchedMat.m

?????文件???????8449??2005-05-12?05:33??cubicbezierlsufit\cubicbezierlsufit\five.txt

?????文件????????668??2009-07-09?17:01??cubicbezierlsufit\cubicbezierlsufit\getcolvector.m

?????文件????????396??2009-07-09?17:01??cubicbezierlsufit\cubicbezierlsufit\isvec.m

?????文件???????1826??2009-07-09?17:01??cubicbezierlsufit\cubicbezierlsufit\main.m

?????文件???????1559??2009-07-09?17:01??cubicbezierlsufit\cubicbezierlsufit\MaxSqDistAndInd4EachSegbw2Mat.m

?????文件???????1364??2009-07-09?17:02??cubicbezierlsufit\cubicbezierlsufit\MaxSqDistAndRowIndexbw2Mat.m

?????文件????????929??2009-07-09?17:02??cubicbezierlsufit\cubicbezierlsufit\plot2d_bz_org_intrp_cp.m

?????文件??????27040??2007-07-10?05:34??cubicbezierlsufit\cubicbezierlsufit\snap.PNG

?????文件???????1337??2009-07-09?10:17??cubicbezierlsufit\license.txt

?????目錄??????????0??2009-10-22?13:32??cubicbezierlsufit\cubicbezierlsufit

?????目錄??????????0??2009-10-22?13:32??cubicbezierlsufit

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

???????????????105961????????????????????18