tpaps.m

演示matlab曲线拟和与插直的基本方法

% TPAPS   Thin-plate暯妸壔僗僾儔僀儞
%
% F = TPAPS(X,Y) 偼丄梌偊傜傟偨僨乕僞僒僀僩 X(:,j) 偲偦傟偵懳墳偡傞僨乕僞
% 抣 Y(:,j) 偵懳偡傞thin-plate暯妸壔僗僾儔僀儞 f 偺 st-宆偱偡丅
% 僨乕僞抣偼丄僗僇儔丄儀僋僩儖丄峴楍丄傑偨偼N師尦攝楍偱偡丅
% X(:,j) 偼丄暯柺撪偺堎側傞揰偱偁傝丄僨乕僞僒僀僩偲尩枾偵摨偠悢偺僨乕僞抣
% 偑側偗傟偽側傝傑偣傫丅
% thin-plate暯妸壔僗僾儔僀儞 f 偼丄廳傒晅偒榓
%
%                     P*E(f) + (1-P)*R(f) ,
%
% 偺偨偩堦偮偺儈僯儅僀僓偱偡丅偙偙偱丄E(f) 偼丄岆嵎婎弨偱偡丅
%
%       E(f) :=  sum_j { | Y(:,j) - f(X(:,j)) |^2 : j=1,...,n }
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% 偝傜偵丄R(f) 偼丄偮偓偺慹偝(roughness)婎弨偱偡丅
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%       R(f) := integral  (D_1 D_1 f)^2 + 2(D_1 D_2 f)^2 + (D_2 D_2 f)^2.
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% 偙偙偱丄愊暘偼丄2偮偺嬻娫慡懱偵搉偭偰峴傢傟傑偡丅D_i 偼丄i斣栚偺堷悢偵
% 娭偡傞旝暘傪帵偟傑偡丅偦偺偨傔丄愊暘偼丄f 偺2師旝暘傪昁梫偲偟傑偡丅
% 暯妸壔僷儔儊乕僞 P 偼丄僒僀僩 X 偵埶懚偡傞屄暿偺曽朄偱慖戰偝傟傑偡丅
%
% TPAPS(X,Y,P) 偼丄0偲1偺娫偺悢偱偁傞丄暯妸壔僷儔儊乕僞 P 傪梌偊傑偡丅
% P 偑0偐傜1傑偱曄壔偡傞偲偒丄僨乕僞偵懳偡傞暯妸壔僗僾儔僀儞偼丄 P 偑
% 0偺偲偒偺慄宍懡崁幃偵傛傞嵟彫擇忔嬤帡偐傜丄P 偑1偺偲偒偺thin-plate
% 僗僾儔僀儞曗娫傑偱曄壔偟傑偡丅
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% [F,P] = TPAPS(...) 偼丄巊梡偝傟偨暯妸壔僷儔儊乕僞傪弌椡偟傑偡丅
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% 寈崘: 暯妸壔僗僾儔僀儞偺寛掕偵偼丄懚嵼偡傞僨乕僞揰偲摨偠悢偺枹抦悢傪
% 傕偮慄宍僔僗僥儉偺夝偑昁梫偱偡丅偙偺慄宍僔僗僥儉偺峴楍偼僼儖偺偨傔丄
% 偦傟傪夝偔偵偼丄728 埲忋偺僨乕僞揰偑懚嵼偟丄孞傝曉偟偺僗僉乕儉偑巊梡
% 偝傟傞偙偙偱偺応崌偱偝偊挿偄帪娫偑偐偐傝傑偡丅偙偺孞傝曉偟偺廂懇偺
% 懍偝偼丄P 偵傛偭偰嫮偔塭嬁傪庴偗丄P 偑戝偒偄傎偳娚傗偐偵側傝傑偡丅
% 廬偭偰丄戝婯柾側栤戣偵懳偟偰偼丄帪娫揑梋桾偑偁傞応崌偺傒丄(P 傪1偲偡傞)
% 曗娫傪巊梡偟偰偔偩偝偄丅 
%
% 椺戣:
%
%      rand('seed',23); nxy = 31;
%      xy = 2*(rand(2,nxy)-.5); vals = sum(xy.^2);
%      noisyvals = vals + (rand(size(vals))-.5)/5;
%      st = tpaps(xy,noisyvals); fnplt(st), hold on
%      avals = fnval(st,xy);
%      plot3(xy(1,:),xy(2,:),vals,'wo','markerfacecolor','k')
%      quiver3(xy(1,:),xy(2,:),avals,zeros(1,nxy),zeros(1,nxy), ...
%               noisyvals-avals,'r'), hold off
% 偼丄 31偺儔儞僟儉側僒僀僩偱丄旕忢偵妸傜偐側娭悢偺抣傪惗惉偟偰丄偁傞
% 僲僀僘傪壛偊丄偦偟偰丄偙傟傜偺僲僀僘偺偁傞僨乕僞偵懳偟偰丄暯妸壔僗僾
% 儔僀儞傪嶌惉偟傑偡丅嵞尰偟傛偆偲偟偰偄傞尦偺僨乕僞偺尩枾側抣(崟娵)偲丄
% 暯妸壔僗僾儔僀儞偱暯妸壔偝傟偨抣偐傜僲僀僘偺偁傞抣偵払偡傞栴報傪
% 僾儘僢僩偟傑偡丅 
%
%      n = 64; t = linspace(0,2*pi,n+1); t(end) = [];
%      values = [cos(t); sin(t)];
%      centers = values./repmat(max(abs(values)),2,1);
%      st = tpaps(centers, values, 1);
%      fnplt(st), axis equal
% 偼丄惗惉偝傟偨恾偵帵偝傟傞傛偆偵丄扨埵惓曽宍 
% {x in R^2: |x(j)|<=1, j=1:2} 偺揰傪扨埵墌斅 {x in R^2: norm(x)<=1} 
% 忋偵丄偐側傝堦抳偡傞傛偆偵堏偡丄暯柺偐傜暯柺傊偺幨憸傪嶌恾偟傑偡丅
%
% 嶲峫 CSAPS, SPAPS.


%   Copyright 1987-2004 C. de Boor and The MathWorks, Inc.