61 lines
2.4 KiB
C++
61 lines
2.4 KiB
C++
// SPDX-License-Identifier: LGPL-2.1-or-later
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// Wild Magic Source Code
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// David Eberly
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// http://www.geometrictools.com
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// Copyright (c) 1998-2007
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//
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// This library is free software; you can redistribute it and/or modify it
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// under the terms of the GNU Lesser General Public License as published by
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// the Free Software Foundation; either version 2.1 of the License, or (at
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// your option) any later version. The license is available for reading at
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// either of the locations:
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// http://www.gnu.org/copyleft/lgpl.html
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// http://www.geometrictools.com/License/WildMagicLicense.pdf
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// The license applies to versions 0 through 4 of Wild Magic.
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//
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// Version: 4.0.0 (2006/06/28)
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#ifndef WM4APPRPOLYFIT3_H
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#define WM4APPRPOLYFIT3_H
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#include "Wm4FoundationLIB.h"
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#include "Wm4System.h"
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namespace Wm4
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{
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// The samples are (x[i],y[i],w[i]) for 0 <= i < S. Think of w as a function
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// of x and y, say w = f(x,y). The function fits the samples with a
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// polynomial of degree d0 in x and degree d1 in y, say
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// w = sum_{i=0}^{d0} sum_{j=0}^{d1} c[i][j]*x^i*y^j
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// The method is a least-squares fitting algorithm. The returned array
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// stores the c[i][j] values according to returned[i+(d0+1)*j] = c[i][j]
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// for a total of (d0+1)*(d1+1) coefficients. The caller is responsible for
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// deleting the input arrays if they were dynamically allocated. The caller
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// is also responsible for deleting the returned array.
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//
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// WARNING. The fitting algorithm for polynomial terms
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// (1,x,x^2,...,x^d0), (1,y,y^2,...,y^d1)
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// is known to be nonrobust for large degrees and for large magnitude data.
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// One alternative is to use orthogonal polynomials
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// (f[0](x),...,f[d0](x)), (g[0](y),...,g[d1](y))
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// and apply the least-squares algorithm to these. Another alternative is to
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// transform
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// (x',y',w') = ((x-xcen)/rng, (y-ycen)/rng, w/rng)
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// where xmin = min(x[i]), xmax = max(x[i]), xcen = (xmin+xmax)/2,
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// ymin = min(y[i]), ymax = max(y[i]), ycen = (ymin+ymax)/2, and
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// rng = max(xmax-xmin,ymax-ymin). Fit the (x',y',w') points,
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// w' = sum_{i=0}^{d0} sum_{j=0}^{d1} c'[i][j]*(x')^i*(y')^j
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// The original polynomial is evaluated as
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// w = rng * sum_{i=0}^{d0} sum_{j=0}^{d1} c'[i][j] *
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// ((x-xcen)/rng)^i * ((y-ycen)/rng)^j
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template <class Real> WM4_FOUNDATION_ITEM
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Real* PolyFit3 (int iSamples, const Real* afX, const Real* afY,
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const Real* afW, int iXDegree, int iYDegree);
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}
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#endif
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