120ca87015
git-svn-id: https://free-cad.svn.sourceforge.net/svnroot/free-cad/trunk@5000 e8eeb9e2-ec13-0410-a4a9-efa5cf37419d
76 lines
2.8 KiB
C++
76 lines
2.8 KiB
C++
// 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 WM4APPRQUADRATICFIT3_H
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#define WM4APPRQUADRATICFIT3_H
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#include "Wm4FoundationLIB.h"
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#include "Wm4Vector3.h"
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namespace Wm4
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{
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// Quadratic fit is
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//
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// 0 = C[0] + C[1]*X + C[2]*Y + C[3]*Z + C[4]*X^2 + C[5]*Y^2
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// + C[6]*Z^2 + C[7]*X*Y + C[8]*X*Z + C[9]*Y*Z
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//
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// subject to Length(C) = 1. Minimize E(C) = C^t M C with Length(C) = 1
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// and M = (sum_i V_i)(sum_i V_i)^t where
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//
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// V = (1, X, Y, Z, X^2, Y^2, Z^2, X*Y, X*Z, Y*Z)
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//
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// Minimum value is the smallest eigenvalue of M and C is a corresponding
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// unit length eigenvector.
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//
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// Input:
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// n = number of points to fit
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// p[0..n-1] = array of points to fit
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//
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// Output:
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// c[0..9] = coefficients of quadratic fit (the eigenvector)
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// return value of function is nonnegative and a measure of the fit
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// (the minimum eigenvalue; 0 = exact fit, positive otherwise)
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// Canonical forms. The quadratic equation can be factored into
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// P^T A P + B^T P + K = 0 where P = (X,Y,Z), K = C[0], B = (C[1],C[2],C[3]),
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// and A is a 3x3 symmetric matrix with A00 = C[4], A11 = C[5], A22 = C[6],
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// A01 = C[7]/2, A02 = C[8]/2, and A12 = C[9]/2. Matrix A = R^T D R where
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// R is orthogonal and D is diagonal (using an eigendecomposition). Define
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// V = R P = (v0,v1,v2), E = R B = (e0,e1,e2), D = diag(d0,d1,d2), and f = K
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// to obtain
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//
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// d0 v0^2 + d1 v1^2 + d2 v^2 + e0 v0 + e1 v1 + e2 v2 + f = 0
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//
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// Characterization depends on the signs of the d_i.
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template <class Real> WM4_FOUNDATION_ITEM
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Real QuadraticFit3 (int iQuantity, const Vector3<Real>* akPoint,
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Real afCoeff[10]);
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// If you think your points are nearly spherical, use this. Sphere is of form
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// C'[0]+C'[1]*X+C'[2]*Y+C'[3]*Z+C'[4]*(X^2+Y^2+Z^2) where Length(C') = 1.
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// Function returns C = (C'[0]/C'[4],C'[1]/C'[4],C'[2]/C'[4],C'[3]/C'[4]), so
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// fitted sphere is C[0]+C[1]*X+C[2]*Y+C[3]*Z+X^2+Y^2+Z^2. Center is
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// (xc,yc,zc) = -0.5*(C[1],C[2],C[3]) and radius is rad =
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// sqrt(xc*xc+yc*yc+zc*zc-C[0]).
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template <class Real> WM4_FOUNDATION_ITEM
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Real QuadraticSphereFit3 (int iQuantity, const Vector3<Real>* akPoint,
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Vector3<Real>& rkCenter, Real& rfRadius);
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}
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#endif
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