/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* This file incorporates work covered by the following license notice:
*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed
* with this work for additional information regarding copyright
* ownership. The ASF licenses this file to you under the Apache
* License, Version 2.0 (the "License"); you may not use this file
* except in compliance with the License. You may obtain a copy of
* the License at http://www.apache.org/licenses/LICENSE-2.0 .
*/
#include "Splines.hxx"
#include <rtl/math.hxx>
#include <osl/diagnose.h>
#include <com/sun/star/drawing/PolyPolygonShape3D.hpp>
#include <vector>
#include <algorithm>
#include <functional>
#include <memory>
namespace chart
{
using namespace ::com::sun::star;
namespace
{
typedef std::pair< double, double > tPointType;
typedef std::vector< tPointType > tPointVecType;
typedef tPointVecType::size_type lcl_tSizeType;
class lcl_SplineCalculation
{
public:
/** @descr creates an object that calculates cubic splines on construction
@param rSortedPoints the points for which splines shall be calculated, they need to be sorted in x values
@param fY1FirstDerivation the resulting spline should have the first
derivation equal to this value at the x-value of the first point
of rSortedPoints. If fY1FirstDerivation is set to infinity, a natural
spline is calculated.
@param fYnFirstDerivation the resulting spline should have the first
derivation equal to this value at the x-value of the last point
of rSortedPoints
*/
lcl_SplineCalculation( const tPointVecType & rSortedPoints,
double fY1FirstDerivation,
double fYnFirstDerivation );
/** @descr creates an object that calculates cubic splines on construction
for the special case of periodic cubic spline
@param rSortedPoints the points for which splines shall be calculated,
they need to be sorted in x values. First and last y value must be equal
*/
explicit lcl_SplineCalculation( const tPointVecType & rSortedPoints);
/** @descr this function corresponds to the function splint in [1].
[1] Numerical Recipes in C, 2nd edition
William H. Press, et al.,
Section 3.3, page 116
*/
double GetInterpolatedValue( double x );
private:
/// a copy of the points given in the CTOR
tPointVecType m_aPoints;
/// the result of the Calculate() method
std::vector< double > m_aSecDerivY;
double m_fYp1;
double m_fYpN;
// these values are cached for performance reasons
lcl_tSizeType m_nKLow;
lcl_tSizeType m_nKHigh;
double m_fLastInterpolatedValue;
/** @descr this function corresponds to the function spline in [1].
[1] Numerical Recipes in C, 2nd edition
William H. Press, et al.,
Section 3.3, page 115
*/
void Calculate();
/** @descr this function corresponds to the algorithm 4.76 in [2] and
theorem 5.3.7 in [3]
[2] Engeln-Müllges, Gisela: Numerik-Algorithmen: Verfahren, Beispiele, Anwendungen
Springer, Berlin; Auflage: 9., überarb. und erw. A. (8. Dezember 2004)
Section 4.10.2, page 175
[3] Hanrath, Wilhelm: Mathematik III / Numerik, Vorlesungsskript zur
Veranstaltung im WS 2007/2008
Fachhochschule Aachen, 2009-09-19
Numerik_01.pdf, downloaded 2011-04-19 via
http://www.fh-aachen.de/index.php?id=11424&no_cache=1&file=5016&uid=44191
Section 5.3, page 129
*/
void CalculatePeriodic();
};
lcl_SplineCalculation::lcl_SplineCalculation(
const tPointVecType & rSortedPoints,
double fY1FirstDerivation,
double fYnFirstDerivation )
: m_aPoints( rSortedPoints ),
m_fYp1( fY1FirstDerivation ),
m_fYpN( fYnFirstDerivation ),
m_nKLow( 0 ),
m_nKHigh( rSortedPoints.size() - 1 ),
m_fLastInterpolatedValue(0.0)
{
::rtl::math::setInf( &m_fLastInterpolatedValue, false );
Calculate();
}
lcl_SplineCalculation::lcl_SplineCalculation(
const tPointVecType & rSortedPoints)
: m_aPoints( rSortedPoints ),
m_fYp1( 0.0 ), /*dummy*/
m_fYpN( 0.0 ), /*dummy*/
m_nKLow( 0 ),
m_nKHigh( rSortedPoints.size() - 1 ),
m_fLastInterpolatedValue(0.0)
{
::rtl::math::setInf( &m_fLastInterpolatedValue, false );
CalculatePeriodic();
}
void lcl_SplineCalculation::Calculate()
{
if( m_aPoints.size() <= 1 )
return;
// n is the last valid index to m_aPoints
const lcl_tSizeType n = m_aPoints.size() - 1;
std::vector< double > u( n );
m_aSecDerivY.resize( n + 1, 0.0 );
if( ::rtl::math::isInf( m_fYp1 ) )
{
// natural spline
m_aSecDerivY[ 0 ] = 0.0;
u[ 0 ] = 0.0;
}
else
{
m_aSecDerivY[ 0 ] = -0.5;
double xDiff = ( m_aPoints[ 1 ].first - m_aPoints[ 0 ].first );
u[ 0 ] = ( 3.0 / xDiff ) *
((( m_aPoints[ 1 ].second - m_aPoints[ 0 ].second ) / xDiff ) - m_fYp1 );
}
for( lcl_tSizeType i = 1; i < n; ++i )
{
tPointType
p_i = m_aPoints[ i ],
p_im1 = m_aPoints[ i - 1 ],
p_ip1 = m_aPoints[ i + 1 ];
double sig = ( p_i.first - p_im1.first ) /
( p_ip1.first - p_im1.first );
double p = sig * m_aSecDerivY[ i - 1 ] + 2.0;
m_aSecDerivY[ i ] = ( sig - 1.0 ) / p;
u[ i ] =
( ( p_ip1.second - p_i.second ) /
( p_ip1.first - p_i.first ) ) -
( ( p_i.second - p_im1.second ) /
( p_i.first - p_im1.first ) );
u[ i ] =
( 6.0 * u[ i ] / ( p_ip1.first - p_im1.first )
- sig * u[ i - 1 ] ) / p;
}
// initialize to values for natural splines (used for m_fYpN equal to
// infinity)
double qn = 0.0;
double un = 0.0;
if( ! ::rtl::math::isInf( m_fYpN ) )
{
qn = 0.5;
double xDiff = ( m_aPoints[ n ].first - m_aPoints[ n - 1 ].first );
un = ( 3.0 / xDiff ) *
( m_fYpN - ( m_aPoints[ n ].second - m_aPoints[ n - 1 ].second ) / xDiff );
}
m_aSecDerivY[ n ] = ( un - qn * u[ n - 1 ] ) * ( qn * m_aSecDerivY[ n - 1 ] + 1.0 );
// note: the algorithm in [1] iterates from n-1 to 0, but as size_type
// may be (usually is) an unsigned type, we can not write k >= 0, as this
// is always true.
for( lcl_tSizeType k = n; k > 0; --k )
{
( m_aSecDerivY[ k - 1 ] *= m_aSecDerivY[ k ] ) += u[ k - 1 ];
}
}
void lcl_SplineCalculation::CalculatePeriodic()
{
if( m_aPoints.size() <= 1 )
return;
// n is the last valid index to m_aPoints
const lcl_tSizeType n = m_aPoints.size() - 1;
// u is used for vector f in A*c=f in [3], vector a in Ax=a in [2],
// vector z in Rtranspose z = a and Dr=z in [2]
std::vector< double > u( n + 1, 0.0 );
// used for vector c in A*c=f and vector x in Ax=a in [2]
m_aSecDerivY.resize( n + 1, 0.0 );
// diagonal of matrix A, used index 1 to n
std::vector< double > Adiag( n + 1, 0.0 );
// secondary diagonal of matrix A with index 1 to n-1 and upper right element in A[n]
std::vector< double > Aupper( n + 1, 0.0 );
// diagonal of matrix D in A=(R transpose)*D*R in [2], used index 1 to n
std::vector< double > Ddiag( n+1, 0.0 );
// right column of matrix R, used index 1 to n-2
std::vector< double > Rright( n-1, 0.0 );
// secondary diagonal of matrix R, used index 1 to n-1
std::vector< double > Rupper( n, 0.0 );
if (n<4)
{
if (n==3)
{ // special handling of three polynomials, that are four points
double xDiff0 = m_aPoints[ 1 ].first - m_aPoints[ 0 ].first ;
double xDiff1 = m_aPoints[ 2 ].first - m_aPoints[ 1 ].first ;
double xDiff2 = m_aPoints[ 3 ].first - m_aPoints[ 2 ].first ;
double xDiff2p1 = xDiff2 + xDiff1;
double xDiff0p2 = xDiff0 + xDiff2;
double xDiff1p0 = xDiff1 + xDiff0;
double fFactor = 1.5 / (xDiff0*xDiff1 + xDiff1*xDiff2 + xDiff2*xDiff0);
double yDiff0 = (m_aPoints[ 1 ].second - m_aPoints[ 0 ].second) / xDiff0;
double yDiff1 = (m_aPoints[ 2 ].second - m_aPoints[ 1 ].second) / xDiff1;
double yDiff2 = (m_aPoints[ 0 ].second - m_aPoints[ 2 ].second) / xDiff2;
m_aSecDerivY[ 1 ] = fFactor * (yDiff1*xDiff2p1 - yDiff0*xDiff0p2);
m_aSecDerivY[ 2 ] = fFactor * (yDiff2*xDiff0p2 - yDiff1*xDiff1p0);
m_aSecDerivY[ 3 ] = fFactor * (yDiff0*xDiff1p0 - yDiff2*xDiff2p1);
m_aSecDerivY[ 0 ] = m_aSecDerivY[ 3 ];
}
else if (n==2)
{
// special handling of two polynomials, that are three points
double xDiff0 = m_aPoints[ 1 ].first - m_aPoints[ 0 ].first;
double xDiff1 = m_aPoints[ 2 ].first - m_aPoints[ 1 ].first;
double fHelp = 3.0 * (m_aPoints[ 0 ].second - m_aPoints[ 1 ].second) / (xDiff0*xDiff1);
m_aSecDerivY[ 1 ] = fHelp ;
m_aSecDerivY[ 2 ] = -fHelp ;
m_aSecDerivY[ 0 ] = m_aSecDerivY[ 2 ] ;
}
else
{
// should be handled with natural spline, periodic not possible.
}
}
else
{
double xDiff_i =1.0; // values are dummy;
double xDiff_im1 =1.0;
double yDiff_i = 1.0;
double yDiff_im1 = 1.0;
// fill matrix A and fill right side vector u
for( lcl_tSizeType i=1; i<n; ++i )
{
xDiff_im1 = m_aPoints[ i ].first - m_aPoints[ i-1 ].first;
xDiff_i = m_aPoints[ i+1 ].first - m_aPoints[ i ].first;
yDiff_im1 = (m_aPoints[ i ].second - m_aPoints[ i-1 ].second) / xDiff_im1;
yDiff_i = (m_aPoints[ i+1 ].second - m_aPoints[ i ].second) / xDiff_i;
Adiag[ i ] = 2 * (xDiff_im1 + xDiff_i);
Aupper[ i ] = xDiff_i;
u [ i ] = 3 * (yDiff_i - yDiff_im1);
}
xDiff_im1 = m_aPoints[ n ].first - m_aPoints[ n-1 ].first;
xDiff_i = m_aPoints[ 1 ].first - m_aPoints[ 0 ].first;
yDiff_im1 = (m_aPoints[ n ].second - m_aPoints[ n-1 ].second) / xDiff_im1;
yDiff_i = (m_aPoints[ 1 ].second - m_aPoints[ 0 ].second) / xDiff_i;
Adiag[ n ] = 2 * (xDiff_im1 + xDiff_i);
Aupper[ n ] = xDiff_i;
u [ n ] = 3 * (yDiff_i - yDiff_im1);
// decomposite A=(R transpose)*D*R
Ddiag[1] = Adiag[1];
Rupper[1] = Aupper[1] / Ddiag[1];
Rright[1] = Aupper[n] / Ddiag[1];
for( lcl_tSizeType i=2; i<=n-2; ++i )
{
Ddiag[i] = Adiag[i] - Aupper[ i-1 ] * Rupper[ i-1 ];
Rupper[ i ] = Aupper[ i ] / Ddiag[ i ];
Rright[ i ] = - Rright[ i-1 ] * Aupper[ i-1 ] / Ddiag[ i ];
}
Ddiag[ n-1 ] = Adiag[ n-1 ] - Aupper[ n-2 ] * Rupper[ n-2 ];
Rupper[ n-1 ] = ( Aupper[ n-1 ] - Aupper[ n-2 ] * Rright[ n-2] ) / Ddiag[ n-1 ];
double fSum = 0.0;
for ( lcl_tSizeType i=1; i<=n-2; ++i )
{
fSum += Ddiag[ i ] * Rright[ i ] * Rright[ i ];
}
Ddiag[ n ] = Adiag[ n ] - fSum - Ddiag[ n-1 ] * Rupper[ n-1 ] * Rupper[ n-1 ]; // bug in [2]!
// solve forward (R transpose)*z=u, overwrite u with z
for ( lcl_tSizeType i=2; i<=n-1; ++i )
{
u[ i ] -= u[ i-1 ]* Rupper[ i-1 ];
}
fSum = 0.0;
for ( lcl_tSizeType i=1; i<=n-2; ++i )
{
fSum += Rright[ i ] * u[ i ];
}
u[ n ] = u[ n ] - fSum - Rupper[ n - 1] * u[ n-1 ];
// solve forward D*r=z, z is in u, overwrite u with r
for ( lcl_tSizeType i=1; i<=n; ++i )
{
u[ i ] = u[i] / Ddiag[ i ];
}
// solve backward R*x= r, r is in u
m_aSecDerivY[ n ] = u[ n ];
m_aSecDerivY[ n-1 ] = u[ n-1 ] - Rupper[ n-1 ] * m_aSecDerivY[ n ];
for ( lcl_tSizeType i=n-2; i>=1; --i)
{
m_aSecDerivY[ i ] = u[ i ] - Rupper[ i ] * m_aSecDerivY[ i+1 ] - Rright[ i ] * m_aSecDerivY[ n ];
}
// periodic
m_aSecDerivY[ 0 ] = m_aSecDerivY[ n ];
}
// adapt m_aSecDerivY for usage in GetInterpolatedValue()
for( lcl_tSizeType i = 0; i <= n ; ++i )
{
m_aSecDerivY[ i ] *= 2.0;
}
}
double lcl_SplineCalculation::GetInterpolatedValue( double x )
{
OSL_PRECOND( ( m_aPoints[ 0 ].first <= x ) &&
( x <= m_aPoints[ m_aPoints.size() - 1 ].first ),
"Trying to extrapolate" );
const lcl_tSizeType n = m_aPoints.size() - 1;
if( x < m_fLastInterpolatedValue )
{
m_nKLow = 0;
m_nKHigh = n;
// calculate m_nKLow and m_nKHigh
// first initialization is done in CTOR
while( m_nKHigh - m_nKLow > 1 )
{
lcl_tSizeType k = ( m_nKHigh + m_nKLow ) / 2;
if( m_aPoints[ k ].first > x )
m_nKHigh = k;
else
m_nKLow = k;
}
}
else
{
while( ( m_nKHigh <= n ) &&
( m_aPoints[ m_nKHigh ].first < x ) )
{
++m_nKHigh;
++m_nKLow;
}
OSL_ENSURE( m_nKHigh <= n, "Out of Bounds" );
}
m_fLastInterpolatedValue = x;
double h = m_aPoints[ m_nKHigh ].first - m_aPoints[ m_nKLow ].first;
OSL_ENSURE( h != 0, "Bad input to GetInterpolatedValue()" );
double a = ( m_aPoints[ m_nKHigh ].first - x ) / h;
double b = ( x - m_aPoints[ m_nKLow ].first ) / h;
return ( a * m_aPoints[ m_nKLow ].second +
b * m_aPoints[ m_nKHigh ].second +
(( a*a*a - a ) * m_aSecDerivY[ m_nKLow ] +
( b*b*b - b ) * m_aSecDerivY[ m_nKHigh ] ) *
( h*h ) / 6.0 );
}
// helper methods for B-spline
// Create parameter t_0 to t_n using the centripetal method with a power of 0.5
bool createParameterT(const tPointVecType& rUniquePoints, double* t)
{ // precondition: no adjacent identical points
// postcondition: 0 = t_0 < t_1 < ... < t_n = 1
bool bIsSuccessful = true;
const lcl_tSizeType n = rUniquePoints.size() - 1;
t[0]=0.0;
double dx = 0.0;
double dy = 0.0;
double fDiffMax = 1.0; //dummy values
double fDenominator = 0.0; // initialized for summing up
for (lcl_tSizeType i=1; i<=n ; ++i)
{ // 4th root(dx^2+dy^2)
dx = rUniquePoints[i].first - rUniquePoints[i-1].first;
dy = rUniquePoints[i].second - rUniquePoints[i-1].second;
// scaling to avoid underflow or overflow
fDiffMax = std::max(fabs(dx), fabs(dy));
if (fDiffMax == 0.0)
{
bIsSuccessful = false;
break;
}
else
{
dx /= fDiffMax;
dy /= fDiffMax;
fDenominator += sqrt(sqrt(dx * dx + dy * dy)) * sqrt(fDiffMax);
}
}
if (fDenominator == 0.0)
{
bIsSuccessful = false;
}
if (bIsSuccessful)
{
for (lcl_tSizeType j=1; j<=n ; ++j)
{
double fNumerator = 0.0;
for (lcl_tSizeType i=1; i<=j ; ++i)
{
dx = rUniquePoints[i].first - rUniquePoints[i-1].first;
dy = rUniquePoints[i].second - rUniquePoints[i-1].second;
fDiffMax = std::max(fabs(dx), fabs(dy));
// same as above, so should not be zero
dx /= fDiffMax;
dy /= fDiffMax;
fNumerator += sqrt(sqrt(dx * dx + dy * dy)) * sqrt(fDiffMax);
}
t[j] = fNumerator / fDenominator;
}
// postcondition check
t[n] = 1.0;
double fPrevious = 0.0;
for (lcl_tSizeType i=1; i <= n && bIsSuccessful ; ++i)
{
if (fPrevious >= t[i])
{
bIsSuccessful = false;
}
else
{
fPrevious = t[i];
}
}
}
return bIsSuccessful;
}
void createKnotVector(const lcl_tSizeType n, const sal_uInt32 p, const double* t, double* u)
{ // precondition: 0 = t_0 < t_1 < ... < t_n = 1
for (lcl_tSizeType j = 0; j <= p; ++j)
{
u[j] = 0.0;
}
for (lcl_tSizeType j = 1; j <= n-p; ++j )
{
double fSum = 0.0;
for (lcl_tSizeType i = j; i <= j+p-1; ++i)
{
fSum += t[i];
}
assert(p != 0);
u[j+p] = fSum / p ;
}
for (lcl_tSizeType j = n+1; j <= n+1+p; ++j)
{
u[j] = 1.0;
}
}
void applyNtoParameterT(const lcl_tSizeType i,const double tk,const sal_uInt32 p,const double* u, double* rowN)
{
// get N_p(t_k) recursively, only N_(i-p) till N_(i) are relevant, all other N_# are zero
// initialize with indicator function degree 0
rowN[p] = 1.0; // all others are zero
// calculate up to degree p
for (sal_uInt32 s = 1; s <= p; ++s)
{
// first element
double fLeftFactor = 0.0;
double fRightFactor = ( u[i+1] - tk ) / ( u[i+1]- u[i-s+1] );
// i-s "true index" - (i-p)"shift" = p-s
rowN[p-s] = fRightFactor * rowN[p-s+1];
// middle elements
for (sal_uInt32 j = s-1; j>=1 ; --j)
{
fLeftFactor = ( tk - u[i-j] ) / ( u[i-j+s] - u[i-j] ) ;
fRightFactor = ( u[i-j+s+1] - tk ) / ( u[i-j+s+1] - u[i-j+1] );
// i-j "true index" - (i-p)"shift" = p-j
rowN[p-j] = fLeftFactor * rowN[p-j] + fRightFactor * rowN[p-j+1];
}
// last element
fLeftFactor = ( tk - u[i] ) / ( u[i+s] - u[i] );
// i "true index" - (i-p)"shift" = p
rowN[p] = fLeftFactor * rowN[p];
}
}
} // anonymous namespace
// Calculates uniform parametric splines with subinterval length 1,
// according ODF1.2 part 1, chapter 'chart interpolation'.
void SplineCalculater::CalculateCubicSplines(
const drawing::PolyPolygonShape3D& rInput
, drawing::PolyPolygonShape3D& rResult
, sal_uInt32 nGranularity )
{
OSL_PRECOND( nGranularity > 0, "Granularity is invalid" );
sal_uInt32 nOuterCount = rInput.SequenceX.getLength();
rResult.SequenceX.realloc(nOuterCount);
rResult.SequenceY.realloc(nOuterCount);
rResult.SequenceZ.realloc(nOuterCount);
if( !nOuterCount )
return;
for( sal_uInt32 nOuter = 0; nOuter < nOuterCount; ++nOuter )
{
if( rInput.SequenceX[nOuter].getLength() <= 1 )
continue; //we need at least two points
sal_uInt32 nMaxIndexPoints = rInput.SequenceX[nOuter].getLength()-1; // is >=1
const double* pOldX = rInput.SequenceX[nOuter].getConstArray();
const double* pOldY = rInput.SequenceY[nOuter].getConstArray();
const double* pOldZ = rInput.SequenceZ[nOuter].getConstArray();
std::vector < double > aParameter(nMaxIndexPoints+1);
aParameter[0]=0.0;
for( sal_uInt32 nIndex=1; nIndex<=nMaxIndexPoints; nIndex++ )
{
aParameter[nIndex]=aParameter[nIndex-1]+1;
}
// Split the calculation to X, Y and Z coordinate
tPointVecType aInputX;
aInputX.resize(nMaxIndexPoints+1);
tPointVecType aInputY;
aInputY.resize(nMaxIndexPoints+1);
tPointVecType aInputZ;
aInputZ.resize(nMaxIndexPoints+1);
for (sal_uInt32 nN=0;nN<=nMaxIndexPoints; nN++ )
{
aInputX[ nN ].first=aParameter[nN];
aInputX[ nN ].second=pOldX[ nN ];
aInputY[ nN ].first=aParameter[nN];
aInputY[ nN ].second=pOldY[ nN ];
aInputZ[ nN ].first=aParameter[nN];
aInputZ[ nN ].second=pOldZ[ nN ];
}
// generate a spline for each coordinate. It holds the complete
// information to calculate each point of the curve
lcl_SplineCalculation* aSplineX;
lcl_SplineCalculation* aSplineY;
// lcl_SplineCalculation* aSplineZ; the z-coordinates of all points in
// a data series are equal. No spline calculation needed, but copy
// coordinate to output
if( pOldX[ 0 ] == pOldX[nMaxIndexPoints] &&
pOldY[ 0 ] == pOldY[nMaxIndexPoints] &&
pOldZ[ 0 ] == pOldZ[nMaxIndexPoints] &&
nMaxIndexPoints >=2 )
{ // periodic spline
aSplineX = new lcl_SplineCalculation( aInputX) ;
aSplineY = new lcl_SplineCalculation( aInputY) ;
// aSplineZ = new lcl_SplineCalculation( aInputZ) ;
}
else // generate the kind "natural spline"
{
double fInfty;
::rtl::math::setInf( &fInfty, false );
double fXDerivation = fInfty;
double fYDerivation = fInfty;
aSplineX = new lcl_SplineCalculation( aInputX, fXDerivation, fXDerivation );
aSplineY = new lcl_SplineCalculation( aInputY, fYDerivation, fYDerivation );
}
// fill result polygon with calculated values
rResult.SequenceX[nOuter].realloc( nMaxIndexPoints*nGranularity + 1);
rResult.SequenceY[nOuter].realloc( nMaxIndexPoints*nGranularity + 1);
rResult.SequenceZ[nOuter].realloc( nMaxIndexPoints*nGranularity + 1);
double* pNewX = rResult.SequenceX[nOuter].getArray();
double* pNewY = rResult.SequenceY[nOuter].getArray();
double* pNewZ = rResult.SequenceZ[nOuter].getArray();
sal_uInt32 nNewPointIndex = 0; // Index in result points
for( sal_uInt32 ni = 0; ni < nMaxIndexPoints; ni++ )
{
// given point is surely a curve point
pNewX[nNewPointIndex] = pOldX[ni];
pNewY[nNewPointIndex] = pOldY[ni];
pNewZ[nNewPointIndex] = pOldZ[ni];
nNewPointIndex++;
// calculate intermediate points
double fInc = ( aParameter[ ni+1 ] - aParameter[ni] ) / static_cast< double >( nGranularity );
for(sal_uInt32 nj = 1; nj < nGranularity; nj++)
{
double fParam = aParameter[ni] + ( fInc * static_cast< double >( nj ) );
pNewX[nNewPointIndex]=aSplineX->GetInterpolatedValue( fParam );
pNewY[nNewPointIndex]=aSplineY->GetInterpolatedValue( fParam );
// pNewZ[nNewPointIndex]=aSplineZ->GetInterpolatedValue( fParam );
pNewZ[nNewPointIndex] = pOldZ[ni];
nNewPointIndex++;
}
}
// add last point
pNewX[nNewPointIndex] = pOldX[nMaxIndexPoints];
pNewY[nNewPointIndex] = pOldY[nMaxIndexPoints];
pNewZ[nNewPointIndex] = pOldZ[nMaxIndexPoints];
delete aSplineX;
delete aSplineY;
// delete aSplineZ;
}
}
// The implementation follows closely ODF1.2 spec, chapter chart:interpolation
// using the same names as in spec as far as possible, without prefix.
// More details can be found on
// Dr. C.-K. Shene: CS3621 Introduction to Computing with Geometry Notes
// Unit 9: Interpolation and Approximation/Curve Global Interpolation
// Department of Computer Science, Michigan Technological University
// http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/
// [last called 2011-05-20]
void SplineCalculater::CalculateBSplines(
const css::drawing::PolyPolygonShape3D& rInput
, css::drawing::PolyPolygonShape3D& rResult
, sal_uInt32 nResolution
, sal_uInt32 nDegree )
{
// nResolution is ODF1.2 file format attribute chart:spline-resolution and
// ODF1.2 spec variable k. Causion, k is used as index in the spec in addition.
// nDegree is ODF1.2 file format attribute chart:spline-order and
// ODF1.2 spec variable p
OSL_ASSERT( nResolution > 1 );
OSL_ASSERT( nDegree >= 1 );
// limit the b-spline degree at 15 to prevent insanely large sets of points
sal_uInt32 p = std::min<sal_uInt32>(nDegree, 15);
sal_Int32 nOuterCount = rInput.SequenceX.getLength();
rResult.SequenceX.realloc(nOuterCount);
rResult.SequenceY.realloc(nOuterCount);
rResult.SequenceZ.realloc(nOuterCount);
if( !nOuterCount )
return; // no input
for( sal_Int32 nOuter = 0; nOuter < nOuterCount; ++nOuter )
{
if( rInput.SequenceX[nOuter].getLength() <= 1 )
continue; // need at least 2 points, next piece of the series
// Copy input to vector of points and remove adjacent double points. The
// Z-coordinate is equal for all points in a series and holds the depth
// in 3D mode, simple copying is enough.
lcl_tSizeType nMaxIndexPoints = rInput.SequenceX[nOuter].getLength()-1; // is >=1
const double* pOldX = rInput.SequenceX[nOuter].getConstArray();
const double* pOldY = rInput.SequenceY[nOuter].getConstArray();
const double* pOldZ = rInput.SequenceZ[nOuter].getConstArray();
double fZCoordinate = pOldZ[0];
tPointVecType aPointsIn;
aPointsIn.resize(nMaxIndexPoints+1);
for (lcl_tSizeType i = 0; i <= nMaxIndexPoints; ++i )
{
aPointsIn[ i ].first = pOldX[i];
aPointsIn[ i ].second = pOldY[i];
}
aPointsIn.erase( std::unique( aPointsIn.begin(), aPointsIn.end()),
aPointsIn.end() );
// n is the last valid index to the reduced aPointsIn
// There are n+1 valid data points.
const lcl_tSizeType n = aPointsIn.size() - 1;
if (n < 1 || p > n)
continue; // need at least 2 points, degree p needs at least n+1 points
// next piece of series
std::unique_ptr<double[]> t(new double [n+1]);
if (!createParameterT(aPointsIn, t.get()))
{
continue; // next piece of series
}
lcl_tSizeType m = n + p + 1;
std::unique_ptr<double[]> u(new double [m+1]);
createKnotVector(n, p, t.get(), u.get());
// The matrix N contains the B-spline basis functions applied to parameters.
// In each row only p+1 adjacent elements are non-zero. The starting
// column in a higher row is equal or greater than in the lower row.
// To store this matrix the non-zero elements are shifted to column 0
// and the amount of shifting is remembered in an array.
std::unique_ptr<double*[]> aMatN(new double*[n+1]);
for (lcl_tSizeType row = 0; row <=n; ++row)
{
aMatN[row] = new double[p+1];
for (sal_uInt32 col = 0; col <= p; ++col)
aMatN[row][col] = 0.0;
}
std::unique_ptr<lcl_tSizeType[]> aShift(new lcl_tSizeType[n+1]);
aMatN[0][0] = 1.0; //all others are zero
aShift[0] = 0;
aMatN[n][0] = 1.0;
aShift[n] = n;
for (lcl_tSizeType k = 1; k<=n-1; ++k)
{ // all basis functions are applied to t_k,
// results are elements in row k in matrix N
// find the one interval with u_i <= t_k < u_(i+1)
// remember u_0 = ... = u_p = 0.0 and u_(m-p) = ... u_m = 1.0 and 0<t_k<1
lcl_tSizeType i = p;
while (!(u[i] <= t[k] && t[k] < u[i+1]))
{
++i;
}
// index in reduced matrix aMatN = (index in full matrix N) - (i-p)
aShift[k] = i - p;
applyNtoParameterT(i, t[k], p, u.get(), aMatN[k]);
} // next row k
// Get matrix C of control points from the matrix equation aMatN * C = aPointsIn
// aPointsIn is overwritten with C.
// Gaussian elimination is possible without pivoting, see reference
lcl_tSizeType r = 0; // true row index
lcl_tSizeType c = 0; // true column index
double fDivisor = 1.0; // used for diagonal element
double fEliminate = 1.0; // used for the element, that will become zero
double fHelp;
tPointType aHelp;
lcl_tSizeType nHelp; // used in triangle change
bool bIsSuccessful = true;
for (c = 0 ; c <= n && bIsSuccessful; ++c)
{
// search for first non-zero downwards
r = c;
while ( r < n && aMatN[r][c-aShift[r]] == 0 )
{
++r;
}
if (aMatN[r][c-aShift[r]] == 0.0)
{
// Matrix N is singular, although this is mathematically impossible
bIsSuccessful = false;
}
else
{
// exchange total row r with total row c if necessary
if (r != c)
{
for ( sal_uInt32 i = 0; i <= p ; ++i)
{
fHelp = aMatN[r][i];
aMatN[r][i] = aMatN[c][i];
aMatN[c][i] = fHelp;
}
aHelp = aPointsIn[r];
aPointsIn[r] = aPointsIn[c];
aPointsIn[c] = aHelp;
nHelp = aShift[r];
aShift[r] = aShift[c];
aShift[c] = nHelp;
}
// divide row c, so that element(c,c) becomes 1
fDivisor = aMatN[c][c-aShift[c]]; // not zero, see above
for (sal_uInt32 i = 0; i <= p; ++i)
{
aMatN[c][i] /= fDivisor;
}
aPointsIn[c].first /= fDivisor;
aPointsIn[c].second /= fDivisor;
// eliminate forward, examine row c+1 to n-1 (worst case)
// stop if first non-zero element in row has an higher column as c
// look at nShift for that, elements in nShift are equal or increasing
for ( r = c+1; r < n && aShift[r]<=c ; ++r)
{
fEliminate = aMatN[r][0];
if (fEliminate != 0.0) // else accidentally zero, nothing to do
{
for (sal_uInt32 i = 1; i <= p; ++i)
{
aMatN[r][i-1] = aMatN[r][i] - fEliminate * aMatN[c][i];
}
aMatN[r][p]=0;
aPointsIn[r].first -= fEliminate * aPointsIn[c].first;
aPointsIn[r].second -= fEliminate * aPointsIn[c].second;
++aShift[r];
}
}
}
}// upper triangle form is reached
if( bIsSuccessful)
{
// eliminate backwards, begin with last column
for (lcl_tSizeType cc = n; cc >= 1; --cc )
{
// In row cc the diagonal element(cc,cc) == 1 and all elements left from
// diagonal are zero and do not influence other rows.
// Full matrix N has semibandwidth < p, therefore element(r,c) is
// zero, if abs(r-cc)>=p. abs(r-cc)=cc-r, because r<cc.
r = cc - 1;
while ( r !=0 && cc-r < p )
{
fEliminate = aMatN[r][ cc - aShift[r] ];
if ( fEliminate != 0.0) // else element is accidentally zero, no action needed
{
// row r -= fEliminate * row cc only relevant for right side
aMatN[r][cc - aShift[r]] = 0.0;
aPointsIn[r].first -= fEliminate * aPointsIn[cc].first;
aPointsIn[r].second -= fEliminate * aPointsIn[cc].second;
}
--r;
}
}
} // aPointsIn contains the control points now.
if (bIsSuccessful)
{
// calculate the intermediate points according given resolution
// using deBoor-Cox algorithm
lcl_tSizeType nNewSize = nResolution * n + 1;
rResult.SequenceX[nOuter].realloc(nNewSize);
rResult.SequenceY[nOuter].realloc(nNewSize);
rResult.SequenceZ[nOuter].realloc(nNewSize);
double* pNewX = rResult.SequenceX[nOuter].getArray();
double* pNewY = rResult.SequenceY[nOuter].getArray();
double* pNewZ = rResult.SequenceZ[nOuter].getArray();
pNewX[0] = aPointsIn[0].first;
pNewY[0] = aPointsIn[0].second;
pNewZ[0] = fZCoordinate; // Precondition: z-coordinates of all points of a series are equal
pNewX[nNewSize -1 ] = aPointsIn[n].first;
pNewY[nNewSize -1 ] = aPointsIn[n].second;
pNewZ[nNewSize -1 ] = fZCoordinate;
std::unique_ptr<double[]> aP(new double[m+1]);
lcl_tSizeType nLow = 0;
for ( lcl_tSizeType nTIndex = 0; nTIndex <= n-1; ++nTIndex)
{
for (sal_uInt32 nResolutionStep = 1;
nResolutionStep <= nResolution && !( nTIndex == n-1 && nResolutionStep == nResolution);
++nResolutionStep)
{
lcl_tSizeType nNewIndex = nTIndex * nResolution + nResolutionStep;
double ux = t[nTIndex] + nResolutionStep * ( t[nTIndex+1] - t[nTIndex]) /nResolution;
// get index nLow, so that u[nLow]<= ux < u[nLow +1]
// continue from previous nLow
while ( u[nLow] <= ux)
{
++nLow;
}
--nLow;
// x-coordinate
for (lcl_tSizeType i = nLow-p; i <= nLow; ++i)
{
aP[i] = aPointsIn[i].first;
}
for (sal_uInt32 lcl_Degree = 1; lcl_Degree <= p; ++lcl_Degree)
{
for (lcl_tSizeType i = nLow; i >= nLow + lcl_Degree - p; --i)
{
double fFactor = ( ux - u[i] ) / ( u[i+p+1-lcl_Degree] - u[i]);
aP[i] = (1 - fFactor)* aP[i-1] + fFactor * aP[i];
}
}
pNewX[nNewIndex] = aP[nLow];
// y-coordinate
for (lcl_tSizeType i = nLow - p; i <= nLow; ++i)
{
aP[i] = aPointsIn[i].second;
}
for (sal_uInt32 lcl_Degree = 1; lcl_Degree <= p; ++lcl_Degree)
{
for (lcl_tSizeType i = nLow; i >= nLow +lcl_Degree - p; --i)
{
double fFactor = ( ux - u[i] ) / ( u[i+p+1-lcl_Degree] - u[i]);
aP[i] = (1 - fFactor)* aP[i-1] + fFactor * aP[i];
}
}
pNewY[nNewIndex] = aP[nLow];
pNewZ[nNewIndex] = fZCoordinate;
}
}
}
for (lcl_tSizeType row = 0; row <=n; ++row)
{
delete[] aMatN[row];
}
} // next piece of the series
}
} //namespace chart
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
↑ V581 The conditional expressions of the 'if' statements situated alongside each other are identical. Check lines: 834, 858.