static inline SplineStore qwtSplinePathX(
const QwtSplineC1 *spline, const QPolygonF &points )
{
SplineStore store;
const int n = points.size();
const QVector<double> m = spline->slopesX( points );
if ( m.size() != n )
return store;
const QPointF *pd = points.constData();
const double *md = m.constData();
store.init( m.size() - 1 );
store.start( pd[0].x(), pd[0].y() );
for ( int i = 0; i < n - 1; i++ )
{
const double dx3 = ( pd[i+1].x() - pd[i].x() ) / 3.0;
store.addCubic( pd[i].x() + dx3, pd[i].y() + md[i] * dx3,
pd[i+1].x() - dx3, pd[i+1].y() - md[i+1] * dx3,
pd[i+1].x(), pd[i+1].y() );
}
return store;
}
static SplineStore qwtSplinePathPleasing( const QPolygonF &points,
bool isClosed, Param param )
{
const int size = points.size();
const QPointF *p = points.constData();
SplineStore store;
store.init( isClosed ? size : size - 1 );
store.start( p[0] );
const QPointF &p0 = isClosed ? p[size-1] : p[0];
double d13 = param(p[0], p[2]);
const QwtSplineCardinalG1::Tension t0 = qwtTension(
param(p0, p[1]), param(p[0], p[1]), d13, p0, p[0], p[1], p[2] );
const QPointF vec0 = ( p[1] - p0 ) * 0.5;
QPointF vec1 = ( p[2] - p[0] ) * 0.5;
store.addCubic( p[0] + vec0 * t0.t1, p[1] - vec1 * t0.t2, p[1] );
for ( int i = 1; i < size - 2; i++ )
{
const double d23 = param(p[i], p[i+1]);
const double d24 = param(p[i], p[i+2]);
const QPointF vec2 = ( p[i+2] - p[i] ) * 0.5;
const QwtSplineCardinalG1::Tension t =
qwtTension( d13, d23, d24, p[i-1], p[i], p[i+1], p[i+2] );
store.addCubic( p[i] + vec1 * t.t1, p[i+1] - vec2 * t.t2, p[i+1] );
d13 = d24;
vec1 = vec2;
}
const QPointF &pn = isClosed ? p[0] : p[size-1];
const double d24 = param( p[size-2], pn );
const QwtSplineCardinalG1::Tension tn = qwtTension(
d13, param( p[size-2], p[size-1] ), d24, p[size-3], p[size-2], p[size-1], pn );
const QPointF vec2 = 0.5 * ( pn - p[size-2] );
store.addCubic( p[size-2] + vec1 * tn.t1, p[size-1] - vec2 * tn.t2, p[size-1] );
if ( isClosed )
{
const double d34 = param( p[size-1], p[0] );
const double d35 = param( p[size-1], p[1] );
const QPointF vec3 = 0.5 * ( p[1] - p[size-1] );
const QwtSplineCardinalG1::Tension tn =
qwtTension( d24, d34, d35, p[size-2], p[size-1], p[0], p[1] );
store.addCubic( p[size-1] + vec2 * tn.t1, p[0] - vec3 * tn.t2, p[0] );
}
return store;
}
static inline SplineStore qwtSplinePathParam(
const QwtSplineC1 *spline, const QPolygonF &points, Param param )
{
const int n = points.size();
QPolygonF px, py;
px += QPointF( 0.0, points[0].x() );
py += QPointF( 0.0, points[0].y() );
double t = 0.0;
for ( int i = 1; i < n; i++ )
{
t += param( points[i-1], points[i] );
px += QPointF( t, points[i].x() );
py += QPointF( t, points[i].y() );
}
const QVector<double> mx = spline->slopesX( px );
const QVector<double> my = spline->slopesX( py );
SplineStore store;
store.init( n - 1 );
store.start( points[0].x(), points[0].y() );
for ( int i = 1; i < n; i++ )
{
const double t3 = param( points[i-1], points[i] ) / 3.0;
const double cx1 = points[i-1].x() + mx[i-1] * t3;
const double cy1 = points[i-1].y() + my[i-1] * t3;
const double cx2 = points[i].x() - mx[i] * t3;
const double cy2 = points[i].y() - my[i] * t3;
store.addCubic( cx1, cy1, cx2, cy2, points[i].x(), points[i].y() );
}
if ( spline->isClosing() )
{
const double t3 = param( points[n-1], points[0] ) / 3.0;
const double cx1 = points[n-1].x() + mx[n-1] * t3;
const double cy1 = points[n-1].y() + my[n-1] * t3;
const double cx2 = points[0].x() - mx[0] * t3;
const double cy2 = points[0].y() - my[0] * t3;
store.addCubic( cx1, cy1, cx2, cy2, points[0].x(), points[0].y() );
store.end();
}
return store;
}
static SplineStore qwtSplinePathG1(
const QwtSplineCardinalG1 *spline, const QPolygonF &points )
{
const int size = points.size();
const int numTensions = spline->isClosing() ? size : size - 1;
const QVector<QwtSplineCardinalG1::Tension> tensions2 = spline->tensions( points );
if ( tensions2.size() != numTensions )
return SplineStore();
const QPointF *p = points.constData();
const QwtSplineCardinalG1::Tension *t = tensions2.constData();
SplineStore store;
store.init( numTensions );
store.start( p[0] );
const QPointF &p0 = spline->isClosing() ? p[size-1] : p[0];
QPointF vec1 = ( p[1] - p0 ) * 0.5;
for ( int i = 0; i < size - 2; i++ )
{
const QPointF vec2 = ( p[i+2] - p[i] ) * 0.5;
store.addCubic( p[i] + vec1 * t[i].t1,
p[i+1] - vec2 * t[i].t2, p[i+1] );
vec1 = vec2;
}
const QPointF &pn = spline->isClosing() ? p[0] : p[size-1];
const QPointF vec2 = 0.5 * ( pn - p[size - 2] );
store.addCubic( p[size - 2] + vec1 * t[size-2].t1,
p[size - 1] - vec2 * t[size-2].t2, p[size - 1] );
if ( spline->isClosing() )
{
const QPointF vec3 = 0.5 * ( p[1] - p[size-1] );
store.addCubic( p[size-1] + vec2 * t[size-1].t1,
p[0] - vec3 * t[size-1].t2, p[0] );
}
return store;
}
static SplineStore qwtSplinePathPleasing( const QPolygonF &points,
bool isClosed, Param param )
{
using namespace QwtSplinePleasingP;
const int size = points.size();
const QPointF *p = points.constData();
SplineStore store;
store.init( isClosed ? size : size - 1 );
store.start( p[0] );
double d13;
QPointF vec1;
if ( isClosed )
{
d13 = qwtChordalLength(p[0], p[2]);
const Tension t0 = qwtTensionPleasing(
qwtChordalLength( p[size-1], p[1]), qwtChordalLength(p[0], p[1]),
d13, p[size-1], p[0], p[1], p[2] );
const QPointF vec0 = qwtVectorCardinal<Param>( param, p[size-1], p[0], p[1] );
vec1 = qwtVectorCardinal<Param>( param, p[0], p[1], p[2] );
store.addCubic( p[0] + vec0 * t0.t1, p[1] - vec1 * t0.t2, p[1] );
}
else
{
d13 = qwtChordalLength(p[0], p[2]);
const Tension t0 = qwtTensionPleasing(
qwtChordalLength( p[0], p[1]), qwtChordalLength(p[0], p[1]),
d13, p[0], p[0], p[1], p[2] );
const QPointF vec0 = 0.5 * qwtVector<Param>( param, p[0], p[1] );
vec1 = qwtVectorCardinal<Param>( param, p[0], p[1], p[2] );
store.addCubic( p[0] + vec0 * t0.t1, p[1] - vec1 * t0.t2, p[1] );
}
for ( int i = 1; i < size - 2; i++ )
{
const double d23 = qwtChordalLength( p[i], p[i+1] );
const double d24 = qwtChordalLength( p[i], p[i+2] );
const QPointF vec2 = qwtVectorCardinal<Param>( param, p[i], p[i+1], p[i+2] );
const Tension t = qwtTensionPleasing(
d13, d23, d24, p[i-1], p[i], p[i+1], p[i+2] );
store.addCubic( p[i] + vec1 * t.t1, p[i+1] - vec2 * t.t2, p[i+1] );
d13 = d24;
vec1 = vec2;
}
if ( isClosed )
{
const double d24 = qwtChordalLength( p[size-2], p[0] );
const Tension tn = qwtTensionPleasing(
d13, qwtChordalLength( p[size-2], p[size-1] ), d24,
p[size-3], p[size-2], p[size-1], p[0] );
const QPointF vec2 = qwtVectorCardinal<Param>( param, p[size-2], p[size-1], p[0] );
store.addCubic( p[size-2] + vec1 * tn.t1, p[size-1] - vec2 * tn.t2, p[size-1] );
const double d34 = qwtChordalLength( p[size-1], p[0] );
const double d35 = qwtChordalLength( p[size-1], p[1] );
const Tension tc = qwtTensionPleasing( d24, d34, d35, p[size-2], p[size-1], p[0], p[1] );
const QPointF vec3 = qwtVectorCardinal<Param>( param, p[size-1], p[0], p[1] );
store.addCubic( p[size-1] + vec2 * tc.t1, p[0] - vec3 * tc.t2, p[0] );
}
else
{
const double d24 = qwtChordalLength( p[size-2], p[size-1] );
const Tension tn = qwtTensionPleasing(
d13, qwtChordalLength( p[size-2], p[size-1] ), d24,
p[size-3], p[size-2], p[size-1], p[size-1] );
const QPointF vec2 = 0.5 * qwtVector<Param>( param, p[size-2], p[size-1] );
store.addCubic( p[size-2] + vec1 * tn.t1, p[size-1] - vec2 * tn.t2, p[size-1] );
}
return store;
}
