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// Description:
// Bezier segment template.
//
// Copyright (C) 2001 Frank Becker
//
// This program is free software; you can redistribute it and/or modify it under
// the terms of the GNU General Public License as published by the Free Software
// Foundation; either version 2 of the License, or (at your option) any later
// version.
//
// This program is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details
//
#include <Trace.hpp>
#include <Bezier.hpp>
//Construct a Bezier segment given 4 points
template<class POINT>
Bezier<POINT>::Bezier( const POINT point[4])
{
XTRACE();
int dim = point[0].dimension();
for( int d=0; d<dim; d++)
{
float val[4];
for( int i=0; i<4; i++)
{
POINT pt = point[ i];
val[ i] = pt[d];
}
calcCoeff( val, pd[d]);
}
}
//Calculate Bezier segment coefficients
template<class POINT>
void Bezier<POINT>::calcCoeff( const float in[ 4], float out[ 4])
{
XTRACE();
out[ 0] = 1*in[0];
out[ 1] = -3*in[0] +3*in[1];
out[ 2] = 3*in[0] -6*in[1] +3*in[2];
out[ 3] = -1*in[0] +3*in[1] -3*in[2] +1*in[3];
}
//Calculate point on the Bezier segment at time 0<=t<=1
template<class POINT>
void Bezier<POINT>::Pos( const float t, POINT &point) const
{
XTRACE();
float tt = t*t;
float ttt = t*tt;
for( int d=0; d<point.dimension(); d++)
{
point.set(d, pd[d][0] + t*pd[d][1] + tt*pd[d][2] + ttt*pd[d][3]);
}
}
//Calculate perpendicular vector at time 0<=t<=1
//Really only makes sense in 2D
template<class POINT>
void Bezier<POINT>::PVec( const float t, POINT &point) const
{
XTRACE();
float t2 = 2*t;
float tt3 = 3*t*t;
if( point.dimension() != 2) return;
//vector perpendicular to tangent at t
// x/y -> -(y/x)
point.set(1, pd[0][1] + t2*pd[0][2] + tt3*pd[0][3]);
point.set(0,-(pd[1][1] + t2*pd[1][2] + tt3*pd[1][3]));
}
//Calculate tangent vector at time 0<=t<=1
template<class POINT>
void Bezier<POINT>::TVec( const float t, POINT &point) const
{
XTRACE();
float t2 = 2*t;
float tt3 = 3*t*t;
for( int d=0; d<point.dimension(); d++)
{
point.set(d, pd[d][1] + t2*pd[d][2] + tt3*pd[d][3]);
}
}
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