F32 CatmullRomBase::arcLength( F32 t1, F32 t2 )
{
if ( t2 <= t1 )
return 0.0f;
if ( t1 < mTimes[0] )
t1 = mTimes[0];
if ( t2 > mTimes[mCount-1] )
t2 = mTimes[mCount-1];
// find segment and parameter
U32 seg1;
for ( seg1 = 0; seg1 < mCount-1; ++seg1 )
{
if ( t1 <= mTimes[seg1+1] )
{
break;
}
}
F32 u1 = (t1 - mTimes[seg1])/(mTimes[seg1+1] - mTimes[seg1]);
// find segment and parameter
U32 seg2;
for ( seg2 = 0; seg2 < mCount-1; ++seg2 )
{
if ( t2 <= mTimes[seg2+1] )
{
break;
}
}
F32 u2 = (t2 - mTimes[seg2])/(mTimes[seg2+1] - mTimes[seg2]);
F32 result;
// both parameters lie in one segment
if ( seg1 == seg2 )
{
result = segmentArcLength( seg1, u1, u2 );
}
// parameters cross segments
else
{
result = segmentArcLength( seg1, u1, 1.0f );
for ( U32 i = seg1+1; i < seg2; ++i )
result += mLengths[i];
result += segmentArcLength( seg2, 0.0f, u2 );
}
return result;
}
void CatmullRomBase::_initialize( U32 count, const F32 *times )
{
//AssertFatal( times, "CatmullRomBase::_initialize() - Got null position!" )
AssertFatal( count > 1, "CatmullRomBase::_initialize() - Must have more than 2 points!" )
// set up arrays
mTimes = new F32[count];
mCount = count;
// set up curve segment lengths
mLengths = new F32[count-1];
mTotalLength = 0.0f;
for ( U32 i = 0; i < count-1; ++i )
{
mLengths[i] = segmentArcLength(i, 0.0f, 1.0f);
mTotalLength += mLengths[i];
}
// copy the times if we have them.
F32 l = 0.0f;
for ( U32 i = 0; i < count; ++i )
{
if ( times )
mTimes[i] = times[i];
else
{
if ( mIsZero( mTotalLength ) )
mTimes[i] = 0.0f;
else
mTimes[i] = l / mTotalLength;
if ( i < count-1 )
l += mLengths[i];
}
}
}
/*!
Init curve with curve points and times. If no control
points are passed they will be calculated automatically
@param points Array of points on the Bézier curve (w = time)
@param controlPoints Array of control points with size = 2*(numPointsAndTimes-1)
*/
void SLCurveBezier::init(const SLVVec4f& points,
const SLVVec3f& controlPoints)
{ assert(points.size() > 1);
dispose();
// set up arrays
_points.clear();
_points.resize(points.size());
_controls.resize(2*(points.size()-1));
// copy interpolated data
SLuint i;
for (i = 0; i < _points.size(); ++i)
{ _points[i] = points[i];
}
if (controlPoints.size()==0)
{
if (points.size() > 2)
{ // create approximating control points
for (i = 0; i < _points.size()-1; ++i)
{ if (i > 0)
_controls[2*i] = (_points[i] + (_points[i+1]-_points[i-1])/3.0f).vec3();
if (i < _points.size()-2)
_controls[2*i+1] = (_points[i+1] - (_points[i+2]-_points[i ])/3.0f).vec3();
}
_controls[0] = (SLVec4f(_controls[1]) - (_points[1] - _points[0])/3.0f).vec3();
_controls[2*_points.size()-3] = (SLVec4f(_controls[2*_points.size()-4]) +
(_points[_points.size()-1] - _points[_points.size()-2])/3.0f).vec3();
} else
{ _controls[0] = (_points[0] + (_points[1]-_points[0])/3.0f).vec3();
_controls[1] = (_points[1] - (_points[1]-_points[0])/3.0f).vec3();
}
}
else
{ // copy approximating control points
for (i = 0; i < 2*(_points.size()-1); ++i)
_controls[i] = controlPoints[i];
}
// set up curve segment lengths
_lengths.clear();
_lengths.resize(_points.size()-1);
_totalLength = 0.0f;
_totalLength = 0.0f;
for (SLuint i = 0; i < _points.size()-1; ++i)
{ _lengths[i] = segmentArcLength(i, 0.0f, 1.0f);
_totalLength += _lengths[i];
}
}
/*!
Calculate length of curve between parameters t1 and t2
*/
SLfloat SLCurveBezier::arcLength(SLfloat t1, SLfloat t2)
{
if (t2 <= t1) return 0.0f;
if (t1 < _points[0].w) t1 = _points[0].w;
if (t2 > _points[_points.size()-1].w) t2 = _points[_points.size()-1].w;
// find segment and parameter
unsigned int seg1;
for (seg1 = 0; seg1 < _points.size()-1; ++seg1)
if (t1 < _points[seg1+1].w)
break;
SLfloat u1 = (t1 - _points[seg1].w)/(_points[seg1+1].w - _points[seg1].w);
// find segment and parameter
unsigned int seg2;
for (seg2 = 0; seg2 < _points.size()-1; ++seg2)
if (t2 <= _points[seg2+1].w)
break;
SLfloat u2 = (t2 - _points[seg2].w)/(_points[seg2+1].w - _points[seg2].w);
// both parameters lie in one segment
SLfloat result;
if (seg1 == seg2)
result = segmentArcLength(seg1, u1, u2);
// parameters cross segments
else
{ result = segmentArcLength(seg1, u1, 1.0f);
for (SLuint i = seg1+1; i < seg2; ++i)
result += _lengths[i];
result += segmentArcLength(seg2, 0.0f, u2);
}
return result;
}
