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//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of NVIDIA CORPORATION nor the names of its
// contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Copyright (c) 2018 NVIDIA Corporation. All rights reserved.
#include "Spline.h"
#include <assert.h>
using namespace nvidia;
static float f(float x)
{
return( x*x*x - x);
}
// build spline.
// copied from Sedgwick's Algorithm's in C, page 548.
void Spline::ComputeSpline(void)
{
uint32_t i;
uint32_t n = mNodes.size();
float *d = new float[n];
float *w = new float[n];
for (i=1; i<(n-1); i++)
{
d[i] = 2.0f * (mNodes[i+1].x - mNodes[i-1].x);
}
for (i=0; i<(n-1); i++)
{
mNodes[i].u = mNodes[i+1].x-mNodes[i].x;}
for (i=1; i<(n-1); i++)
{
w[i] = 6.0f*((mNodes[i+1].y - mNodes[i].y) / mNodes[i].u - (mNodes[i].y - mNodes[i-1].y) / mNodes[i-1].u);
}
mNodes[0].p = 0.0f;
mNodes[n-1].p = 0.0f;
for (i=1; i<(n-2); i++)
{
w[i+1] = w[i+1] - w[i]*mNodes[i].u /d[i];
d[i+1] = d[i+1] - mNodes[i].u * mNodes[i].u / d[i];
}
for (i=n-2; i>0; i--)
{
mNodes[i].p = (w[i] - mNodes[i].u * mNodes[i+1].p ) / d[i];
}
delete[]d;
delete[]w;
}
float Spline::Evaluate(float v,uint32_t &index,float &fraction) const
{
float t;
uint32_t i=0;
uint32_t n = mNodes.size();
while ( i < (n-1) && v > mNodes[i+1].x )
{
i++;
}
if ( i == (n-1) )
{
i = n-2;
}
index = (uint32_t)i;
t = (v - mNodes[i].x ) / mNodes[i].u;
fraction = t;
return( t*mNodes[i+1].y + (1-t)*mNodes[i].y + mNodes[i].u * mNodes[i].u * (f(t)*mNodes[i+1].p + f(1-t)*mNodes[i].p )/6.0f );
}
void Spline::AddNode(float x,float y)
{
SplineNode s;
s.x = x;
s.y = y;
mNodes.pushBack(s);
}
float SplineCurve::AddControlPoint(const PxVec3& p) // add control point.
{
int32_t size = mXaxis.GetSize();
if ( size )
{
size--;
PxVec3 last;
last.x = mXaxis.GetEntry(size);
last.y = mYaxis.GetEntry(size);
last.z = mZaxis.GetEntry(size);
PxVec3 diff = last-p;
float dist = diff.magnitude();
mTime+=dist;
}
else
{
mTime = 0;
}
mXaxis.AddNode(mTime,p.x);
mYaxis.AddNode(mTime,p.y);
mZaxis.AddNode(mTime,p.z);
return mTime;
}
void SplineCurve::AddControlPoint(const PxVec3& p,float t) // add control point.
{
int32_t size = mXaxis.GetSize();
if ( size )
{
size--;
PxVec3 last;
last.x = mXaxis.GetEntry(size);
last.y = mYaxis.GetEntry(size);
last.z = mZaxis.GetEntry(size);
}
mTime = t;
mXaxis.AddNode(mTime,p.x);
mYaxis.AddNode(mTime,p.y);
mZaxis.AddNode(mTime,p.z);
}
void SplineCurve::ComputeSpline(void) // compute spline.
{
mXaxis.ComputeSpline();
mYaxis.ComputeSpline();
mZaxis.ComputeSpline();
}
PxVec3 SplineCurve::Evaluate(float dist,uint32_t &index,float &fraction)
{
PxVec3 p;
uint32_t index1,index2,index3;
float t1,t2,t3;
p.x = mXaxis.Evaluate(dist,index1,t1);
p.y = mYaxis.Evaluate(dist,index2,t2);
p.z = mZaxis.Evaluate(dist,index3,t3);
assert( index1 == index2 && index1 == index3 && index2 == index3 );
index = index1;
fraction = t1;
return p;
}
PxVec3 SplineCurve::GetEntry(int32_t i)
{
PxVec3 p;
if ( i >= 0 && i < GetSize() )
{
p.x = mXaxis.GetEntry(i);
p.y = mYaxis.GetEntry(i);
p.z = mZaxis.GetEntry(i);
}
return p;
}
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