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#include <iostream>
#include <Eigen/Geometry>
#include <bench/BenchTimer.h>
using namespace Eigen;
using namespace std;
template<typename Q>
EIGEN_DONT_INLINE Q nlerp(const Q& a, const Q& b, typename Q::Scalar t)
{
return Q((a.coeffs() * (1.0-t) + b.coeffs() * t).normalized());
}
template<typename Q>
EIGEN_DONT_INLINE Q slerp_eigen(const Q& a, const Q& b, typename Q::Scalar t)
{
return a.slerp(t,b);
}
template<typename Q>
EIGEN_DONT_INLINE Q slerp_legacy(const Q& a, const Q& b, typename Q::Scalar t)
{
typedef typename Q::Scalar Scalar;
static const Scalar one = Scalar(1) - dummy_precision<Scalar>();
Scalar d = a.dot(b);
Scalar absD = internal::abs(d);
if (absD>=one)
return a;
// theta is the angle between the 2 quaternions
Scalar theta = std::acos(absD);
Scalar sinTheta = internal::sin(theta);
Scalar scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
Scalar scale1 = internal::sin( ( t * theta) ) / sinTheta;
if (d<0)
scale1 = -scale1;
return Q(scale0 * a.coeffs() + scale1 * b.coeffs());
}
template<typename Q>
EIGEN_DONT_INLINE Q slerp_legacy_nlerp(const Q& a, const Q& b, typename Q::Scalar t)
{
typedef typename Q::Scalar Scalar;
static const Scalar one = Scalar(1) - epsilon<Scalar>();
Scalar d = a.dot(b);
Scalar absD = internal::abs(d);
Scalar scale0;
Scalar scale1;
if (absD>=one)
{
scale0 = Scalar(1) - t;
scale1 = t;
}
else
{
// theta is the angle between the 2 quaternions
Scalar theta = std::acos(absD);
Scalar sinTheta = internal::sin(theta);
scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
scale1 = internal::sin( ( t * theta) ) / sinTheta;
if (d<0)
scale1 = -scale1;
}
return Q(scale0 * a.coeffs() + scale1 * b.coeffs());
}
template<typename T>
inline T sin_over_x(T x)
{
if (T(1) + x*x == T(1))
return T(1);
else
return std::sin(x)/x;
}
template<typename Q>
EIGEN_DONT_INLINE Q slerp_rw(const Q& a, const Q& b, typename Q::Scalar t)
{
typedef typename Q::Scalar Scalar;
Scalar d = a.dot(b);
Scalar theta;
if (d<0.0)
theta = /*M_PI -*/ Scalar(2)*std::asin( (a.coeffs()+b.coeffs()).norm()/2 );
else
theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );
// theta is the angle between the 2 quaternions
// Scalar theta = std::acos(absD);
Scalar sinOverTheta = sin_over_x(theta);
Scalar scale0 = (Scalar(1)-t)*sin_over_x( ( Scalar(1) - t ) * theta) / sinOverTheta;
Scalar scale1 = t * sin_over_x( ( t * theta) ) / sinOverTheta;
if (d<0)
scale1 = -scale1;
return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());
}
template<typename Q>
EIGEN_DONT_INLINE Q slerp_gael(const Q& a, const Q& b, typename Q::Scalar t)
{
typedef typename Q::Scalar Scalar;
Scalar d = a.dot(b);
Scalar theta;
// theta = Scalar(2) * atan2((a.coeffs()-b.coeffs()).norm(),(a.coeffs()+b.coeffs()).norm());
// if (d<0.0)
// theta = M_PI-theta;
if (d<0.0)
theta = /*M_PI -*/ Scalar(2)*std::asin( (-a.coeffs()-b.coeffs()).norm()/2 );
else
theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );
Scalar scale0;
Scalar scale1;
if(theta*theta-Scalar(6)==-Scalar(6))
{
scale0 = Scalar(1) - t;
scale1 = t;
}
else
{
Scalar sinTheta = std::sin(theta);
scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
scale1 = internal::sin( ( t * theta) ) / sinTheta;
if (d<0)
scale1 = -scale1;
}
return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());
}
int main()
{
typedef double RefScalar;
typedef float TestScalar;
typedef Quaternion<RefScalar> Qd;
typedef Quaternion<TestScalar> Qf;
unsigned int g_seed = (unsigned int) time(NULL);
std::cout << g_seed << "\n";
// g_seed = 1259932496;
srand(g_seed);
Matrix<RefScalar,Dynamic,1> maxerr(7);
maxerr.setZero();
Matrix<RefScalar,Dynamic,1> avgerr(7);
avgerr.setZero();
cout << "double=>float=>double nlerp eigen legacy(snap) legacy(nlerp) rightway gael's criteria\n";
int rep = 100;
int iters = 40;
for (int w=0; w<rep; ++w)
{
Qf a, b;
a.coeffs().setRandom();
a.normalize();
b.coeffs().setRandom();
b.normalize();
Qf c[6];
Qd ar(a.cast<RefScalar>());
Qd br(b.cast<RefScalar>());
Qd cr;
cout.precision(8);
cout << std::scientific;
for (int i=0; i<iters; ++i)
{
RefScalar t = 0.65;
cr = slerp_rw(ar,br,t);
Qf refc = cr.cast<TestScalar>();
c[0] = nlerp(a,b,t);
c[1] = slerp_eigen(a,b,t);
c[2] = slerp_legacy(a,b,t);
c[3] = slerp_legacy_nlerp(a,b,t);
c[4] = slerp_rw(a,b,t);
c[5] = slerp_gael(a,b,t);
VectorXd err(7);
err[0] = (cr.coeffs()-refc.cast<RefScalar>().coeffs()).norm();
// std::cout << err[0] << " ";
for (int k=0; k<6; ++k)
{
err[k+1] = (c[k].coeffs()-refc.coeffs()).norm();
// std::cout << err[k+1] << " ";
}
maxerr = maxerr.cwise().max(err);
avgerr += err;
// std::cout << "\n";
b = cr.cast<TestScalar>();
br = cr;
}
// std::cout << "\n";
}
avgerr /= RefScalar(rep*iters);
cout << "\n\nAccuracy:\n"
<< " max: " << maxerr.transpose() << "\n";
cout << " avg: " << avgerr.transpose() << "\n";
// perf bench
Quaternionf a,b;
a.coeffs().setRandom();
a.normalize();
b.coeffs().setRandom();
b.normalize();
//b = a;
float s = 0.65;
#define BENCH(FUNC) {\
BenchTimer t; \
for(int k=0; k<2; ++k) {\
t.start(); \
for(int i=0; i<1000000; ++i) \
FUNC(a,b,s); \
t.stop(); \
} \
cout << " " << #FUNC << " => \t " << t.value() << "s\n"; \
}
cout << "\nSpeed:\n" << std::fixed;
BENCH(nlerp);
BENCH(slerp_eigen);
BENCH(slerp_legacy);
BENCH(slerp_legacy_nlerp);
BENCH(slerp_rw);
BENCH(slerp_gael);
}
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