#ifndef TCG_NUMERIC_OPS_H
#define TCG_NUMERIC_OPS_H
// tcg includes
#include "traits.h"
#include "sfinae.h"
#include "macros.h"
// STD includes
#include <cmath>
#include <limits>
/*!
\file tcg_numeric_ops.h
\brief This file contains small function snippets to manipulate scalars
or numerical objects.
*/
//***************************************************************************
// Numerical Operations
//***************************************************************************
namespace tcg
{
/*!
Contains small function snippets to manipulate scalars
or numerical objects.
*/
namespace numeric_ops
{
template <typename Scalar>
//inline Scalar NaN() {return (std::numeric_limits<Scalar>::quiet_NaN)();}
inline Scalar NaN()
{
return (std::numeric_limits<Scalar>::max)();
}
//-------------------------------------------------------------------------------------------
/*!
Calculates the sign of a scalar.
\remark This function returns the \a integral values \p 1 in case the input value is
\a positive, \p -1 in case it's negative, and \p 0 in case it's \a exactly \p 0.
\return The sign of the input scalar.
*/
template <typename Scalar>
inline int sign(Scalar val, Scalar tol = 0)
{
return (val > tol) ? 1 : (val < -tol) ? -1 : 0;
}
//-------------------------------------------------------------------------------------------
//! Computes the nearest integer not greater in magnitude than the given value
template <typename Scalar>
Scalar trunc(Scalar val)
{
return (val < 0) ? std::ceil(val) : std::floor(val);
}
//! Computes the nearest integer \b strictly not greater in magnitude than the given value
template <typename Scalar>
Scalar truncStrict(Scalar val)
{
return (val < 0) ? std::floor(val + 1) : std::ceil(val - 1);
}
//! Computes the nearest integer not lesser in magnitude than the given value
template <typename Scalar>
Scalar grow(Scalar val)
{
return (val < 0) ? std::floor(val) : std::ceil(val);
}
//! Computes the nearest integer \b strictly not lesser in magnitude than the given value
template <typename Scalar>
Scalar growStrict(Scalar val)
{
return (val < 0) ? std::ceil(val - 1) : std::floor(val + 1);
}
//-------------------------------------------------------------------------------------------
template <typename Scalar>
inline bool areNear(Scalar a, Scalar b, Scalar tolerance)
{
return (std::abs(b - a) < tolerance);
}
//-------------------------------------------------------------------------------------------
template <typename Scalar>
inline typename tcg::disable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
mod(Scalar val, Scalar mod)
{
Scalar m = val % mod;
return (m >= 0) ? m : m + mod;
}
template <typename Scalar>
inline typename tcg::enable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
mod(Scalar val, Scalar mod)
{
Scalar m = fmod(val, mod);
return (m >= 0) ? m : m + mod;
}
//-------------------------------------------------------------------------------------------
template <typename Scalar>
inline Scalar mod(Scalar val, Scalar a, Scalar b)
{
return a + mod(val - a, b - a);
}
//-------------------------------------------------------------------------------------------
//! Returns the modular shift value with minimal abs: <TT>mod(val2, m) = mod(val1 + shift, m)</TT>
template <typename Scalar>
inline Scalar modShift(Scalar val1, Scalar val2, Scalar m)
{
Scalar shift1 = mod(val2 - val1, m), shift2 = m - shift1;
return (shift2 < shift1) ? -shift2 : shift1;
}
//-------------------------------------------------------------------------------------------
//! Returns the modular shift value with minimal abs: <TT>mod(val2, a, b) = mod(val1 + shift, a, b)</TT>
template <typename Scalar>
inline Scalar modShift(Scalar val1, Scalar val2, Scalar a, Scalar b)
{
return modShift(val1 - a, val2 - a, b - a);
}
//-------------------------------------------------------------------------------------------
/*!
Returns the \a quotient associated to the remainder calculated with mod().
\return Integral quotient of the division of \p val by \p d.
*/
template <typename Scalar>
inline typename tcg::disable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
div(Scalar val, Scalar d)
{
TCG_STATIC_ASSERT(-3 / 5 == 0);
TCG_STATIC_ASSERT(3 / -5 == 0);
return (val < 0 || d < 0) ? (val / d) - 1 : val / d;
}
/*!
Returns the \a quotient associated to the remainder calculated with mod().
\return Integral quotient of the division of \p val by \p d.
*/
template <typename Scalar>
inline typename tcg::enable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
div(Scalar val, Scalar d)
{
return std::floor(val / d);
}
//-------------------------------------------------------------------------------------------
/*!
Returns the \a quotient associated to the remainder calculated with mod().
\return Integral quotient of the division of \p val by <TT>(b-a)</TT>.
*/
template <typename Scalar>
inline Scalar div(Scalar val, Scalar a, Scalar b)
{
return div(val - a, b - a);
}
//-------------------------------------------------------------------------------------------
//! Linear interpolation of values \p v0 and \p v1 with parameter \p t.
template <typename T, typename Scalar>
inline T lerp(const T &v0, const T &v1, Scalar t)
{
return (1 - t) * v0 + t * v1;
}
//-------------------------------------------------------------------------------------------
/*!
\brief Computes the second degree Bezier curve of control points \p c0, \p c1 and \p c2
at parameter \p t.
*/
template <typename T, typename Scalar>
inline T bezier(const T &c0, const T &c1, const T &c2, Scalar t)
{
Scalar one_t = 1 - t, t_one_t = t * one_t; // 3 Scalar-Scalar products
return (one_t * one_t) * c0 + (t_one_t + t_one_t) * c1 + (t * t) * c2; // 3 Scalar-T products
// return (c0 * one_t + c1 * t) * one_t + (c1 * one_t + c2 * t) * t; // 6 Scalar-T products
}
//-------------------------------------------------------------------------------------------
//! \deprecated
template <typename UScalar>
inline UScalar GE_2Power(UScalar val)
{
if (!val)
return 0;
--val;
UScalar i;
for (i = 0; val; ++i)
val = val >> 1;
return 1 << i;
}
}
} // namespace tcg::numeric_ops
#endif // TCG_NUMERIC_OPS_H