ImathRoots.h File Reference

#include "ImathMath.h"
#include "ImathNamespace.h"
#include <complex>

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Functions
template<class T >
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int	solveLinear (T a, T b, T &x)
template<class T >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int	solveQuadratic (T a, T b, T c, T x[2])
template<class T >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int	solveNormalizedCubic (T r, T s, T t, T x[3])
template<class T >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int	solveCubic (T a, T b, T c, T d, T x[3])
template<class T >
IMATH_CONSTEXPR14 int	solveLinear (T a, T b, T &x)
template<class T >
IMATH_CONSTEXPR14 int	solveQuadratic (T a, T b, T c, T x[2])
template<class T >
IMATH_CONSTEXPR14 int	solveNormalizedCubic (T r, T s, T t, T x[3])
template<class T >
IMATH_CONSTEXPR14 int	solveCubic (T a, T b, T c, T d, T x[3])

Function Documentation

template<class T >

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int solveCubic	(	T	a,
		T	b,
		T	c,
		T	d,
		T	x[3]
	)

Solve for x in the cubic equation:

a * x*x*x + b * x*x + c * x + d == 0

The equation is solved using Cardano's Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).

Returns

0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions.

Definition at line 197 of file ImathRoots.h.

template<class T >

IMATH_CONSTEXPR14 int solveCubic	(	T	a,
		T	b,
		T	c,
		T	d,
		T	x[3]
	)

Solve for x in the cubic equation:

a * x*x*x + b * x*x + c * x + d == 0

The equation is solved using Cardano's Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).

Returns

0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions.

Definition at line 197 of file ImathRoots.h.

template<class T >

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int solveLinear	(	T	a,
		T	b,
		T &	x
	)

Solve for x in the linear equation:

a * x + b == 0

Returns

1 if the equation has a solution, 0 if there is no solution, and -1 if all real numbers are solutions.

Definition at line 88 of file ImathRoots.h.

template<class T >

IMATH_CONSTEXPR14 int solveLinear	(	T	a,
		T	b,
		T &	x
	)

Solve for x in the linear equation:

a * x + b == 0

Returns

1 if the equation has a solution, 0 if there is no solution, and -1 if all real numbers are solutions.

Definition at line 88 of file ImathRoots.h.

template<class T >

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int solveNormalizedCubic	(	T	r,
		T	s,
		T	t,
		T	x[3]
	)

Solve for x in the normalized cubic equation:

x*x*x + r * x*x + s * x + t == 0

The equation is solved using Cardano's Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).

Returns

0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions.

Definition at line 140 of file ImathRoots.h.

template<class T >

IMATH_CONSTEXPR14 int solveNormalizedCubic	(	T	r,
		T	s,
		T	t,
		T	x[3]
	)

Solve for x in the normalized cubic equation:

x*x*x + r * x*x + s * x + t == 0

The equation is solved using Cardano's Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).

Returns

0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions.

Definition at line 140 of file ImathRoots.h.

template<class T >

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 int solveQuadratic	(	T	a,
		T	b,
		T	c,
		T	x[2]
	)

Solve for x in the quadratic equation:

a * x*x + b * x + c == 0

Returns

2 if the equation has two solutions, 1 if the equation has a single solution, 0 if there is no solution, and -1 if all real numbers are solutions.

Definition at line 107 of file ImathRoots.h.

template<class T >

IMATH_CONSTEXPR14 int solveQuadratic	(	T	a,
		T	b,
		T	c,
		T	x[2]
	)

Solve for x in the quadratic equation:

a * x*x + b * x + c == 0

Returns

2 if the equation has two solutions, 1 if the equation has a single solution, 0 if there is no solution, and -1 if all real numbers are solutions.

Definition at line 107 of file ImathRoots.h.