simplex.h File Reference

Linear interpolation for a simplex. More...

#include "../defs.h"
#include "../../ads/array/FixedArray.h"
#include "simplex.ipp"

Go to the source code of this file.

Functions
template<int N, int M, typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< M+1, ads::FixedArray< N, T > > &positions, const ads::FixedArray< M+1, F > &values, const ads::FixedArray< N, T > &location)
	General interface for linear interpolation.
template<typename T , typename F >
const F &	linear_interpolation (const T a, T b, const F &alpha, const F &beta, T x)
	Specialization for a 1-D simplex in 1-D space.
template<typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< 2, T > &positions, const ads::FixedArray< 2, F > &values, const T location)
	Specialization for a 1-D simplex in 1-D space.
template<typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const F &alpha, const F &beta, const ads::FixedArray< 2, T > &x)
	Specialization for a 1-D simplex in 2-D space.
template<typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, const F &alpha, const F &beta, const F &gamma, const ads::FixedArray< 2, T > &x)
	Specialization for a 2-D simplex in 2-D space.
template<typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c, const F &alpha, const F &beta, const F &gamma, const ads::FixedArray< 3, T > &x)
	Specialization for a 2-D simplex in 3-D space.
template<typename T , typename F >
const F &	linear_interpolation (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c, const ads::FixedArray< 3, T > &d, const F &alpha, const F &beta, const F &gamma, const F &delta, const ads::FixedArray< 3, T > &x)
	Specialization for a 3-D simplex in 3-D space.

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Detailed Description

Linear interpolation for a simplex.

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Function Documentation

template<typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< 3, T > &	a,
		const ads::FixedArray< 3, T > &	b,
		const ads::FixedArray< 3, T > &	c,
		const ads::FixedArray< 3, T > &	d,
		const F &	alpha,
		const F &	beta,
		const F &	gamma,
		const F &	delta,
		const ads::FixedArray< 3, T > &	x
	)			[inline]

Specialization for a 3-D simplex in 3-D space.

template<typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< 3, T > &	a,
		const ads::FixedArray< 3, T > &	b,
		const ads::FixedArray< 3, T > &	c,
		const F &	alpha,
		const F &	beta,
		const F &	gamma,
		const ads::FixedArray< 3, T > &	x
	)			[inline]

Specialization for a 2-D simplex in 3-D space.

template<typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< 2, T > &	a,
		const ads::FixedArray< 2, T > &	b,
		const ads::FixedArray< 2, T > &	c,
		const F &	alpha,
		const F &	beta,
		const F &	gamma,
		const ads::FixedArray< 2, T > &	x
	)			[inline]

Specialization for a 2-D simplex in 2-D space.

template<typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< 2, T > &	a,
		const ads::FixedArray< 2, T > &	b,
		const F &	alpha,
		const F &	beta,
		const ads::FixedArray< 2, T > &	x
	)			[inline]

Specialization for a 1-D simplex in 2-D space.

template<typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< 2, T > &	positions,
		const ads::FixedArray< 2, F > &	values,
		const T	location
	)			[inline]

Specialization for a 1-D simplex in 1-D space.

References linear_interpolation().

template<typename T , typename F >

const F& linear_interpolation	(	const T	a,
		T	b,
		const F &	alpha,
		const F &	beta,
		T	x
	)			[inline]

Specialization for a 1-D simplex in 1-D space.

template<int N, int M, typename T , typename F >

const F& linear_interpolation	(	const ads::FixedArray< M+1, ads::FixedArray< N, T > > &	positions,
		const ads::FixedArray< M+1, F > &	values,
		const ads::FixedArray< N, T > &	location
	)			[inline]

General interface for linear interpolation.

Parameters:

	positions	are the positions of the simplex nodes. The positions must be distinct. (This is checked with an assertion.)
	values	are the field values at the simplex nodes.
	location	is the point at which to interpolate the field.

• N is the dimension of the space.
• M is the dimension of the simplex.
• T is the number type.
• F is the field type.

Note:

This function is not implemented. Only specializations for certain values of N and M are implemented.

Returns:

The interpolated value of the field.

Referenced by linear_interpolation().