Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis > Class Template Reference

Detailed Description

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
class Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >

Represents a fixed Euler rotation system.

This meta-class goal is to represent the Euler system in compilation time, for EulerAngles.

You can use this class to get two things:

  • Build an Euler system, and then pass it as a template parameter to EulerAngles.
  • Query some compile time data about an Euler system. (e.g. Whether it's tait bryan)

Euler rotation is a set of three rotation on fixed axes. (see EulerAngles) This meta-class store constantly those signed axes. (see EulerAxis)

### Types of Euler systems ###

All and only valid 3 dimension Euler rotation over standard signed axes{+X,+Y,+Z,-X,-Y,-Z} are supported:

  • all axes X, Y, Z in each valid order (see below what order is valid)
  • rotation over the axis is supported both over the positive and negative directions.
  • both tait bryan and proper/classic Euler angles (i.e. the opposite).

Since EulerSystem support both positive and negative directions, you may call this rotation distinction in other names:

  • _right handed_ or _left handed_
  • _counterclockwise_ or _clockwise_

Notice all axed combination are valid, and would trigger a static assertion. Same unsigned axes can't be neighbors, e.g. {X,X,Y} is invalid. This yield two and only two classes:

  • _tait bryan_ - all unsigned axes are distinct, e.g. {X,Y,Z}
  • _proper/classic Euler angles_ - The first and the third unsigned axes is equal, and the second is different, e.g. {X,Y,X}

### Intrinsic vs extrinsic Euler systems ###

Only intrinsic Euler systems are supported for simplicity. If you want to use extrinsic Euler systems, just use the equal intrinsic opposite order for axes and angles. I.e axes (A,B,C) becomes (C,B,A), and angles (a,b,c) becomes (c,b,a).

### Convenient user typedefs ###

Convenient typedefs for EulerSystem exist (only for positive axes Euler systems), in a form of EulerSystem{A}{B}{C}, e.g. EulerSystemXYZ.

### Additional reading ###

More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles

Template Parameters:
_AlphaAxisthe first fixed EulerAxis
_AlphaAxisthe second fixed EulerAxis
_AlphaAxisthe third fixed EulerAxis

List of all members.

Public Types

enum  {
  AlphaAxisAbs,
  BetaAxisAbs,
  GammaAxisAbs,
  IsAlphaOpposite,
  IsBetaOpposite,
  IsGammaOpposite,
  IsOdd,
  IsEven,
  IsTaitBryan
}

Static Public Attributes

static const int AlphaAxis
static const int BetaAxis
static const int GammaAxis

Member Enumeration Documentation

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
anonymous enum
Enumerator:
AlphaAxisAbs 

the first rotation axis unsigned

BetaAxisAbs 

the second rotation axis unsigned

GammaAxisAbs 

the third rotation axis unsigned

IsAlphaOpposite 

weather alpha axis is negative

IsBetaOpposite 

weather beta axis is negative

IsGammaOpposite 

weather gamma axis is negative

IsOdd 

weather the Euler system is odd

IsEven 

weather the Euler system is even

IsTaitBryan 

weather the Euler system is tait bryan


Member Data Documentation

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::AlphaAxis [static]

The first rotation axis

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::BetaAxis [static]

The second rotation axis

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::GammaAxis [static]

The third rotation axis


The documentation for this class was generated from the following file:
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