User Manual 4.0 Rotations and quaternions - Historique des versions

Admin le 28 juin 2018 à 12:18

2018-06-28T12:18:49Z

← Version précédente		Version du 28 juin 2018 à 12:18
Ligne 13 :		Ligne 13 :
	\|-		\|-
	\| Patrius		\| Patrius
	\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/package-summary.html Package fr.cnes.sirius.patrius.math.geometry.euclidean.threed]		\|[{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/package-summary.html Package fr.cnes.sirius.patrius.math.geometry.euclidean.threed]
	\|-		\|-
	\| Patrius		\| Patrius
	\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/package-summary.html Package fr.cnes.sirius.patrius.math.complex]		\|[{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/complex/package-summary.html Package fr.cnes.sirius.patrius.math.complex]
	\|}		\|}

Ligne 39 :		Ligne 39 :
	The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.		The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.

	The Rotation is represented by a [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a [{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>
	The [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.		In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.
Ligne 194 :		Ligne 194 :

	=== Building Rotations ===		=== Building Rotations ===
	Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].		Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].
	In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.		In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.

Ligne 253 :		Ligne 253 :

	==== Others representations ====		==== Others representations ====
	See [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].		See [{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].

	=== Using Rotations ===		=== Using Rotations ===
Ligne 260 :		Ligne 260 :

	The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>
	The [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	==== Rotate a vector ====		==== Rotate a vector ====

	A rotation is an operator which basically rotates three dimensional [{{JavaDoc4.0}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{JavaDoc4.0}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.		A rotation is an operator which basically rotates three dimensional [{{JavaDoc4.1}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{JavaDoc4.1}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.

	<syntaxhighlight lang="java">		<syntaxhighlight lang="java">
Ligne 440 :		Ligne 440 :
	\|'''Quaternion'''		\|'''Quaternion'''
	\|This class implements quaternions.		\|This class implements quaternions.
	\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html ...]		\|[{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html ...]
	\|-		\|-
	\|'''Rotation'''		\|'''Rotation'''
	\|This class implements rotations in a three-dimensional space.		\|This class implements rotations in a three-dimensional space.
	\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html ...]		\|[{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html ...]
	\|-		\|-
	\|'''RotationOrder'''		\|'''RotationOrder'''
	\|This class is a utility representing a rotation order specification for Cardan or Euler angles specification.		\|This class is a utility representing a rotation order specification for Cardan or Euler angles specification.
	\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/RotationOrder.html ...]		\|[{{JavaDoc4.1}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/RotationOrder.html ...]
	\|}		\|}

	[[Category:User_Manual_4.~~0_Mathematics~~]]		[[Category:User_Manual_4.1_Mathematics]]

Admin le 21 février 2018 à 14:03

2018-02-21T14:03:02Z

← Version précédente		Version du 21 février 2018 à 14:03
Ligne 39 :		Ligne 39 :
	The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.		The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.

	The Rotation is represented by a [{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>
	The [{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.		In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.
Ligne 194 :		Ligne 194 :

	=== Building Rotations ===		=== Building Rotations ===
	Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].		Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].
	In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.		In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.

Ligne 253 :		Ligne 253 :

	==== Others representations ====		==== Others representations ====
	See [{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].		See [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].

	=== Using Rotations ===		=== Using Rotations ===
Ligne 260 :		Ligne 260 :

	The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>
	The [{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	==== Rotate a vector ====		==== Rotate a vector ====

	A rotation is an operator which basically rotates three dimensional [{{~~PathCurrentJavaDoc~~}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{~~PathCurrentJavaDoc~~}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.		A rotation is an operator which basically rotates three dimensional [{{JavaDoc4.0}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{JavaDoc4.0}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.

	<syntaxhighlight lang="java">		<syntaxhighlight lang="java">

Admin : /* Classes */

2018-02-21T08:46:35Z

Classes

← Version précédente		Version du 21 février 2018 à 08:46
Ligne 432 :		Ligne 432 :
	The relevant classes are :		The relevant classes are :

	\|=Class\|=~~Summary~~\|=Javadoc		{\| class="wikitable"
	\|'''Quaternion'''\|This class implements quaternions.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html ...]		\|-
	\|'''Rotation'''\|This class implements rotations in a three-dimensional space.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html ...]		! scope="col"\| Class
	\|'''RotationOrder'''\|This class is a utility representing a rotation order specification for Cardan or Euler angles specification.\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/RotationOrder.html ...]		! scope="col"\| Summary
			! scope="col"\| Javadoc
			\|-
			\|'''Quaternion'''
			\|This class implements quaternions.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html ...]
			\|-
			\|'''Rotation'''
			\|This class implements rotations in a three-dimensional space.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html ...]
			\|-
			\|'''RotationOrder'''
			\|This class is a utility representing a rotation order specification for Cardan or Euler angles specification.
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/RotationOrder.html ...]
			\|}

	[[Category:User_Manual_4.0_Mathematics]]		[[Category:User_Manual_4.0_Mathematics]]

Admin : /* Javadoc */

2018-02-21T08:45:39Z

Javadoc

← Version précédente		Version du 21 février 2018 à 08:45
Ligne 6 :		Ligne 6 :
	=== Javadoc ===		=== Javadoc ===
	The relevant packages are documented here :		The relevant packages are documented here :
	\|=Library\|=Javadoc
	\| Patrius \|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/package-summary.html Package fr.cnes.sirius.patrius.math.geometry.euclidean.threed]		{\| class="wikitable"
	\| Patrius\|[{{~~PathCurrentJavaDoc~~}}/fr/cnes/sirius/patrius/math/complex/package-summary.html Package fr.cnes.sirius.patrius.math.complex]		\|-
			! scope="col"\| Library
			! scope="col"\| Javadoc
			\|-
			\| Patrius
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/package-summary.html Package fr.cnes.sirius.patrius.math.geometry.euclidean.threed]
			\|-
			\| Patrius
			\|[{{JavaDoc4.0}}/fr/cnes/sirius/patrius/math/complex/package-summary.html Package fr.cnes.sirius.patrius.math.complex]
			\|}

	=== Links ===		=== Links ===

Admin le 20 février 2018 à 16:46

2018-02-20T16:46:29Z

← Version précédente		Version du 20 février 2018 à 16:46
Ligne 1 :		Ligne 1 :
			__NOTOC__

	== Introduction ==		== Introduction ==
	=== Scope ===		=== Scope ===

Admin le 19 février 2018 à 10:57

2018-02-19T10:57:03Z

← Version précédente		Version du 19 février 2018 à 10:57
Ligne 376 :		Ligne 376 :
	Same example given in Scilab using Celestlab macros library:		Same example given in Scilab using Celestlab macros library:

	<syntaxhighlight lang="~~cpp~~">		<syntaxhighlight lang="scilab">
	alpha1 = CL_deg2rad(30.);		alpha1 = CL_deg2rad(30.);
	q1 = CL_rot_axAng2quat([1;1;1],alpha1);		q1 = CL_rot_axAng2quat([1;1;1],alpha1);
Ligne 407 :		Ligne 407 :
	Same example given in Scilab using Celestlab macros library:		Same example given in Scilab using Celestlab macros library:

	<syntaxhighlight lang="~~cpp~~">		<syntaxhighlight lang="scilab">
	alpha1 = CL_deg2rad(30.);		alpha1 = CL_deg2rad(30.);
	q1 = CL_rot_axAng2quat([1;1;1],alpha1);		q1 = CL_rot_axAng2quat([1;1;1],alpha1);

Admin le 19 février 2018 à 10:55

2018-02-19T10:55:20Z

← Version précédente		Version du 19 février 2018 à 10:55
Ligne 376 :		Ligne 376 :
	Same example given in Scilab using Celestlab macros library:		Same example given in Scilab using Celestlab macros library:

	<syntaxhighlight lang="~~c++~~">		<syntaxhighlight lang="cpp">
	alpha1 = CL_deg2rad(30.);		alpha1 = CL_deg2rad(30.);
	q1 = CL_rot_axAng2quat([1;1;1],alpha1);		q1 = CL_rot_axAng2quat([1;1;1],alpha1);
Ligne 407 :		Ligne 407 :
	Same example given in Scilab using Celestlab macros library:		Same example given in Scilab using Celestlab macros library:

	<syntaxhighlight lang="~~c++~~">		<syntaxhighlight lang="cpp">
	alpha1 = CL_deg2rad(30.);		alpha1 = CL_deg2rad(30.);
	q1 = CL_rot_axAng2quat([1;1;1],alpha1);		q1 = CL_rot_axAng2quat([1;1;1],alpha1);

Admin le 19 février 2018 à 10:54

2018-02-19T10:54:14Z

← Version précédente		Version du 19 février 2018 à 10:54
Ligne 256 :		Ligne 256 :
	==== Rotate a vector ====		==== Rotate a vector ====

	A rotation is an operator which basically rotates three dimensional [{{PathCurrentJavaDoc}}''fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{PathCurrentJavaDoc}}''fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.		A rotation is an operator which basically rotates three dimensional [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] into other three dimensional [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Vector3D.html vectors] using '''''applyTo()'''''.

	<syntaxhighlight lang="java">		<syntaxhighlight lang="java">

Admin le 19 février 2018 à 10:53

2018-02-19T10:53:22Z

← Version précédente		Version du 19 février 2018 à 10:53
Ligne 31 :		Ligne 31 :
	The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.		The Rotation is part of the math package fr.cnes.sirius.patrius.math.geometry.euclidean.threed.

	The Rotation is represented by a [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a [{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/complex/Quaternion.html quaternion]: it is a unit quaternion (a quaternion of norm one).<br>
	The [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.		In a three dimensional space, a rotation <math>r</math> is a function that maps vectors to vectors <math>r: \vec{v} \mapsto \vec{w}</math>. The rotation can be defined by one angle <math>\theta</math> and one axis <math>\vec{u}</math>, transforming <math>\vec{v}</math> into <math>\vec{w}</math> as described in the following figure.
Ligne 186 :		Ligne 186 :

	=== Building Rotations ===		=== Building Rotations ===
	Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].		Rotations can be represented by several different mathematical entities (matrices, axis and angle, Cardan or Euler angles, quaternions). The user can build a rotation from any of these representations, and any of these representations can be retrieved from a [{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation instance].
	In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.		In addition, a rotation can also be built implicitly from a set of vectors and their image or just a vector and its image.

Ligne 245 :		Ligne 245 :

	==== Others representations ====		==== Others representations ====
	See [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].		See [{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation javadoc].

	=== Using Rotations ===		=== Using Rotations ===
Ligne 252 :		Ligne 252 :

	The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>		The Rotation is represented by a rotation quaternion : it is a unit quaternion (a quaternion of norm one).<br>
	The [{{PathCurrentJavaDoc}}//fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).		The [{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/geometry/euclidean/threed/Rotation.html Rotation class] represents an algebraic rotation (i.e. a mathematical rotation).

	==== Rotate a vector ====		==== Rotate a vector ====

Admin le 19 février 2018 à 10:51

2018-02-19T10:51:01Z

Voir les modifications