Setting Material Orientation - Revision history

Nairnj: /* Rotation Matrix for Axial Direction */

2021-02-22T21:16:37Z

Rotation Matrix for Axial Direction

← Older revision		Revision as of 21:16, 22 February 2021
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	<RotateY>-φ</RotateY>		<RotateY>-φ</RotateY>

	and note that φ and θ need to be in degrees and negated from the standard definition in [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates]. For example to rotate axial direction to the x axis, use (θφ)=(0,90) an to rotate to the y axis use (θφ)=(90,0) (and these need not be negated).		and note that φ and θ need to be in degrees and negated from the standard definition in [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates]. For example to rotate axial direction to the x axis, use (θ,φ)=(0,90) an to rotate to the y axis use (θ,φ)=(90,0) (and these special cases need not be negated).

	== Rotation Specifics ==		== Rotation Specifics ==

Nairnj: /* Rotation Matrix for Axial Direction */

2021-02-22T21:14:37Z

Rotation Matrix for Axial Direction

← Older revision		Revision as of 21:14, 22 February 2021
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	<RotateY>-φ</RotateY>		<RotateY>-φ</RotateY>

	and note that φ and θ need to be in degrees and negated from the standard definition in [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates].		and note that φ and θ need to be in degrees and negated from the standard definition in [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates]. For example to rotate axial direction to the x axis, use (θφ)=(0,90) an to rotate to the y axis use (θφ)=(90,0) (and these need not be negated).

	== Rotation Specifics ==		== Rotation Specifics ==

Nairnj: /* Rotation Matrix for Axial Direction */

2021-02-22T21:06:37Z

Rotation Matrix for Axial Direction

← Older revision		Revision as of 21:06, 22 February 2021
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	=== Rotation Matrix for Axial Direction ===		=== Rotation Matrix for Axial Direction ===

	One relatively common numerical task in 3D is to model a [[Transversely Isotropic Material\|transversely isotropic material]] where the only need is to orient the material's axial direction. ~~If we use the~~ [[Transversely Isotropic Material#Transvers 1\|transversely isotropic material with the axial direction along the material's z axis]], we ~~can~~ define the initial orientation of the material using angles in standard [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates]. In other words, the material's z axis in the global axes is defined by:		One relatively common numerical task in 3D is to model a [[Transversely Isotropic Material\|transversely isotropic material]] where the only need is to orient the material's axial direction. Because 3D modeling only allows a [[Transversely Isotropic Material#Transvers 1\|transversely isotropic material with the axial direction along the material's z axis]], we need to define the initial orientation of the material using angles in standard [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates]. In other words, the material's z axis in the global axes is defined by:

Nairnj: /* Introduction */

2021-02-22T21:04:56Z

Introduction

← Older revision		Revision as of 21:04, 22 February 2021
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	The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] only lets you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.		The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] only lets you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.

	The <tt>Rotate</tt> command solves both these issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies ~~bnot~~ to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.		The <tt>Rotate</tt> command solves both these issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies both to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.

	== Rotate Command ==		== Rotate Command ==

Nairnj: /* Introduction */

2017-04-07T17:23:34Z

Introduction

← Older revision		Revision as of 17:23, 7 April 2017
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	== Introduction ==		== Introduction ==

	The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] ~~(or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let~~ you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.		The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] only lets you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.

	The <tt>Rotate</tt> command solves both these issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies bnot to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.		The <tt>Rotate</tt> command solves both these issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies bnot to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.

Nairnj: /* Introduction */

2017-04-07T17:22:51Z

Introduction

← Older revision		Revision as of 17:22, 7 April 2017
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	The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.		The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.

	The <tt>Rotate</tt> command solves both ~~this~~ issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies bnot to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.		The <tt>Rotate</tt> command solves both these issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies bnot to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.

	== Rotate Command ==		== Rotate Command ==

Nairnj: /* Introduction */

2017-04-07T17:22:36Z

Introduction

← Older revision		Revision as of 17:22, 7 April 2017
Line 5:		Line 5:
	The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.		The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.

	The <tt>Rotate</tt> command solves both this issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using		The <tt>Rotate</tt> command solves both this issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using <tt>(anglesPath)</tt> files. This page documents the <tt>Rotate</tt> command. The [[#Rotation Matrix\|Rotation Matrix]] section applies bnot to angles picked using the <tt>Rotate</tt> command and to angles picked with <tt>(anglesPath)</tt> files.

	== Rotate Command ==		== Rotate Command ==

Nairnj: /* Introduction */

2017-04-07T17:20:40Z

Introduction

← Older revision		Revision as of 17:20, 7 April 2017
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	== Introduction ==		== Introduction ==

	The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This ~~options~~ has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations. The <tt>Rotate</tt> command solves both this issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well.		The [[MPM Region and Hole Commands\|<tt>Region</tt> command]] (or <tt><Body></tt> command in <tt>XML</tt>) and the [[BMPRegion Command\|<tt>BMPRegion</tt> command]] let you specify a single rotation angle for material rotation about the z axis. This option has two limitations. First, the angle has to be constant or the same for all material points. Second, it is only rotation about the z axis and therefore insufficient for specifying arbitrary orientation in 3D simulations.

			The <tt>Rotate</tt> command solves both this issues because it can set variable angles (with a [[User Defined Functions\|user-defined function]]) and can set rotation about x and y axes as well as the z axis. In addition to the <tt>Rotate</tt> command, a [[BMPRegion Command\|<tt>BMPRegion</tt> command]] can set rotations and x, y, and z axes by using

	== Rotate Command ==		== Rotate Command ==

Nairnj: /* Rotation Matrix for Axial Direction */

2017-04-05T22:46:02Z

Rotation Matrix for Axial Direction

← Older revision		Revision as of 22:46, 5 April 2017
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	<RotateY>-φ</RotateY>		<RotateY>-φ</RotateY>

	and note that φ and θ need to be in degrees and negated.		and note that φ and θ need to be in degrees and negated from the standard definition in [http://mathworld.wolfram.com/SphericalCoordinates.html spherical coordinates].

	== Rotation Specifics ==		== Rotation Specifics ==

Nairnj: /* Rotation Matrix for Axial Direction */

2017-04-05T22:45:26Z

Rotation Matrix for Axial Direction

← Older revision		Revision as of 22:45, 5 April 2017
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	where θ is the azimuthal angle and φ is the polar angle. This orientation is constructed in scripted files using:		where θ is the azimuthal angle and φ is the polar angle. This orientation is constructed in scripted files using:

	Rotate "z",-θ"y",-φ,		Rotate "z",-θ,"y",-φ,

	In <tt>XML</tt> files, the commands would be		In <tt>XML</tt> files, the commands would be