Get your science in Shape
Translations and rotations are non-deforming transformation that change the position and orientation of an object, respectively.
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In Shape there are three groups of these transformations that distinguish themselves through their effect on the local coordinate system or the restrictions on their directions with respect to the observer.
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The Translation, Rotations and PA/Inc Rotation Modifiers have the important property that they carry along the local coordinate system and operate in the coordinate system that is obtained after previous translations and rotations.
Contrary to these, the Displacement and GeoRotation modifiers only transform the geometry. i.e. the mesh position and orientation as an enclosure for the region to be rendered. All coordinate information for the local properties, such as density, velocity, etc., does not change. These are according to any prior transformation of the other type.
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Commutative Properties:
Since several of the Position Transform can be concatenated in the Modifier Stack, it is important to know whether the order in which they are applied changes the result or not.
Translations among themselves can be interchanged without changing the outcome (they are commutative). However, combinations of rotation with translations or other rotations are not commutative and therefore the order in the Modifier Stack is very important. So, make sure they are in an order that produces the desired result.
Translation:
Moves the object to a new position in the World Coordinate System. The local coordinate system is carried along.
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When using the interactive System Translation from the System tab on the right side of the 3-D Module, a new Translation Modifier is added to the Modifier Stack if there is not one already at the end. This modifier can then also me changed numerically.
By pressing the x,y or z keys while interactively moving an object, the translation can be restricted along these axes.
Rotation:
Rotates the object in the current coordinate system. The local coordinate system is carried along. If there is a Translation applied before, then the Rotation is still applied around the translated coordinate system.
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When using the interactive System Rotation from the System tab on the right side of the 3-D Module, a new Rotation Modifier is added to the Modifier Stack if there is not one already at the end. This modifier can then also me changed numerically.
By pressing the x,y or z keys while interactively rotating an object, the rotation can be restricted around these axes.
PA/Inc Rotation:
Rotates the object in the coordinate system observer´s coordinate system as inclination Inc and position angle PA.
PA rotates around the line of sight with zero along the world y-axis (up).
Inc rotates around the horizontal line in the plane of the sky with zero in the plane of the sky.
The inclination Inc is applied first and the the position angle PA..
Displacement & GeoRotation:
These two modifiers have the same functionality as Translation & Rotation, except that they only transform the mesh, but do not alter the current coordinate system. This means that other modifiers such as density, velocity, etc., will remain centered at the same position.
This is often useful when a mesh is a substructure of a larger object. In such a case it is often useful to have instanced copies of modifiers that are meant to remain the same as those of the main structure or other sub-structures.
Modifiers: Position Transforms
Translation, Rotation
Displacement, GeoRotation
PA/Inc Rotation
