Transformations in the geom3d Package
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Description
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The help page geom3d[transformation] describes the transformations that can be applied directly to a specific geometric object.
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In general, to define a transformation without specifying the object to which the transformation is to be applied, use the ``verb'' form of the above transformations.
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rotation
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rotate
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translation
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translate
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ScrewDisplacement
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ScrewDisplace
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reflection
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reflect
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RotatoryReflection
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RotatoryReflect
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GlideReflection
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GlideReflect
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homothety
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dilate
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homology
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StretchRotate
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Using the function geom3d[inverse], one can compute the inverse of a given product of transformations, the function geom3d[transprod] converts a given transformation or product of transformations into a product of three ``primitive'' transformations (translate, rotate, and dilate), while the function geom3d[transform] is to apply the ``result'' transformation to a specific geometric object.
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Examples
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Define t1 which is a homothety with ratio 3, center of homothety (0,0,0)
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Define the plane oxy
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Define t2 which is a glide-reflection with p as the plane of reflection and AB as the vector of translation
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Define t3 as a screw-displacement with l3 as the rotational axis and AB as a vector of translation
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Compute q1 which is the product of t2^t1*t3
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Compute the inverse of q1
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Compute the product of q1*q2; one can quickly recognize that this is an identity transformation
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Simple check
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Hence, the two objects are the same
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Download Help Document
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