Transformations in the geom3d Package - Maple Programming Help

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Transformations in the geom3d Package

 

Description

Examples

Description

• 

The help page geom3d[transformation] describes the transformations that can be applied directly to a specific geometric object.

• 

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.

rotation

rotate

translation

translate

ScrewDisplacement

ScrewDisplace

reflection

reflect

RotatoryReflection

RotatoryReflect

GlideReflection

GlideReflect

homothety

dilate

homology

StretchRotate

• 

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.

Examples

withgeom3d:

Define t1 which is a homothety with ratio 3, center of homothety (0,0,0)

t1dilate3,pointo,0,0,0

t1:=geom3d:-dilate3,o

(1)

Define the plane oxy

pointA,1,0,0,pointB,0,0,1:

linel1,o,A,linel2,o,B,planep,l1,l2:

dsegmentAB,A,B:

Define t2 which is a glide-reflection with p as the plane of reflection and AB as the vector of translation

t2GlideReflectp,AB

t2:=geom3d:-GlideReflectp,AB

(2)

Define t3 as a screw-displacement with l3 as the rotational axis and AB as a vector of translation

t3ScrewDisplaceπ2,linel3,A,B,AB

t3:=geom3d:-ScrewDisplace12π,l3,AB

(3)

Compute q1 which is the product of t2t1t3

q1transprodt2t1,t3

q1:=geom3d:-transprodgeom3d:-dilate13,o,geom3d:-reflectp,geom3d:-translateAB,geom3d:-dilate3,o,geom3d:-rotate12π,l3,geom3d:-translateAB

(4)

Compute the inverse of q1

q2inverseq1

q2:=geom3d:-transprodgeom3d:-translate_AB,geom3d:-rotate32π,l3,geom3d:-dilate13,o,geom3d:-translate_AB,geom3d:-reflectp,geom3d:-dilate3,o

(5)

Compute the product of q1q2; one can quickly recognize that this is an identity transformation

qtransprodq1,q2

q:=geom3d:-transprodgeom3d:-dilate13,o,geom3d:-reflectp,geom3d:-translateAB,geom3d:-dilate3,o,geom3d:-rotate12π,l3,geom3d:-translateAB,geom3d:-translate_AB,geom3d:-rotate32π,l3,geom3d:-dilate13,o,geom3d:-translate_AB,geom3d:-reflectp,geom3d:-dilate3,o

(6)

Simple check

tetrahedronte,o,1

te

(7)

transformte1,te,q

te1

(8)

AreDistinctte,te1

false

(9)

Hence, the two objects are the same

See Also

geom3d[draw]

geom3d[objects]

geom3d[transformation]

 


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