ABSTRACT
Transformations of geometric objects can be easily described within Compass Ruler Algebra according to Table 8.1. The description of transformations of a geometric object o in Compass Ruler Algebra.
Transformation
Operator
Usage
Reflection
Line L = n + de ∞
oL = −LoL
Rotation
Rotor R = cos ( ϕ 2 ) − sin ( ϕ 2 ) e 1 ∧ e 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_1.tif"/>
o R = R o R ˜ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_2.tif"/>
Translation
Translator T = 1 − 1 2 t e ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_3.tif"/>
o T = T o T ˜ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_4.tif"/>
Rigid Body Motion
Motor M = cos ( ϕ 2 ) − sin ( ϕ 2 ) ( P ∧ e ∞ ) ∗ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_5.tif"/>
o M = M o M ˜ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152172/05b92b15-682a-4737-aabb-5365e4b7c38b/content/inq_chapter8_95_6.tif"/>
