Applications of dual quaternions to 2D geometry: Difference between revisions

Revision as of 15:49, 30 June 2022

Revision as of 15:52, 30 June 2022

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<math display="block"> (A + Bi + C\varepsilon j + D\varepsilon k)^{-1} = \frac{A - Bi - C\varepsilon j - D\varepsilon k}{A^2+B^2}</math>

The set <math>\{1, i, \varepsilon j, \varepsilon k\}</math> forms a basis of the vector space ofdiscussed dual-complexin numbersthis article, where the scalars are real numbers.

The magnitude of a dual-complex numberquaternions of the form, discussed here is <math>q</math> is defined to be <math display="block">|q| = \sqrt{A^2 + B^2}.</math>

For applications in computer graphics, the number <math>A + Bi + C\varepsilon j + D\varepsilon k</math> is commonly represented as the 4-[[tuple]] <math>(A,B,C,D)</math>.