Alexa, Marc (2002)
Linear Combinations of Transformations.
In: ACM Transactions on Graphics, 21 (3)
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
Geometric transformations are most commonly represented as square matrices in computer graphics. Following simple geometric arguments we derive a natural and geometrically meaningful definition of scalar multiples and a commutative addition of transformations based on the matrix representation, given that the matrices have no negative real eigenvalues. Together, these operations allow the linear combination of transformations. This provides the ability to create weighted combination of transformations, interpolate between transformations, and to construct or use arbitrary transformations in a structure similar to a basis of a vector space. These basic techniques are useful for synthesis and analysis of motions or animations. Animations through a set of key transformations are generated using standard techniques such as subdivision curves. For analysis and progressive compression a PCA can be applied to sequences of transformations. We describe an implementation of the techniques that enables an easy-to-use and transparent way of dealing with geometric transformations in graphics software. We compare and relate our approach to other techniques such as matrix decomposition and quaternion interpolation.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2002 |
| Autor(en): | Alexa, Marc |
| Art des Eintrags: | Bibliographie |
| Titel: | Linear Combinations of Transformations |
| Sprache: | Englisch |
| Publikationsjahr: | 2002 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | ACM Transactions on Graphics |
| Jahrgang/Volume einer Zeitschrift: | 21 |
| (Heft-)Nummer: | 3 |
| Kurzbeschreibung (Abstract): | Geometric transformations are most commonly represented as square matrices in computer graphics. Following simple geometric arguments we derive a natural and geometrically meaningful definition of scalar multiples and a commutative addition of transformations based on the matrix representation, given that the matrices have no negative real eigenvalues. Together, these operations allow the linear combination of transformations. This provides the ability to create weighted combination of transformations, interpolate between transformations, and to construct or use arbitrary transformations in a structure similar to a basis of a vector space. These basic techniques are useful for synthesis and analysis of motions or animations. Animations through a set of key transformations are generated using standard techniques such as subdivision curves. For analysis and progressive compression a PCA can be applied to sequences of transformations. We describe an implementation of the techniques that enables an easy-to-use and transparent way of dealing with geometric transformations in graphics software. We compare and relate our approach to other techniques such as matrix decomposition and quaternion interpolation. |
| Freie Schlagworte: | Transformations, Linear spaces, Exponential map, Matrix |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 16 Apr 2018 09:05 |
| Letzte Änderung: | 16 Apr 2018 09:05 |
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| Suche nach Titel in: | TUfind oder in Google |
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