Mathematisch-Informationstheoretische Untersuchung von 3D-Metaphern. Lutz Kettner. Diplomarbeit, Universität Karlsruhe, Institut für Betriebs- und Dialogsysteme. 140 pages, 1993.
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A Mathematical and Information-Theoretical Survey of 3D-Metaphors
This work supplies first contributions to the theoretical foundations of three-dimensional interaction. Up to now, research in this direction was principally empirical or was not published at all.
Metaphors play a fundamental role in learning new fields. In the context of 3D-graphics applications, metaphors are known as so called 3D-metaphors. These explain the two-dimensional user interface of a 3D-graphics application by establishing relations to user's experiences with the three-dimensional real world. Additionally, the transformation from user interface events to the internal mathematical model is called the implementation of a 3D-metaphor.
Current developments emphasize new input devices with higher degrees of freedom for interaction with three-dimensional graphics application. Nonetheless, two-dimensional devices like mice or digitizers in pen computers still possess several advantages like wide propagation and good ergonomics. Also, two-dimensional devices will be in use for the two-dimensional user interface around the 3D-application and changing devices will outweigh advantages of specialized devices. Dependant on the application, three-dimensional interaction will even gain advantages from restrictions of the degree of freedom. Since many degrees of freedom can introduce noise by uncontrollable movements, the interaction time is limited due to correcting errors introduced by the users themselves.
To formalize descriptions, the implementations of 3D-metaphors are located in the Seeheim-model for user interface management systems (UIMS). These influence part of the dialog flow control and the parameter transformation process from the dialog events to the application-function's parameters: the former is modelled with augmented recursive transition networks (ARTN) and the latter uses mathematical notations in a generalized application framework. To evaluate metaphors, results from cognitive sciences like mental rotation times or time requirements for visual feedback delay are reported and applicated.
The investigation of literature found 42 metaphors that are presented, subdevided into their metaphorical concepts, their participation in the dialog flow and the transformations to the application-function's parameters. The metaphors for rotation exceed - both in amount and in complexity - the metaphors for other 3D-operations.
The analysis extracts relevant features for metaphors and systematize the great variety of small but relevant variants in the design of metaphors. The observable behaviour and the underlying concepts lead to a classification for metaphors. The feature space of the classification scheme has remarkable gaps, where some of these lead to new, intuitive metaphors. Three examples are investigated and discussed in detail.
To measure speed and accuracy of the input capabilities of different metaphors, Fitts' law is adapted and extended to these cases. The accuracy in the three-dimensional space of the graphics application is distinguished from the accuracy in the two-dimensional projection on screen, so that a new term, the so called control precision, is introduced into Fitts' law. The control precision describes the relation of three-dimensional manipulations and their two-dimensional, observable projections on screen. In special cases, singularities in transformations results in loss of control, which can be recognized as a disruption of information flow.