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dc.contributor.advisor Hanson, Andrew J. en_US Zhang, Hui en_US 2010-06-08T17:19:19Z 2027-02-08T18:19:19Z 2012-04-18T18:22:08Z 2010-06-08T17:19:19Z 2009 en_US
dc.description Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009 en_US
dc.description.abstract People have long been fascinated with understanding the fourth dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another. The research presented here creates physically realistic models for simple interactions with objects and materials in a virtual 4D world. We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object. Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings. en_US
dc.language.iso EN en_US
dc.publisher [Bloomington, Ind.] : Indiana University en_US
dc.subject Visualization en_US
dc.subject Haptics en_US
dc.subject 4D en_US
dc.subject Mathematical Visualization en_US
dc.subject HCI en_US
dc.subject.classification Computer Science en_US
dc.title Physically Interacting With Four Dimensions en_US
dc.type Doctoral Dissertation en_US

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