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On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
Senior Independent Study Theses
Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.
Grasping The Void: Immersion Tactics Using Gesture Controlled Physics Interaction Systems In Virtual Reality, Avery Rapson
Grasping The Void: Immersion Tactics Using Gesture Controlled Physics Interaction Systems In Virtual Reality, Avery Rapson
Senior Independent Study Theses
This thesis uses the HTC Vive in Unity to compare two different types of object interaction systems in order to determine the effectiveness of physics based interaction systems in a virtual environment. The research problem that motivates this project is the fact that there is no standardized method for defining successful object interaction techniques in VR. There are numerous interaction techniques in VR that fall short of simulating realistic object interaction. This project explores a physics based interaction system and examines how effective it is by comparing it to a non-physics based system. A model house with various interactable objects …