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6 results on '"Kiazyk, Stephen"'

1. Dihedral angles and orthogonal polyhedra

Author

Biedl, Therese, Derka, Martin, Kiazyk, Stephen, Lubiw, Anna, and Vosoughpour, Hamide

Subjects
Computer Science - Computational Geometry
Abstract

Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a suitable rotation) all faces are perpendicular to a coordinate axis, and hence all edges are parallel to a coordinate axis. Clearly, any facial angle and any dihedral angle is a multiple of $\pi/2$. In this note we explore the converse: if the facial and/or dihedral angles are all multiples of $\pi /2$, is the polyhedron necessarily orthogonal? The case of facial angles was answered previously. In this note we show that if both the facial and dihedral angles are multiples of $\pi /2$ then the polyhedron is orthogonal (presuming connectivity), and we give examples to show that the condition for dihedral angles alone does not suffice., Comment: 3 pages

Published
2013

3. Minimum Length Embedding of Planar Graphs at Fixed Vertex Locations

Author

Chan, Timothy M., Hoffmann, Hella-Franziska, Kiazyk, Stephen, Lubiw, Anna, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Wismath, Stephen, editor, and Wolff, Alexander, editor

Published
2013
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5. Star Unfolding from a Geodesic Curve

Author

Kiazyk, Stephen, Lubiw, Anna, Kiazyk, Stephen, and Lubiw, Anna

Abstract

There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the source unfolding, both of which use shortest paths from vertices to a source point on the surface of the polyhedron. Non-overlap of the source unfolding is straightforward; non-overlap of the star unfolding was proved by Aronov and O'Rourke in 1992. Our first contribution is a much simpler proof of non-overlap of the star unfolding. Both the source and star unfolding can be generalized to use a simple geodesic curve instead of a source point. The star unfolding from a geodesic curve cuts the geodesic curve and a shortest path from each vertex to the geodesic curve. Demaine and Lubiw conjectured that the star unfolding from a geodesic curve does not overlap. We prove a special case of the conjecture. Our special case includes the previously known case of unfolding from a geodesic loop. For the general case we prove that the star unfolding from a geodesic curve can be separated into at most two non-overlapping pieces.

Published
2015
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6. Star Unfolding from a Geodesic Curve

Author

Stephen Kiazyk and Anna Lubiw, Kiazyk, Stephen, Lubiw, Anna, Stephen Kiazyk and Anna Lubiw, Kiazyk, Stephen, and Lubiw, Anna

Abstract

There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the source unfolding, both of which use shortest paths from vertices to a source point on the surface of the polyhedron. Non-overlap of the source unfolding is straightforward; non-overlap of the star unfolding was proved by Aronov and O'Rourke in 1992. Our first contribution is a much simpler proof of non-overlap of the star unfolding. Both the source and star unfolding can be generalized to use a simple geodesic curve instead of a source point. The star unfolding from a geodesic curve cuts the geodesic curve and a shortest path from each vertex to the geodesic curve. Demaine and Lubiw conjectured that the star unfolding from a geodesic curve does not overlap. We prove a special case of the conjecture. Our special case includes the previously known case of unfolding from a geodesic loop. For the general case we prove that the star unfolding from a geodesic curve can be separated into at most two non-overlapping pieces.

Published
2015
Full Text
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