Polygon Reconstruction from Visibility Information - CiteSeerX
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Polygon Reconstruction from Visibility Information
LILLANNE ELAINE JACKSON B.St\. University of A h V r i n . l«)S:i
A Thesis S u b m i t t e d to the; Council on G r a d u a t e Studies of t h e University of Lethbridge in Partial Fulfillment of the R e q u i r e m e n t s for t h e Degree MASTER O F SCIENCE
Reconstruction results attempt, to rebuild polygons from visibility information. R m m s t r u c t i o n of a general polygon from its visibility graph is still open a n d only known to be in P S P A C E : t h u s additional information, such as t h e ordering of t h e cdg
t i m e , t h e H a m i l t o n i a n cycle t h a t
corresponds to t h e b o u n d a r y of t h e polygon from t h e polygon's ordered visibility g r a p h . Also, it converts an unordered visibility graph a n d H a m i l t o n i a n cycle to t h e ordered visibility graph for t h a t polygon in 0(E)
time.
T h e second, and major result is an algorithm to reconstruct an orthogonal poly gon t h a t is consistent with t h e Hamiltonian cycle a n d visibility s t a b s of t h e sides of an unknown polygon. col linear sides, a n d 0(rr)
T h e algorithm uses O ( n l o g n ) t i m e , a s s u m i n g there are no t i m e otherwise.
iv
Acknowledgements
T h e r e a r e many people who have contributed substantially to this thesis.
My
appreciation goes out. to every person. My supervisor, Professor Stephen K. Wismat.h, is an excellent teacher a n d re searcher whose patience, encouragement and motivation were instrumental in com pleting this thesis. T h e friendship Steve, his family and colleagues have provided t h r o u g h o u t this educational t i m e in my life is greatly a p p r e c i a t e d . T h e M a t h and C o m p u t e r Science d e p a r t m e n t at t h e University of Lethbridge ami t h e Electronics Engineering Technology d e p a r t m e n t a t the Letlihridge C o m m u n i t y College a r e two groups of incredibly supportive; people whose positive fe
