TY - GEN

T1 - Visibility with reflection

AU - Aronov, Boris

AU - Davis, Alan R.

AU - Dey, Tamal K.

AU - Pal, Sudebkumar P.

AU - Prasad, D. Chithra

N1 - Funding Information:
versity, Jamaica, NY 11439, USA. 3Dept. of Computer Science and En~iucering, Indian Institute of Technology, Kllaragpur, Kharagpur 721302, India. Work on this paper by S.P. Pal is partially supported by a research grant from the Jawaharlal Nehru Center, Bangalore, India.
Funding Information:
1Computer Science Department, Polyteclmic University, Brooklyn, NY 11201, LJSA. Work on this paper by Boris Aronov has been supported by NSF Grant CCR-92-1 1541. zDiv. of Col,lputer Science, Math. and Science, St. Johns ~Jni-
Publisher Copyright:
© 1995 ACM.

PY - 1995/9/1

Y1 - 1995/9/1

N2 - We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n2) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n2 log2 n) time algorithms for constructing the sets.

AB - We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n2) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n2 log2 n) time algorithms for constructing the sets.

UR - http://www.scopus.com/inward/record.url?scp=0038850747&partnerID=8YFLogxK

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U2 - 10.1145/220279.220313

DO - 10.1145/220279.220313

M3 - Conference contribution

AN - SCOPUS:0038850747

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 316

EP - 325

BT - Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995

PB - Association for Computing Machinery

T2 - 11th Annual Symposium on Computational Geometry, SCG 1995

Y2 - 5 June 1995 through 7 June 1995

ER -