an:06030953
Zbl 1237.68234
??brego, B. M.; Cetina, M.; Lea??os, J.; Salazar, G.
Visibility-preserving convexifications using single-vertex moves
EN
Inf. Process. Lett. 112, No. 5, 161-163 (2012).
00296032
2012
j
68U05
computational geometry; convexification; visibility; visibility-maintaining; visibility-preserving; polygon; single-vertex moves
Summary: Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one vertex is moved at a time (that is, using single-vertex moves)? We prove the redundancy of the ``single-vertex moves'' condition: an affirmative answer to (1) implies an affirmative answer to (2). Since Aichholzer et al. recently proved (1), this settles (2).