6 research outputs found
Flipturning polygons
A flipturn is an operation that transforms a nonconvex simple polygon into
another simple polygon, by rotating a concavity 180 degrees around the midpoint
of its bounding convex hull edge. Joss and Shannon proved in 1973 that a
sequence of flipturns eventually transforms any simple polygon into a convex
polygon. This paper describes several new results about such flipturn
sequences. We show that any orthogonal polygon is convexified after at most n-5
arbitrary flipturns, or at most 5(n-4)/6 well-chosen flipturns, improving the
previously best upper bound of (n-1)!/2. We also show that any simple polygon
can be convexified by at most n^2-4n+1 flipturns, generalizing earlier results
of Ahn et al. These bounds depend critically on how degenerate cases are
handled; we carefully explore several possibilities. We describe how to
maintain both a simple polygon and its convex hull in O(log^4 n) time per
flipturn, using a data structure of size O(n). We show that although flipturn
sequences for the same polygon can have very different lengths, the shape and
position of the final convex polygon is the same for all sequences and can be
computed in O(n log n) time. Finally, we demonstrate that finding the longest
convexifying flipturn sequence of a simple polygon is NP-hard.Comment: 26 pages, 32 figures, see also
http://www.uiuc.edu/~jeffe/pubs/flipturn.htm
Quadratic-time, linear-space algorithms for generating orthogonal polygons with a given number of vertices
Programa de Financiamento Plurianual, Fundação para a Ciéncia e TecnologiaPrograma POSIPrograma POCTI, FCTFondo Europeo de Desarrollo Regiona
Control of objects with a high degree of freedom
In this thesis, I present novel strategies for controlling objects with high degrees of
freedom for the purpose of robotic control and computer animation, including articulated
objects such as human bodies or robots and deformable objects such as ropes and
cloth. Such control is required for common daily movements such as folding arms,
tying ropes, wrapping objects and putting on clothes. Although there is demand in
computer graphics and animation for generating such scenes, little work has targeted
these problems.
The difficulty of solving such problems are due to the following two factors: (1)
The complexity of the planning algorithms: The computational costs of the methods
that are currently available increase exponentially with respect to the degrees of freedom
of the objects and therefore they cannot be applied for full human body structures,
ropes and clothes . (2) Lack of abstract descriptors for complex tasks. Models for quantitatively
describing the progress of tasks such as wrapping and knotting are absent for
animation generation.
In this work, we employ the concept of a task-centric manifold to quantitatively
describe complex tasks, and incorporate a bi-mapping scheme to bridge this manifold
and the configuration space of the controlled objects, called an object-centric manifold.
The control problem is solved by first projecting the controlled object onto the task-centric
manifold, then getting the next ideal state of the scenario by local planning,
and finally projecting the state back to the object-centric manifold to get the desirable
state of the controlled object. Using this scheme, complex movements that previously
required global path planning can be synthesised by local path planning.
Under this framework, we show the applications in various fields. An interpolation
algorithm for arbitrary postures of human character is first proposed. Second, a
control scheme is suggested in generating Furoshiki wraps with different styles. Finally,
new models and planning methods are given for quantitatively control for wrapping/
unwrapping and dressing/undressing problems