978 research outputs found
Shape Animation with Combined Captured and Simulated Dynamics
We present a novel volumetric animation generation framework to create new
types of animations from raw 3D surface or point cloud sequence of captured
real performances. The framework considers as input time incoherent 3D
observations of a moving shape, and is thus particularly suitable for the
output of performance capture platforms. In our system, a suitable virtual
representation of the actor is built from real captures that allows seamless
combination and simulation with virtual external forces and objects, in which
the original captured actor can be reshaped, disassembled or reassembled from
user-specified virtual physics. Instead of using the dominant surface-based
geometric representation of the capture, which is less suitable for volumetric
effects, our pipeline exploits Centroidal Voronoi tessellation decompositions
as unified volumetric representation of the real captured actor, which we show
can be used seamlessly as a building block for all processing stages, from
capture and tracking to virtual physic simulation. The representation makes no
human specific assumption and can be used to capture and re-simulate the actor
with props or other moving scenery elements. We demonstrate the potential of
this pipeline for virtual reanimation of a real captured event with various
unprecedented volumetric visual effects, such as volumetric distortion,
erosion, morphing, gravity pull, or collisions
Hyperbolic tilings and formal language theory
In this paper, we try to give the appropriate class of languages to which
belong various objects associated with tessellations in the hyperbolic plane.Comment: In Proceedings MCU 2013, arXiv:1309.104
Asymptotically rigid mapping class groups and Thompson's groups
We consider Thompson's groups from the perspective of mapping class groups of
surfaces of infinite type. This point of view leads us to the braided Thompson
groups, which are extensions of Thompson's groups by infinite (spherical) braid
groups. We will outline the main features of these groups and some applications
to the quantization of Teichm\"uller spaces. The chapter provides an
introduction to the subject with an emphasis on some of the authors results.Comment: survey 77
A Census of Vertices by Generations in Regular Tessellations of the Plane
We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q \u3c 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation
Perfect domination in regular grid graphs
We show there is an uncountable number of parallel total perfect codes in the
integer lattice graph of . In contrast, there is just one
1-perfect code in and one total perfect code in
restricting to total perfect codes of rectangular grid graphs (yielding an
asymmetric, Penrose, tiling of the plane). We characterize all cycle products
with parallel total perfect codes, and the -perfect and
total perfect code partitions of and , the former
having as quotient graph the undirected Cayley graphs of with
generator set . For , generalization for 1-perfect codes is
provided in the integer lattice of and in the products of cycles,
with partition quotient graph taken as the undirected Cayley graph
of with generator set .Comment: 16 pages; 11 figures; accepted for publication in Austral. J. Combi
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