71,265 research outputs found
Implicit Blending Revisited
International audienceBlending is both the strength and the weakness of functionally based implicit surfaces (such as F-reps or softobjects). While it gives them the unique ability to smoothly merge into a single, arbitrary shape, it makes implicit modelling hard to control since implicit surfaces blend at a distance, in a way that heavily depends on the slope of the field functions that define them. This paper presents a novel, generic solution to blending of functionally-based implicit surfaces: the insight is that to be intuitive and easy to control, blends should be located where two objects overlap, while enabling other parts of the objects to come as close to each other as desired without being deformed. Our solution relies on automatically defined blending regions around the intersection curves between two objects. Outside of these volumes, a clean union of the objects is computed thanks to a new operator that guarantees the smoothness of the resulting field function; meanwhile, a smooth blend is generated inside the blending regions. Parameters can automatically be tuned in order to prevent small objects from blurring out when blended into larger ones, and to generate a progressive blend when two animated objects come in contact
Feature based volumes for implicit intersections.
The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures
Voids in cosmological simulations over cosmic time
We study evolution of voids in cosmological simulations using a new method
for tracing voids over cosmic time. The method is based on tracking watershed
basins (contiguous regions around density minima) of well developed voids at
low redshift, on a regular grid of density field. It enables us to construct a
robust and continuous mapping between voids at different redshifts, from
initial conditions to the present time. We discuss how the new approach
eliminates strong spurious effects of numerical origin when voids evolution is
traced by matching voids between successive snapshots (by analogy to halo
merger trees). We apply the new method to a cosmological simulation of a
standard LambdaCDM cosmological model and study evolution of basic properties
of typical voids (with effective radii between 6Mpc/h and 20Mpc/h at redshift
z=0) such as volumes, shapes, matter density distributions and relative
alignments. The final voids at low redshifts appear to retain a significant
part of the configuration acquired in initial conditions. Shapes of voids
evolve in a collective way which barely modifies the overall distribution of
the axial ratios. The evolution appears to have a weak impact on mutual
alignments of voids implying that the present state is in large part set up by
the primordial density field. We present evolution of dark matter density
profiles computed on iso-density surfaces which comply with the actual shapes
of voids. Unlike spherical density profiles, this approach enables us to
demonstrate development of theoretically predicted bucket-like shape of the
final density profiles indicating a wide flat core and a sharp transition to
high-density void walls.Comment: 13 pages, 13 figures; accepted for publication in MNRA
A prescription for probabilities in eternal inflation
Some of the parameters we call ``constants of Nature'' may in fact be
variables related to the local values of some dynamical fields. During
inflation, these variables are randomized by quantum fluctuations. In cases
when the variable in question (call it ) takes values in a continuous
range, all thermalized regions in the universe are statistically equivalent,
and a gauge invariant procedure for calculating the probability distribution
for is known. This is the so-called ``spherical cutoff method''. In
order to find the probability distribution for it suffices to consider a
large spherical patch in a single thermalized region. Here, we generalize this
method to the case when the range of is discontinuous and there are
several different types of thermalized region. We first formulate a set of
requirements that any such generalization should satisfy, and then introduce a
prescription that meets all the requirements. We finally apply this
prescription to calculate the relative probability for different bubble
universes in the open inflation scenario.Comment: 15 pages, 5 figure
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