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Smooth parametric surfaces and n-sided patches
The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed
A survey of partial differential equations in geometric design
YesComputer aided geometric design is an area
where the improvement of surface generation techniques
is an everlasting demand since faster and more accurate
geometric models are required. Traditional methods
for generating surfaces were initially mainly based
upon interpolation algorithms. Recently, partial differential
equations (PDE) were introduced as a valuable
tool for geometric modelling since they offer a number
of features from which these areas can benefit. This work
summarises the uses given to PDE surfaces as a surface
generation technique togethe
A parametric study of aliasing error for a narrow field of view scanning radiometer
Starting from the general measurement equation, it is shown that a NFOV scanner can be approximated by a spatially invariant system whose point spread function depends on the detector shape and angular characteristics and electrical filter transfer function for given patches at the top of the atmosphere. The radiometer is modeled by a detector, electrical filter, analog to digital converter followed by a reconstruction filter. The errors introduced by aliasing and blurring into a reconstruction of the input radiant exitance are modeled and analyzed for various detector shapes, sampling intervals, electrical filters and scan types. Quantitative results on the errors introduced are presented showing the various tradeoffs between design parameters. The results indicate that proper selection of detector shape coupled with electrical filter can reduce aliasing errors significantly
Multisided B-spline Patches Over Extraordinary Regions
We propose a generalised B-spline construction that extends uniform bi-degree B-splines to multisided regions spanned over extraordinary regions in quad-dominant meshes. We show how the structure of the existing cubic multisided B-spline patch can be generalised to work with B-spline basis functions of arbitrary degree and can be spanned over extraordinary vertices as well as extraordinary faces of quad-dominant meshes. The resulting multisided surfaces are Cd-1 continuous internally and connect with Gd-1 continuity to adjacent regular and other multisided B-splines patches. In addition, we design several specialised functions that increase the visual quality of the patches, in both the extraordinary vertex and face settings.<br/
Formal Verification of Probabilistic SystemC Models with Statistical Model Checking
Transaction-level modeling with SystemC has been very successful in
describing the behavior of embedded systems by providing high-level executable
models, in which many of them have inherent probabilistic behaviors, e.g.,
random data and unreliable components. It thus is crucial to have both
quantitative and qualitative analysis of the probabilities of system
properties. Such analysis can be conducted by constructing a formal model of
the system under verification and using Probabilistic Model Checking (PMC).
However, this method is infeasible for large systems, due to the state space
explosion. In this article, we demonstrate the successful use of Statistical
Model Checking (SMC) to carry out such analysis directly from large SystemC
models and allow designers to express a wide range of useful properties. The
first contribution of this work is a framework to verify properties expressed
in Bounded Linear Temporal Logic (BLTL) for SystemC models with both timed and
probabilistic characteristics. Second, the framework allows users to expose a
rich set of user-code primitives as atomic propositions in BLTL. Moreover,
users can define their own fine-grained time resolution rather than the
boundary of clock cycles in the SystemC simulation. The third contribution is
an implementation of a statistical model checker. It contains an automatic
monitor generation for producing execution traces of the
model-under-verification (MUV), the mechanism for automatically instrumenting
the MUV, and the interaction with statistical model checking algorithms.Comment: Journal of Software: Evolution and Process. Wiley, 2017. arXiv admin
note: substantial text overlap with arXiv:1507.0818
Gn blending multiple surfaces in polar coordinates
International audienceThis paper proposes a method of Gn blending multiple parametric surfaces in polar coordinates. It models the geometric continuity conditions of parametric surfaces in polar coordinates and presents a mechanism of converting a Cartesian parametric surface into its polar coordinate form. The basic idea is first to reparameterize the parametric blendees into the form of polar coordinates. Then they are blended simultaneously by a basis function in the complex domain. To extend its compatibility, we also propose a method of converting polar coordinate blending surface into N NURBS patches. One application of this technique is to fill N-sided holes. Examples are presented to show its feasibility and practicability
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