Crash frequency analysis is a crucial tool to investigate traffic safety problems. With the objective of revealing hazardous factors which would affect crash occurrence, crash frequency analysis has been undertaken at the macroscopic and microscopic levels. At the macroscopic level, crashes from a spatial aggregation (such as traffic analysis zone or county) are considered to quantify the impac...

We outline a procedure for implementing a virtual CNC lathe prototype using software for creating virtual environments. The prototype constructed focus on the lathe’s interlocking system (its functionality) and on its geometric model (its physical design). This project allowed us to identify the possibilities and limitations of applying current Virtual Reality technology for virtual prototyping...

The subject of geometric modelling is a blend of different types of geometry, some mathematical modelling, some numerical analysis, and discipline specific applications. In these course notes, we will concentrate of the subdiscipline of geometric modelling known as computeraided geometric design, which was formed from the mathematical structures and methods used in CAD/CAM systems and subsequen...

We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based on geometric modeling ideas from Computer Aided Geometric Design (CAGD). The unstable manifold of a hyperbolic fixed point is modeled by a piecewise Bézier interpolant (a Catmull–Rom spline) and properties of such curves are used to define a rule for adaptively...

Keywords: Arbitrary order derivative Derivative formula Rational Bézier curve a b s t r a c t In this paper, we develop the exact arbitrary order derivative formula of a rational Bézier curve at its corner. Some examples are presented to demonstrate the computation of the exact derivatives. Derivative formula of a parametric curve has important applications in geometric design and applied mathe...

A method for fast evaluation of spherical polynomials (band-limited functions) at many scattered points on the unit 2-d sphere is presented. The method relies on the sub-exponential localization of the father needlet kernels and their compatibility with spherical harmonics. It is fast, local, memory efficient, numerically stable and with guaranteed (prescribed) accuracy. The speed is independen...

We discuss using projected manifolds in geometric design and processing. Curves and surfaces are defined in n-space as algebraic sets of the appropriate dimensionality, and their projection into a three-dimensional subspace is considered. In this approach, the additional variables serve to express simply geometric constraints, and so complex surfaces such as offsets, equi-distance surfaces, rou...

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