We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD(Computer Aided Geometric Design). We also present the numerical results for these appli...

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard modeling tools. In this discipline, a geometric form is specified by the relations that the components of this form must verify instead of explicitly specifying...

Frontage roads are most frequently used in rural and urban environments along freeway and full-controlled principal arterial corridors. Their primary function is to distribute and collect traffic between local streets and interchanges. They have been the primary design solution for providing access along Texas rural freeways and full-controlled principal arterials. With the growing public deman...

Case-based design (CBD) overcomes certain dficulties associated with traditional knowledge-based design systems. When novel designs are created by adapting cases, design integrity can be maintained through careful formulation of adaptation procedures. We describe a prototype design system called case adaptation by dimensionality reasoning (CADRE). Geometrical information is treated through simu...

Within traditional Islamic geometric design, there is a small but distinct subset of patterns which incorporate notions of self-similarity. Such patterns typically use exactly two overlapping levels of self-similarity, with each level comprising similar motifs at two different, related scales. Recently I have constructed a large number of fractal Islamic patterns that pursue a different notion ...

In photogrammetric applications the use of a digital panoramic camera with 360° field of view may provide an interesting alternative to conventional methods. As the image geometry does not obey a central perspective it was necessary to establish a geometric model for digital panoramic cameras. This model was tested using a camera prototype produced by KST (Kamera & System Technik). Several mech...

Stroke patterns for Purcell's three-link swimmer are optimized. We model the swimmer as a jointed chain of three slender rods moving in an inertialess flow. The swimmer is optimized for efficiency and speed. We were able to attain swimmer designs significantly more efficient than those previously suggested by authors who only consider geometric design rather than kinematic criteria. The influen...

We study the workload process of the M/G/1 queueing system. Firstly, we give the explicit criteria for the geometric rate of convergence and the geometric decay of stationary tail. And the parameters ε 0 and s 0 for the geometric rate of convergence and the geometric decay of the stationary tail are obtained, respectively. Then, we give the explicit criteria for the rate of convergence and deca...

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...