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The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to determine and find the standard form. In this paper, we present algorithms to determine whether a given implicit surface is a rational ruled surface. A parametrizat...

In a recent paper (Computer Aided Geometric Design 23 (3), 243–260), Yang presented a novel kind of nonlinear and geometry driven subdivision scheme for curve interpolation. The author declared that this scheme was shape preserving when all free parameters were explicitly selected by some specific rules. In this note, we demonstrate that the author (a) ignored the consistency of the definition ...

A variational formulation of a general form fourth order geometric partial differential equation is derived, and based on which a mixed finite element method is developed. Several surface modeling problems, including surface blending, hole filling and surface mesh refinement with the G continuity, are taken into account. The used geometric partial differential equation is universal, containing ...

Preface This thesis considers problems derived from industrial engineering, and treats them in a rather theoretical setting, called ªcomputational geometryº. This work has been carried out within the research group of Mark Overmars, which is centered around applied algorithms, i.e. solving problems that are inspired by practical implications. My ®rst introduction to computational geometry was v...

The purpose of this paper is to demonstrate a systems modeling and design approach based on universal geometry. Systems modeling and design can be enhanced with a structural representation of system requirements (which are often written), and system models (which are often mathematical). Written and mathematical approaches show system structure, boundary, and feedback either in words or equatio...

In the permanent magnet linear synchronous motor (PMLSM), force ripple is harmful, useless and disturbing. The force ripple is basically composed of two components: detent force and mutual force ripple. This force is influenced by the geometric parameters of the permanent magnet (PM) motors; such as width, thickness and length of the magnet poles, length and thickness of the rotor and stato...

When an artifact is designed the typical output consists of documents describing the final result of a long series of deliberations and tradeoffs by the participants of collaborative design (AKA concurrent engineering) teams. The underlying intent and logical support (i.e.the rationale) for the decisions captured therein is usually lost, or is represented at best as a scattered, difficult-to-ac...

Computer-aided geometric design (CAGD) is the design of geometrical shapes using computer technology, and is used extensively in many applications, such as the automotive, shipbuilding, and aerospace industries, architectural design, and computer animation. A popular way of modelling geometry in CAGD is to represent the outer surface, or curve, of the object as a patchwork of parametric polynom...

In the permanent magnet linear synchronous motor (PMLSM), force ripple is harmful, useless and disturbing. The force ripple is basically composed of two components: detent force and mutual force ripple. This force is influenced by the geometric parameters of the permanent magnet (PM) motors; such as width, thickness and length of the magnet poles, length and thickness of the rotor and stato...