THE RIGHT PLACE OF CAD-COURSES IN ENGINEERING EDUCATION

An educational conception of teaching CAD for beginners is presented based upon the geometric backgrounds of CAD. Teaching of geometric modelling is proposed as an extension of the fundamental geometry courses

O zakrivljenostima na trokutnim mrežama

A face-based curvature estimation on triangle meshes is presented in this paper. A flexible disk is laid on the mesh around a given triangle. Such a bent disk is used as a geodesic neighborhood of the face for approximating normal and principal curvatures. The radius of the disk is free input data in the algorithm. Its influence on the curvature values and the stability of estimated principal directions are investigated in the examples.U članku je prikazana procjena zakrivljenosti na trokutnim mrežama, bazirana na stranicama. Gipki disk položen je na mrežu oko danog trokuta. Takav prilagodljiv disk koristi se kao geodetska okolina stranice za aproksimaciju normalnih i glavnih zakrivljenosti. Polumjer diska je nezavisni ulazni podatak u algoritmu. U primjerima se istražuje njegov utjecaj na vrijednosti zakrivljenosti i na stabilnost procijenjenih glavnih smjerova

Filling triangular holes by convex combination of surfaces

A surface generation method is presented based on convex combination of surfaces with rational weight functions. The three constituents and the resulting surface are defined over the same triangular domain. The constructed surface matches each component along one of its boundary curves with C0 or C1 continuity depending on the weight functions in the combination. The method can be applied in surface modelling for filling triangular holes

FLEXIBLE METHODS OF SURFACE DESIGN WITH FASTSURF

This paper illustrates the powerful design methods of FastSURF, the surface modelling system of CADKEY. It contains several surface definitions and offers a number of highly developed methods of constructions and manipulations on surfaces. Solutions for fitting and trimming problems arising at the construction of composed surfaces are shown on three practical models

PARABOLIC BLENDING SURFACES ALONG POLYHEDRON EDGES

In this paper parabolic blending surfaces are defined along a chain of polyhedron edges. The profile curve of each sweep surface generated for a given edge is a conic section, and every point of it moves on a conic section around a vertex. According to this, the patches at the corners are given in rational biquadratic form and they join to the cylindrical surfaces replacing the edges with 1st order continuity

Order bound for the realization of a combination of positive filters

In a problem on the realization of digital ¯lters, initiated by Gersho and Gopinath [8], we extend and complete a remarkable result of Benvenuti, Farina and Anderson [4] on decomposing the transfer function t(z) of an arbitrary linear, asymptotically stable, discrete, time-invariant SISO system as a di®erence t(z) = t1(z) ¡ t2(z) of two positive, asymptotically stable linear systems. We give an easy-to-compute algorithm to handle the general problem, in particular, also the case of transfer functions t(z) with multiple poles, which was left open in [4]. One of the appearing positive, asymptotically stable systems is always 1-dimensional, while the other has dimension depending on the order and, in the case of nonreal poles, also on the location of the poles of t(z). The appearing dimension is seen to be minimal in some cases and it can always be calculated before carrying out the realization

B-splajn dijelovi koji pristaju na plohe i triangularne mreže

In this paper a technique for the construction of quartic polynomial B-spline patches fitting on analytical surfaces and triangle meshes is presented.The input data are curvature values and principal directions at a given surface point which can be computed directly, if the surface is represented by a vector function. In the case of discrete surface representation, i.e. on a triangle mesh the required input data are computed from a circular neighborhood of a specified triangle face. Such a surface patch may replace a well defined region of the mesh, and can be used e.g. in re-triangulation, mesh-simplification and rendering algorithms.U ovom se radu prikazuje metoda za konstrukciju kvartnog polinoma B-splajn dijela podesnog za analitičke plohe i mreže trokuta. Ulazni podaci su vrijednosti zakrivljenosti i glavni smjerovi u danoj točki plohe, koji se mogu izravno računati za plohu zadanu vektorskom funkcijom. Za slučaj diskretne reprezentacije plohe, tj. za triangularnu mrežu, odgovarajući ulazni podaci računaju se iz kružne okoline određ-enog trokuta mreže. Takvi dijelovi mogu zamijeniti dobro definirano područje mreže, i mogu se upotrijebiti npr. u retriangulaciji, simplifikaciji mreže i renderiranju

Coonsovo povezivanje klase C1 trokutnih dijelova

A Gordon-Coons-type surface construction starts from three differentiable triangular surface patches, which are defined on the same triangular parameter domain. If one boundary curve of each fits a curvilinear triangle, then the defined surface interpolates to these curves. The connection between the resulting surface and the constituents is C1 continuous along the common boundary curves with the exception of the corner points. This surface definition is an extension of the Gordon--Coons definition of a triangular surface patch constructed from three boundary curves.Gordon-Coonsova konstrukcija plohe kreće od tri diferencijabilna trokutna plošna dijela koji su definirani na istom trokutnom parametarskom području. Ako po jedna rubna krivulja svakog od njih odgovara krivuljnom trokutu, tada definirana ploha interpolira te krivulje. Veza između dobivene plohe i sastavnih dijelova je klase C1 duž zajedničkih rubnih krivulja, s izuzetkom vrhova. Ova definicija plohe je proširenje Gordon-Coonsove definicije trokutnog plošnog dijela konstruiranog iz tri granične točke