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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
Intersection of three-dimensional geometric surfaces
Calculating the line of intersection between two three-dimensional objects and using the information to generate a third object is a key element in a geometry development system. Techniques are presented for the generation of three-dimensional objects, the calculation of a line of intersection between two objects, and the construction of a resultant third object. The objects are closed surfaces consisting of adjacent bicubic parametric patches using Bezier basis functions. The intersection determination involves subdividing the patches that make up the objects until they are approximately planar and then calculating the intersection between planes. The resulting straight-line segments are connected to form the curve of intersection. The polygons in the neighborhood of the intersection are reconstructed and put back into the Bezier representation. A third object can be generated using various combinations of the original two. Several examples are presented. Special cases and problems were encountered, and the method for handling them is discussed. The special cases and problems included intersection of patch edges, gaps between adjacent patches because of unequal subdivision, holes, or islands within patches, and computer round-off error
Active and passive component embedding into low-cost plastic substrates aimed at smart system applications
The technology development for a low-cost, roll-to-roll compatible chip embedding process is described in this paper. Target applications are intelligent labels and disposable sensor patches. Two generations of the technology are depicted. In the first version of the embedding technology, the chips are embedded in an adhesive layer between a copper foil and a PET film. While this results in a very thin (< 200 Āµm) and flexible system, the single-layer routing and the incompatibility with passive components restricts the application of this first generation. The double-sided circuitry embedding technology is an extension of the single-sided, foil-based chip embedding, where the PET film is replaced by a second metal foil. To obtain sufficient mechanical strength and to further reduce cost, the adhesive film is replaced by a substrate material which is compatible with the chip embedding concept. Both versions of the foil-based embedding technology are very versatile, as they are compatible with a broad range of polymer materials, for which the specifications can be tuned to the final application
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
C2 popunjavanje praznina pomoÄu konveksne kombinacije ploha pod rubnim ograniÄenjima
Two surface generation methods are presented, one for connecting two surfaces with C2 continuity while matching also two prescribed border lines on the free sides of the gap, and one for G1 filling a three-sided hole in a special case. The surfaces are generated as convex combination of surface and curve constituents with an appropriate correction function, and are represented in parametric form.Dane su dvije metode za izvoÄenje ploha. Jedna za povezivanje dviju ploha sa C2 neprekinutoÅ”Äu koja odgovara i dvjema graniÄnim linijama, a druga za G1 popunjavanje posebnog sluÄaja trostrane rupe. Plohe se izvode kao konveksna kombinacija ploÅ”nih i krivuljnih sastavnih dijelova sa odgovarajuÄom korektivnom funkcijom, a dane su u parametarskom obliku
A unified approach to blending of constant and varying parametric surfaces with curvature continuity
In this paper, we develop a new approach to blending of
constant and varying parametric surfaces with curvature
continuity. We propose a new mathematical model consisting of a
vector-valued sixth-order partial differential equation (PDE) and
time-dependent blending boundary constraints, and develop an
approximate analytical solution of the mathematical model. The
good accuracy and high computational efficiency are
demonstrated by comparing the new approximate analytical
solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on
the continuity at trimlines, and apply the new approximate
analytical solution in blending of constant and varying parametric
surfaces with curvature continuit
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