5,442 research outputs found
Görbék és felületek a geometriai modellezésben = Curves and surfaces in geometric modelling
B-spline görbĂ©k/felĂĽletek pontjai által, az alakzat kĂ©t csomóértĂ©kĂ©nek szimmetrikus változtatásakor leĂrt pályagörbĂ©ket vizsgáltuk, Ă©s olyan alakmĂłdosĂtási eljárást adtunk, amivel a felĂĽlet adott pontját/paramĂ©tervonalát elĹ‘re megadott helyre mozgathatjuk a csomóértĂ©kek változtatásával. A C-BĂ©zier, C-B-spline Ă©s F-B-spline görbĂ©k pályagörbĂ©inek geometriai tulajdonságait Ărtuk le, Ă©s erre alapozva geometriai kĂ©nyszereket kielĂ©gĂtĹ‘ alakmĂłdosĂtásokat vizsgáltuk. Olyan általános leĂrási mĂłdot (linear blending) adtunk, mely egysĂ©gesen kezeli az alakparamĂ©terekkel rendelkezĹ‘ görbĂ©k szĂ©les osztályát, továbbá konkrĂ©t esetekben e paramĂ©terek geometriai hatását Ărtuk le Ă©s kĂ©nyszeres alakmĂłdosĂtásokra adtunk megoldást. A csomóértĂ©keknek az interpolálĂł görbĂ©re gyakorolt hatását vizsgáltuk, mely alapján a harmadfokĂş interpoláciĂł esetĂ©re interaktĂv alakmĂłdosĂtĂł eljárást dolgoztunk ki. Kontrollpontokkal adott görbĂ©k szingularitásainak detektálására a kontrollpontok helyzetĂ©n alapulĂł megoldást adtunk. Kontrollpont alapĂş szĂĽksĂ©ges Ă©s elĂ©gsĂ©ges feltĂ©telt adtunk arra, hogy a BĂ©zier-felĂĽlet paramĂ©tervonalai egyenesek legyenek. Olyan Monte Carlo mĂłdszert dolgoztunk ki, amely rendezetlen ponthalmaz felĂĽlettel valĂł interpolálásához nĂ©gyszöghálĂłt hoz lĂ©tre a pontfelhĹ‘ (mely elágazásokat Ă©s hurkokat is tartalmazhat) Ă©s annak topolĂłgikus gráfja ismeretĂ©ben. A csonkolt Fourier-sorok terĂ©ben olyan ciklikus bázist adtunk meg, amellyel vĂ©gtelen simaságĂş zárt görbĂ©ket Ă©s felĂĽleteket Ărhatunk le. | We studied paths of points of B-spline curves/surfaces obtained by the symmetric alteration of two knot values and provided a constrained shape modification method that is capable of moving a point/isoparametric line of the surface to a user specified position. We described the geometric properties of paths of C-BĂ©zier, C-B-spline and F-B-spline curves and on this basis we studied shape modifications subject to geometric constraints. We developed the general linear blending method that treats a wide class of curves with shape parameters in a uniform way; in special cases we described the geometric effects of shape parameters and provided constrained shape modification methods. We examined the impact of knots on the shape of interpolating curves, based on which we developed an interactive shape modification method for cubic interpolation. We proposed a control point based solution to the problem of singularity detection of curves described by control points. We provided control point based necessary and sufficient conditions for BĂ©zier surfaces to have linear isoparametric lines. We developed a Monte Carlo method to generate a quadrilateral mesh (for surface interpolation) from point clouds (with possible junctions and loops) and their topological graph. We specified a cyclic basis in the space of truncated Fourier series by means of which we can describe closed curves and surfaces with C^infinity
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ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication
Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
T-spline based unifying registration procedure for free-form surface workpieces in intelligent CMM
With the development of the modern manufacturing industry, the free-form surface is widely used in various fields, and the automatic detection of a free-form surface is an important function of future intelligent three-coordinate measuring machines (CMMs). To improve the intelligence of CMMs, a new visual system is designed based on the characteristics of CMMs. A unified model of the free-form surface is proposed based on T-splines. A discretization method of the T-spline surface formula model is proposed. Under this discretization, the position and orientation of the workpiece would be recognized by point cloud registration. A high accuracy evaluation method is proposed between the measured point cloud and the T-spline surface formula. The experimental results demonstrate that the proposed method has the potential to realize the automatic detection of different free-form surfaces and improve the intelligence of CMMs
Key Challenges and Opportunities in Hull Form Design Optimisation for Marine and Offshore Applications
New environmental regulations and volatile fuel
prices have resulted in an ever-increasing need for reduction
in carbon emission and fuel consumption. Designs of marine
and offshore vessels are more demanding with complex
operating requirements and oil and gas exploration
venturing into deeper waters and hasher environments.
Combinations of these factors have led to the need to
optimise the design of the hull for the marine and offshore
industry. The contribution of this paper is threefold. Firstly,
the paper provides a comprehensive review of the state-ofthe-
art techniques in hull form design. Specifically, it
analyses geometry modelling, shape transformation,
optimisation and performance evaluation. Strengths and
weaknesses of existing solutions are also discussed.
Secondly, key challenges of hull form optimisation specific
to the design of marine and offshore vessels are identified
and analysed. Thirdly, future trends in performing hull
form design optimisation are investigated and possible
solutions proposed. A case study on the design optimisation
of bulbous bow for passenger ferry vessel to reduce wavemaking
resistance is presented using NAPA software.
Lastly, main issues and challenges are discussed to stimulate
further ideas on future developments in this area, including
the use of parallel computing and machine intelligence
Fast generation of 3D deformable moving surfaces
Dynamic surface modeling is an important subject of geometric modeling due to their extensive applications in engineering design, entertainment and medical visualization. Many deformable objects in the real world are dynamic objects as their shapes change over time. Traditional geometric modeling methods are mainly concerned with static problems, therefore unsuitable for the representation of dynamic objects. Apart from the definition of a dynamic modeling problem, another key issue is how to solve the problem. Because of the complexity of the representations, currently the finite element method or finite difference method is usually used. Their major shortcoming is the excessive computational cost, hence not ideal for applications requiring real-time performance. We propose a representation of dynamic surface modeling with a set of fourth order dynamic partial differential equations (PDEs). To solve these dynamic PDEs accurately and efficiently, we also develop an effective resolution method. This method is further extended to achieve local deformation and produce n-sided patches. It is demonstrated that this new method is almost as fast and accurate as the analytical closed form resolution method and much more efficient and accurate than the numerical methods
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