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In this work, a simple geometric method to characterize drop trajectories on parametric surfaces is presented. It is assumed that: (1) the drops are subjected to a given force and (2) they always remain on the surface. The method arises in a natural way from the geometry of the problem, leading to a system of first-order ODEs with some initial cond...
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Recently, the NURBS technique has been widely used in the 3D design software for ships. However, in most research, the NURBS technique is only applied to the mathematical representation of hull curves and surfaces, and the parametric deformation of hull surfaces based on geometric feature parameters is less understood. The aims of this paper are to...
A novel scheme of combining non-uniform rational B- splines (NURBS) model with higher-order moment method (HOMM) is presented. The mesh precision of conforming to practical object is a major factor for HOMM to yield accurate results. In the present paper, NURBS technique is employed to model complex objects accurately with large curved Bezier patch...
A high statistics measurement of the reaction π-p →
π0n has been performed at the Serpukhov accelerator for
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set-up with its associated 648-channel hodoscope spectrometer for
γ-ray detection. More than 3 million charge-exchange events have
been recorded in total. It is found that the...
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This expository article is devoted to some results about non-trivial asymptotical estimates of mean value points in analytical and geometrical theorems. In particular, we provide detailed proofs of the first and the second Ionin’s conjectures, respectively concerning with the first mean value theorem for integrals and the Taylor formula with the La...
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This paper presents an innovative curve reparameterization method for kinematically smoothing trajectories based on jerk minimization. In this research, not only the trajectory is expressed in terms of a parametric NURBS curve, but also the curve parameter is related to the execution time by means of a NURBS reparameterization function. Meanwhile,...
Citations
... Therefore, building the approximating model with a Hermite surface can be simplified to building a set of Hermite surface triangles based on the originally used triangle mesh. The expression of the third-order Hermite surface triangles [14] can be defined as shown in Equation (1): S(u, v) = C 00 + C 10 u + C 01 v + C 20 u 2 + C 11 uv + C 02 v 2 +C 21 u 2 v + C 12 uv 2 + C 30 ...
... A trend calculation method is adopted to judge whether the curved triangle intersects with the slicing plane, as shown in Figure 2b. This method uses the water droplets model [30] and transitions the problem into the problem of calculating the minimum distance between the curved triangle and the slicing plane. As shown in Figure 4, subject to the action of force D , one point P above T carries out a slight motion on the tangent plane Π . ...
... The table of the preliminary result of the thickness of interval j could be written as shown in Equation (30). ...
This paper presents an adaptive slicing method for Hermite non-planar tessellated surfaces models to improve the geometric accuracy of Rapid Prototyping (RP). Based on the bending characteristics of Hermite curved triangles, a slicing method for a complete Hermite surface model, including the grouping, the construction of the topological relationships, and the calculation of the intersection contours, was employed. The adaptive layering method considering the normal vector at the vertexes of the Hermite curved triangles was employed to grain the variable thickness of all layers of the Hermite surface model. The classical Stanford bunny model illustrates the significant improvement in the accuracy of the proposed method compared to the traditional method.
... A further objection to such an approach lies in the fact that the water droplets can hardly be considered as rigid bodies. A recent similar approach [43] addressed the same problem by using a differential geometry analysis leading to a system of ordinary differential equations which are integrated by using an adaptive fourth-fifth order Runge–Kutta method. The method is very general and can be applied to any differentiable parametric surface . ...
A key topic in computer graphics is the realistic representation of natural phenomena. Among the natural objects, one of the most interesting (and most difficult to deal with) is water. Its inherent complexity, far beyond that of most artificial objects, represents an irresistible challenge for the computer graphics world. Thus, during the last two decades we have witnessed an increasing number of papers addressing this problem from several points of view. However, the computer graphics community still lacks a survey classifying the vast literature on this topic, which is certainly unorganized and dispersed and hence, difficult to follow. This paper aims to fill this gap by offering a historical survey on the most relevant computer graphics techniques developed during the 1980s and 1990s for realistic modeling, rendering and animation of water.
... Otra aplicación del método puede ser la identificación de los puntos de contacto entre la superficie y el plano tangente con un vector normal de dirección dada. 6 Porúltimo, este método puede ser también aplicado para la determinación de las curvas geodésicas que parten desde un punto sobre una superficie, escogido como referencia por su interés para la interrogación. Las geodésicas se definen como las curvas sobre una superficie cuya curvatura geodésica se anula idénticamente. ...
En este trabajo se describen algunos métodos de interrogación de superficies utilizados en la industria del automóvil. Dichos métodos se aplican al caso de superficies NURBS, las superficies más habituales en esta industria. Para ello, se introducen las fórmulas más importantes de manejo de estas superficies y sus derivadas. Los métodos descritos han sido aplicados por los autores para evaluar la “calidad” de diferentes piezas de la carrocería del automóvil.
Generating parallel curves on parametric surfaces is an important issue in many industrial settings. Given an initial curve (called the base curve or generator) on a parametric surface, the goal is to obtain curves on the surface that are parallel to the generator. By parallel curves we mean curves that are at a given distance from the generator, where distance is measured point-wise along certain characteristic curves (on the surface) orthogonal to the generator. Except for a few particular cases, computing these parallel curves is a very difficult and challenging problem. In fact, only partial, incomplete solutions have been reported so far in the literature. In this paper we introduce a simple yet efficient method to fill this gap. In clear contrast with other existing techniques, the most important feature of our method is its generality: it can be successfully applied to any differentiable parametric surface and to any kind of characteristic curves on surfaces. To evaluate our proposal, some illustrative examples (not addressed with previous methods) for the cases of section, vector-field, and geodesic parallels are discussed. Our experimental results show the excellent performance of the method even for the complex case of NURBS surfaces.
This paper presents a method for simulating the motion of water drops on a surface in real time. We describe the dynamics of a drop moving on the surface, and then we present our simulation model. We use a geometry-based representation of a drop. Each drop is modeled by a deformable 3D mesh. This geometrical representation allows drops to be on the surface or in the air. We also propose a simple method to handle drop merging and separation. For the rendering, we simulate reflection and refraction. The drop trace is also taken into account. Our method is fast and robust and yields realistic results when applied to treat condensation on a surface or human sweating in real time. Copyright © 2012 John Wiley & Sons, Ltd.
Simulating fluid flows for visualization purposes is known to be one of the most challenging fields of the computer graphics
domain. While rendering vast liquid areas has been widely addressed this last decade, few papers have tackled the problematic
of on-surface flows, even though real-time applications such as drive simulators or video games could greatly benefit from
such methods. We present a novel empirical method for the animation of liquid droplets lying on a flat surface, the core of
our technique being a simulation operating on a 2D grid which is implementable on GPU. The wetted surface can freely be oriented
in space and is not limited to translucent materials, the liquid flow being governed by external forces, the viscosity parameter
and the presence of obstacles. Furthermore, we show how to simply incorporate in our simulation scheme two enriching visual
effects, namely absorption and ink transport. Rendering can be achieved from an arbitrary view point using a GPU image based
raycasting approach and takes into account the refraction and reflection of light. Even though our method doesn’t benefit
from the literature of fluid mechanics, we show that convincing animations in terms of realism can be achieved in real-time.
In this paper, we focus on the parametric-implicit surface intersection problem. In our approach, this problem is formulated
in terms of an initial value problem of first-order ordinary differential equations (ODEs). To this end, we take advantage
of the orthogonality at any point on the intersection curve between the tangent vector to that curve and the normal vector
to the implicit surface. This yields an initial value system of ODEs that is numerically integrated through an adaptive Runge-Kutta
method. In order to determine the initial value for this system, a simple procedure based on the scalar and vector fields
associated with the function defining the implicit surface and its gradient is described. Such a procedure yields a starting
point on the nearest branch of the intersection curve. The performance of the presented method is analyzed by means of some
illustrative examples.
