Energy minimization has been widely used for constructing curve and surface in the fields such as computer-aided geometric design, computer graphics. However, our testing examples show that energy minimization does not optimize the shape of the curve sometimes.This paper studies the relationship between minimizing strain energy and curve shapes, the study is carried out by constructing a cubic Hermite curve with satisfactory shape. The cubic Hermite curve interpolates the positions and tangent vectors of two given endpoints. Computer simulation technique has become one of the methods of scientific discovery, the study process is carried out by numerical computation and computer simulation technique. Our result shows that:(1) cubic Hermite curves cannot be constructed by solely minimizing the strain energy;(2)by adoption of a local minimum value of the strain energy, the shapes of cubic Hermite curves could be determined for about 60 percent of all cases, some of which have unsatisfactory shapes,however. Based on strain energy model and analysis, a new model is presented for constructing cubic Hermite curves with satisfactory shapes, which is a modification of strain energy model.The new model uses an explicit formula to compute the magnitudes of the two tangent vectors,and has the properties:(1) it is easy to compute;(2) it makes the cubic Hermite curves have satisfactory shapes while holding the good property of minimizing strain energy for some cases in curve construction. The comparison of the new model with the minimum strain energy model is included.
LI Xue-meiZHANG Yong-xiaMA LongZHOU Yuan-fengZHANG Cai-ming
It is challenging to consistently smooth natural images, yet smoothing results determine the quality of a broad range of applications in computer vision. To achieve consistent smoothing, we propose a novel optimization model making use of the redundancy of natural images, by defining a nonlocal concentration regularization term on the gradient. This nonlocal constraint is carefully combined with a gradientsparsity constraint, allowing details throughout the whole image to be removed automatically in a datadriven manner. As variations in gradient between similar patches can be suppressed effectively, the new model has excellent edge preserving, detail removal,and visual consistency properties. Comparisons with state-of-the-art smoothing methods demonstrate the effectiveness of the new method. Several applications,including edge manipulation, image abstraction,detail magnification, and image resizing, show the applicability of the new method.
In this paper we present a novel image decomposition method via credible data fitting with local total variation filter. The oscillation rate is used to measure the image complexity and characteristics. The filter parameter can be determined by a fitting curve which is reconstructed by oscillation rate. In addition, the approximate Gaussian algorithm and integral image are used to reduce the algorithm computation and the sensitivity of the filter window selection. Experiments show the new method is better than the existing methods.
Point-based surface has been widely used in computer graphics for modeling,animation,visualization,simulation of liquid and so on.Furthermore,particle-based approach can distribute the surface sampling points and control its parameters according to the needs of the application.In this paper,we examine several kinds of algorithms presented over the last decades,with the main focus on particle sampling technologies for implicit surface.Therefore,we classify various algorithms into categories,describe main ideas behind each categories,and compare the advantages and shortcomings of the algorithms in each category.
In CAGD and CG,energy model is often used to control the curves and surfaces shape.In curve/surface modeling,we can get fair curve/surface by minimizing the energy of curve/surface.However,our research indicates that in some cases we can't get fair curves/surface using the current energy model.So an improved energy model is presented in this paper.Examples are also included to show that fair curves can be obtained using the improved energy model.
