Quad meshes can be interpreted as tensor-product spline control meshes as long as they form a regular grid, locally. We present a new option for complementing bi-3 splines by bi-4 splines near irregularities in the mesh layout, where less or more than four quadrilaterals join. These new generalized surface and IGA (isogeometric analysis) elements have as their degrees of freedom the vertices of...

A digital grayscale image can be described by intensity or pixel values. The gray levels are spread over the images as irregular or inhomogeneous fashion. A number of proposed methods for calculating the optimal thresholding value for image segmentation, but the fractal analysis is an expeditious and significant mathematical approach that distributes with irregular geometric objects. In the rec...

Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN). Compared to traditional CNN applying regular convolutional kernels like 3× 3, our approach trains irregular kernel shapes to better fit the geometric variations o...

Irregular to Completely Regular Meshing in Computer Graphics This talk will provide a quick overview of meshing structures used in computer graphics. Maximizing rendering performance is a key goal, and irregular meshes provide the greatest geometric fidelity for a given mesh complexity. Level-ofdetail representations like progressive meshes allow selective refinement of such meshes even in real...

The nofit polygon an important tool in the area of irregular shape stock cutting problems. It provides efficient handling of the geometric characteristics of the problem. The paper presents a new algorithmic procedure for deriving this tool. Abstract The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing...

In this paper I propose a real-time method for the detection of hexagonal tiles arranged in an irregular lattice. The method exploits the geometric properties of hexagons to aid detection. The recognition algorithm works by detecting objects on the boundary and peeling them away possibly exposing further internal objects. The algorithm terminates when no further objects can be detected.

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...

We establish results on convergence and smoothness of subdivision rules operating on manifoldvalued data which are based on a general dilation matrix. In particular we cover irregular combinatorics. For the regular grid case results are not restricted to isotropic dilation matrices. The nature of the results is that intrinsic subdivision rules which operate on geometric data inherit smoothness ...