The effective reuse of freeform features represented by NURBS is still an open issue. In this paper, a novel approach to the reuse of freeform features with NURBS representation is proposed. Firstly, the conditions for preserving differential properties of reused freeform features are derived, and a reuse-oriented representation of freeform features is put forward. Based on them, a reuse algori...

In this paper, a hybrid and adaptive tool-path generation approach, which is able to improve geometrical accuracy and build time of Rapid Prototyping/Manufacturing (RP/M) for complex biomedical models, is presented. Firstly, NURBS (Non-Uniform Rational B-Spline)-based curves were introduced to represent the boundary contours of sliced layers to keep the high-fidelity information of original mod...

Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C blends between these surfaces, such that interactive design of trim lines and surface tension is p...

Abstract—A novel scheme of combining non-uniform rational Bsplines (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 patches and no factitious geometric discontin...

We construct a new family of analytic models of black hole accretion disks in dynamical equilibria. Our construction is based on assuming distributions of angular momentum and entropy. For a particular choice of the distribution of angular momentum, we calculate the shapes of equipressure surfaces. The equipressure surfaces we find are similar to those in thick, slim and thin disks, and to thos...

This paper proposed a new approach for optimum path planning in 2D environments cluttered with static obstacles. The presented model consists of four steps.In the first step, the skeleton of free obstacles space is extracted. The thin lines are converted into a graph in the second step. the determination of shortest length trajectory is done in the third step. The last step is consacred to cons...

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves ...

In this paper, we study high order methods for solving the time domain Maxwell equations using spline finite elements on domains defined by NURBS. Convenient basis functions for the discrete exact sequence of spaces introduced by Buffa et al [4] are exhibited which provided the same discrete structure as for classical Whitney Finite Elements. An analysis of stability of the time scheme is also ...

In this paper, we are interested in giving bounds for exponential sums over certain curves defined over Galois rings. We first define summation subsets as the images of lifts of affine pieces of the reduced curve, and most of the work is devoted to giving bounds for the degrees of their defining functions. Then we get bounds for exponential sums, generalizing results of Kumar et al., Winnie Li ...