2,623 research outputs found
Computing the minimum distance between a point and a NURBS curve
International audienceA new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, which leads to very few subdivision steps in the new method. Examples are shown to illustrate the efficiency and robustness of the new method
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier extraction and subdivision are performed on each boundary curve in
order to generate a high-quality planar parameterization; then a robust planar
domain partition framework is proposed to construct high-quality patch-meshing
results with few singularities from the discrete boundary formed by connecting
the end points of the resulting boundary segments. After the topology
information generation of quadrilateral decomposition, the optimal placement of
interior B\'ezier curves corresponding to the interior edges of the
quadrangulation is constructed by a global optimization method to achieve a
patch-partition with high quality. Finally, after the imposition of
C1=G1-continuity constraints on the interface of neighboring B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained local optimization
method to achieve uniform and orthogonal iso-parametric structures while
keeping the continuity conditions between patches. The efficiency and
robustness of the proposed method are demonstrated by several examples which
are compared to results obtained by the skeleton-based parameterization
approach
Computing the minimum distance between two BĂ©zier curves
International audienceA sweeping sphere clipping method is presented for computing the minimum distance between two BĂ©zier curves. The sweeping sphere is constructed by rolling a sphere with its center point along a curve. The initial radius of the sweeping sphere can be set as the minimum distance between an end point and the other curve. The nearest point on a curve must be contained in the sweeping sphere along the other curve, and all of the parts outside the sweeping sphere can be eliminated. A simple sufficient condition when the nearest point is one of the two end points of a curve is provided, which turns the curve/curve case into a point/curve case and leads to higher efficiency. Examples are shown to illustrate efficiency and robustness of the new method
An integrated design-analysis framework for three dimensional composite panels
We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the isogeometric concept recently emerged in the computational mechanics community. Using the presented approach, finite element analysis of composite panels can be performed with the only input is the geometry representation of the composite surface. In this paper, non-uniform rational B-splines (NURBS) are used to represent the panel surfaces. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework
Real-Time Jerk Limited Feedrate Profiling and Interpolation for Linear Motor Multiaxis Machines Using NURBS Toolpaths
In this article, a NURBS toolpath feedrate profile generation algorithm for a biaxial linear motor control system is presented. High achievable velocities and accelerations of linear motor machines present new computational challenges in implementing feedrate generation and toolpath interpolation algorithms in real-time controllers. The proposed algorithm is capable of online generation of the feedrate profile with axial acceleration and jerk constraints. Each stage of the feedrate profiling algorithm is described with attention being given to both performance and implementation aspects. Furthermore, an alternative to the commonly used Taylor series interpolation method is also tested to ensure minimal interpolation errors. The feedrate profiling and interpolation algorithmsâ implementation in a PC-based controller with real-time Linux kernel is described. Experimental results are presented that confirm that the algorithm is capable of limiting acceleration and jerk in the machineâs axes and it is low computation time enables real-time on-line operation in a PC-based CNC controller
The generation of triangular meshes for NURBS-enhanced FEM
This paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the soâcalled nonâuniform rational Bâspline (NURBS)âenhanced finite element method (NEFEM). The meshes generated with the proposed approach account for the computerâaided design boundary representation of the domain given by NURBS curves. The characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features. The proposed strategy allows to circumvent the timeâconsuming process of deâfeaturing complex geometric models before a finite element mesh suitable for the analysis can be produced. A generalisation of the original definition of a NEFEM element is also proposed, enabling to treat more complicated elements with an edge defined by several NURBS curves or more than one edge defined by different NURBS. Three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators. Finally, a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis
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