This paper presents a method for isogeometric analysis using rational Triangular Bézier Splines (rTBS) where optimal convergence rates are achieved. In this method, both the geometry and the physical field are represented by bivariate splines in Bernstein Bézier form over the triangulation of a domain. From a given physical domain bounded by NURBS curves, a parametric domain and its triangulati...

Probe radius compensation is necessary in metrology applications that employ contact probes, but it can be a signi® cant source of systematic measurement errors when dealing with freeform part geometry. The paper presents implementation and performance analysis of a proposed new compensation technique based on the nominal computer aided design (CAD) model, which is assumed to be de® ned using n...

In this paper, we introduce a new type of splines—polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local suppor...

A novel and effective formulation that combines the eXtended IsoGeometric Approach (XIGA) and Higher-order Shear Deformation Theory (HSDT) is proposed to study the free vibration of cracked Functionally Graded Material (FGM) plates. Herein, the general HSDT model with five unknown variables per node is applied for calculating the stiffness matrix without needing Shear Correction Factor (SCF). I...

Trimmed NURBS are the standard surface representation used in CAD/CAM systems and accurate visualization of trimmed NURBS models at interactive frame rates is of great interest for industry. To support modification and/or animation of such surfaces, a GPU-based trimming and tessellation algorithm has been developed recently. First, the NURBS is approximated with a bi-cubic hierarchy of Bézier p...

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data). We use...

One of the most difficult problems in reverse engineering is the processing of unstructured data. NURBS (Non-uniform Rational B-splines) surfaces are a popular tool for surface modeling. However, they cannot be directly created from unstructured data, as they are defined on a four-sided domain with explicit parametric directions. Therefore, in reverse engineering, it is necessary to process uns...

We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its graph. We take advantage of the projectiv...