Merging NURBS surfaces together and extending existing ones are common problems in CAD systems. Extending existing surface is usually done by creating a new separate surface and applying some merging function – result is one continuous surface. In this paper, full description of a method of direct extending existing surfaces is introduced. The extension of the surface is recomputed during its c...

Symbolic computation of NURBS plays an important role in many areas of NURBSbased geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider incl...

Constructing a CAD model from a physical model plays a key role in some productdevelopment processes. To be presented is an “indirect” method of fitting NURBS-surfaces for rotational-freeform shapes: 1) Cloud-of-points data representing a rotational-freeform shape are transformed into an orthogonal-coordinate (sphericalor cylindrical-) system, 2) a single-valued Bspline surface is fitted to the...

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible use such NURBS geometries for numerical directly. Analyzing fluid flows, however, requires complex three-dimensional flow domains. Defining a parametrization of volumetric domains can be challenging and s...

Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin collocation formulations. Exploiting the same high-order non-uniform rational B-spline (NURBS) bases that span physical domain solution space leads to increased accuracy fast computat...

We present a parallel GPU-accelerated algorithm for computing the directed Hausdorff distance from one NURBS surface to another, within a bound. We make use of axis-aligned bounding-box hierarchies that bound the NURBS surfaces to accelerate the computations. We dynamically construct as well as traverse the bounding-box hierarchies for the NURBS surfaces using operations that are optimized for ...

Deformable objects can be used to model soft objects such as clothing, human faces and animal characters. They are important as they can improve the realism of the applications. However, most existing hardware accelerators cannot render deformable objects directly. A tessellation process is often used to convert a deformable object into polygons so that the hardware graphics accelerator may ren...

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...

The mapping method was introduced in [1] for highly accurate Isogeometric Analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned with constructions of novel geometrical mappings by which push-forwards of B-splines from the parameter space into the physical space generate singular functions that resemble the singularities. In other words, the...