Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method

Weakly Enforced Boundary Conditions for the Nurbs-based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the...

The Trimmed Nurbs Age

Efficient Trimmed NURBS Tessellation

Interactive rendering of trimmed NURBS models is of great importance for CAD systems. For this the model needs to be transformed into a polygonal representation. This transformation can be either performed in a preprocessing step, at the cost of losing the capability to edit the surfaces, or on the fly during rendering. Since the number of frames per second is usually critical, efficient on the...

Efficient Ray Tracing of Trimmed NURBS Surfaces

The goal of this master thesis is to study, compare, and improve existing approaches for direct ray tracing trimmed NURBS surfaces. In order to be able to study the topic efficiently, a library for NURBS evaluation has been implemented. The library is supposed to be easily integrated in any ray tracing application to make it support direct ray tracing trimmed NURBS surfaces.

Eecient Rendering of Trimmed Nurbs Surfaces

We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to B ezier surfaces and NURBS trimming curves into B ezier curves. It tessellates each trimmed B ezier surface into triangles and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for uniform tessel-lation of B...