A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel. This paper also differs from prior work in that the details of an efficient implementation are fleshed out. Throughout, emphasis is placed on practical methods suitable to implementation in general ray trac...

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profilewith desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processeswhichmake generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ah...

We propose a constructive solution to the problem of finding a cubic parametric curve in a plane if the tangent vectors (derivatives with respect to the parameter) and signed curvatures are given at its end-points but the end-points themselves are unknown. We also show how these curves can be applied to construct blending curves subject to curvature, arc length, inflection and area constraints.

A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order e...

Scalar multiplication on Koblitz curves can be very efficient due to the elimination of point doublings. Modular reduction of scalars is commonly performed to reduce the length of expansions, and τ -adic NonAdjacent Form (NAF) can be used to reduce the density. However, such modular reduction can be costly. An alternative to this approach is to use a random τ -adic NAF, but some cryptosystems (...

Horocyclic surfaces are surfaces in hyperbolic 3-space that are foliated by horocycles. We construct horocyclic surfaces associated with spacelike curves in the lightcone and investigate their geometric properties. In particular, we classify their singularities using invariants of corresponding spacelike curves.

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.

Gernot Beer, Benjamin Marussig, Jürgen Zechner , Christian Dünser and Thomas-Peter Fries 1 Emeritus professor , TU Graz, Lessingstrasse 25, Graz, Austria and conjoint professor Centre for Geotechnical and Materials Modeling, University of Newcastle, Callaghan, Australia, [email protected] 2 PhD Student, TU Graz , Lessingstrasse 25, Graz, Austria [email protected] 3 Postdoc, TU Graz , Lessi...

ROC curves and cost curves are two popular ways of visualising classifier performance, finding appropriate thresholds according to the operating condition, and deriving useful aggregated measures such as the area under the ROC curve (AUC) or the area under the optimal cost curve. In this note we present some new findings and connections between ROC space and cost space, by using the expected lo...

A detailed algebraic-geometric background is presented for the tropical approach to enumeration of singular curves on toric surfaces, which consists of reducing the enumeration of algebraic curves to that of non-Archimedean amoebas, the images of algebraic curves by a real-valued non-Archimedean valuation. This idea was proposed by Kontsevich and recently realized by Mikhalkin, who enumerated t...