The Picard curves are genus three curves with a non trivial automorphism, which have been intensively studied due their connection with interesting number theoretic problems. In 1989, R. Pellikaan obtained an algorithm decoding geometric codes up to b(d ? 1)=2c-errors, where d is the designed distance of the code. His algorithm is not completely eeective, but recently some authors have given an...

In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division polynomials, we show recursive formulas for ...

By simulating motion and deformation of a set of 3D characteristic curves defining surfaces, we introduce a new skin deformation technique to animate skin deformation of character models. This technique consists of two parts, representation of characteristic curves and dynamic skin deformation. The first part is to extract characteristic curves of an existing model, that is a polygon model or a...

We introduce a facial deformation system that allows artists to define and customize a facial rig and later apply the same rig to different face models. The method uses a set of landmarks that define specific facial features and deforms the rig anthropometrically. We find the correspondence of the main attributes of a source rig, transfer them to different three-demensional (3D) face models and...

Receiver Operating Characteristic (ROC) analysis is one of the most widely used methods for summarizing intrinsic properties of a diagnostic system, and is often used in evaluation and comparison of diagnostic technologies, practices or systems. These methods play an important role in public health since they enable researchers to achieve a greater insight into the properties of diagnostic test...

This paper proposes explicit formulae for the addition step and doubling step in Miller’s algorithm to compute Tate pairing on Jacobi quartic curves. We present a geometric interpretation of the group law on Jacobi quartic curves, which leads to formulae for Miller’s algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully c...

We present a new approach for the fast visualization and evaluation of large point clouds derived from different structured light 3D-scanners. By using the underlying measuring principle, we generate regular quadrilateral meshes in nearly real-time. These meshes are additionally used for a partial NURBS approximation. Based on the derived parameterized surfaces we are able to calculate and meas...

We present a novel framework for modeling hair using simplified representations. The set of representations, including individual strands, clusters and patches, are derived from Dynamic-NURBS and have the same underlying base skeleton. Our framework supports automatic simplification of dynamic simulation, collision detection and graphical rendering of hair, and offers flexibility to balance bet...

We introduce a method for approximating a given surface by a developable surface. It will be either a G surface consisting of pieces of cones or cylinders of revolution or a G NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce robust approximation of given scattered data. The presented technique can be applied in computer aided ...

We describe a new geometric representation scheme suitable for finite element mesh generation. The representation is by boundaries (i.e., brep) and relations between boundaries are stored as a directed acyclic graph. The geometry itself is based on NURBS curves and surfaces. The new geometry proposal has been been adopted by the CornellMississippi State joint ITR project. We describe why the ge...