Article
Mathematics, Applied
Leonardo Fernandez-Jambrina
Summary: This paper provides a characterization of rational developable surfaces using the blossoms of bounding curves and three rational functions Lambda, M, nu. It presents a closed algebraic formula for the regression edge of the surface in terms of these functions. All rational developable surfaces can be described as the set of surfaces constructed with constant Lambda, M, nu. The results are also applicable to rational spline developable surfaces.
JOURNAL OF COMPUTATIONAL MATHEMATICS
(2021)
Article
Computer Science, Software Engineering
Jan Groselj, Ada Sadl Praprotnik
Summary: The paper presents several possibilities for exact representation of the sphere using rational multisided Bezier patches known as S-patches. The authors derive a general method using the stereographic projection to represent a sphere section with an S-patch over a regular polygon. They then apply the method to the faces of Platonic solids inscribed into the sphere, resulting in S-patches defined over triangular, square, or pentagonal domains. This approach unifies previously known constructions based on triangular and tensor product Bezier patches.
COMPUTER AIDED GEOMETRIC DESIGN
(2022)
Article
Computer Science, Information Systems
Yongha Shin, Bong-Soo Sohn, Heewon Kye
Summary: This study proposes a method to accelerate high-quality MIP volume rendering by skipping unnecessary volume data regions and efficient GPU parallelization. By accurately approximating the maximum value of each block, it achieves faster rendering speed, maintaining high-quality MIP volume rendering at interactive speed.
MULTIMEDIA TOOLS AND APPLICATIONS
(2021)
Article
Engineering, Marine
Le Zha, Renchuan Zhu, Liang Hong, Shan Huang
Summary: This paper presents a high-efficiency potential-flow based ship hydrodynamic optimization tool for reducing calm-water resistance and improving vertical motion performance in irregular head waves. The study shows that the tool can achieve optimal ships with reduced resistance and improved vertical motion performance by altering hull forms.
Article
Engineering, Civil
Min-Geun Kim, Geun-Ho Lee, Hanmin Lee, Bonyong Koo
Summary: In this study, isogeometric analysis for geometrically exact shells considering the first-order shear deformation was investigated. The assumed natural strain method and the Bezier extraction method were employed to address locking phenomena and improve accuracy in shell analysis. Numerical examples demonstrate the effectiveness and robustness of the proposed approach.
THIN-WALLED STRUCTURES
(2022)
Article
Mathematics
Javier Sanchez-Reyes
AMERICAN MATHEMATICAL MONTHLY
(2019)
Article
Engineering, Multidisciplinary
M. A. Caminero, I. Garcia-Moreno, G. P. Rodriguez, J. M. Chacon
COMPOSITES PART B-ENGINEERING
(2019)
Article
Polymer Science
Miguel Angel Caminero, Jesus Miguel Chacon, Eustaquio Garcia-Plaza, Pedro Jose Nunez, Jose Maria Reverte, Jean Paul Becar
Article
Mathematics
Javier Sanchez-Reyes
AMERICAN MATHEMATICAL MONTHLY
(2020)
Article
Computer Science, Software Engineering
Javier Sanchez-Reyes, Jesus M. Chacon
COMPUTER AIDED GEOMETRIC DESIGN
(2020)
Article
Chemistry, Physical
Jose Maria Reverte, Miguel Angel Caminero, Jesus Miguel Chacon, Eustaquio Garcia-Plaza, Pedro Jose Nunez, Jean Paul Becar
Article
Computer Science, Software Engineering
Javier Sanchez-Reyes
Summary: This article discusses the Pythagorean-hodograph curves of Tschirnhaus type, and their connection to typical curves and sinusoidal spirals. Several relevant results are rederived in the process.
COMPUTER AIDED GEOMETRIC DESIGN
(2022)
Letter
Engineering, Multidisciplinary
Javier Sanchez-Reyes
JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS
(2021)
Article
Mathematics
Javier Sanchez-Reyes
Summary: He et al. recently derived remarkable properties of typical Bezier curves, proving that these curves have at most one curvature extremum and providing an explicit formula for the extremum parameter. Subdividing a curve at this point results in two new typical curves. Typical curves are segments of sinusoidal spirals with specific properties, which have been studied since the 18th century.
Article
Mathematics, Applied
Javier Sanchez-Reyes, Leonardo Fernandez-Jambrina
Summary: This paper investigates the relationship between the smoothness of pipes and offsets and the reach of their progenitor. The reach is a fundamental concept that determines the minimal distance between the progenitor and its cut locus. The study shows that under certain conditions, pipes and offsets can inherit the smoothness of their progenitor.
Article
Computer Science, Software Engineering
Javier Sanchez-Reyes
Summary: Research shows that in the Bezier model, the control polygon of a properly parameterized rational Bezier curve of irreducible degree is unique. However, in the rational form associated with other normalized polynomial bases, Moebius reparameterizations can change the control polygon, resulting in different polygons for the same curve segment.
COMPUTER AIDED GEOMETRIC DESIGN
(2022)
Article
Engineering, Mechanical
Jesus Miguel Chacon, Javier Sanchez-Reyes, Javier Vallejo, Pedro Jose Nunez
Summary: This paper discusses how to adhere to the NURBS standard in all phases of the additive manufacturing workflow to avoid unnecessary polygonal approximations, resulting in a considerable improvement in quality. By using commercial CAD systems, circular arcs can be directly expressed as G2/G3 G-code commands, and free-form paths can be rewritten as cubic Bezier curves for exact translation into G5 commands, streamlining the workflow and minimizing errors associated with approximations.
RAPID PROTOTYPING JOURNAL
(2022)
Article
Computer Science, Software Engineering
Javier Sanchez-Reyes
Summary: The weights of rational Bezier curves are not true independent shape factors due to their lack of invariance under Moebius reparametrization. However, there exist shape factors that are associated with each inner control point and can be computed as the ratio of weight ratios for three consecutive control points. These shape factors provide a more localized shape control and can be controlled geometrically by setting the conic rho-factor via moving the associated shoulder point.
COMPUTER-AIDED DESIGN
(2023)
Letter
Multidisciplinary Sciences
J. Sanchez-Reyes
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2020)