U-splines: Splines over unstructured meshes Thomas, Derek C.; Engvall, Luke; Schmidt, Steven K. ...
Computer methods in applied mechanics and engineering,
11/2022, Volume:
401
Journal Article
Peer reviewed
Open access
U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a ...piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and quadrilateral cells in the same mesh) and T-junctions are also supported, although the continuity of interfaces with triangle and tetrahedral cells is limited in the present work. The U-spline algorithm introduces a new technique for using local null space solutions to construct basis functions for the global spline null space problem. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. A set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.
Dupin cyclides are classical algebraic surfaces of low degree. Recently, they have gained popularity in computer-aided geometric design (CAGD) and architecture owing to the fact that they contain ...many circles. We derive algebraic conditions that fully characterize the Dupin cyclides passing through a fixed circle. The results are applied to the basic problem in CAGD of the blending of Dupin cyclides along circles.
This introductory paper provides an overview of a selection of contributions presented at the 2nd International Conference on Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and ...Refinability in ITaly (SMART2017 - Gaeta, September 17-21, 2017). The SMART2017 special issue is also an opportunity to honor the memory of Laura Gori, who was one of the proposers of this conference series.
A cubic trigonometric Bézier curve analogous to the cubic Bézier curve, with two shape parameters, is presented in this work. The shape of the curve can be adjusted by altering the values of shape ...parameters while the control polygon is kept unchanged. With the shape parameters, the cubic trigonometric Bézier curves can be made close to the cubic Bézier curves or closer to the given control polygon than the cubic Bézier curves. The ellipses can be represented exactly using cubic trigonometric Bézier curves.
Additive manufacturing is a vanguard technology that is currently being used in several fields in medicine. This study aims to evaluate the viability in clinical practice of a patient-specific 3D ...model that helps to improve the strategies of the doctor-patient assistance. Data obtained from a corneal topographer were used to make a virtual 3D model by using CAD software, to later print this model by FDM and get an exact replica of each patient’s cornea in consultation. Used CAD and printing software were open-source, and the printing material was biodegradable and its cost was low. Clinic users gave their feedback by means of a survey about their feelings when perceiving with their senses their own printed cornea. There was 82 surveyed, 73.8% (9.74; SD: 0.45) of them considered that the model had helped them a lot to understand their disease, expressing 100% of them their intention of taking home the printed model. The majority highlighted that this new concept improves both quality and clinical service in consultation. Custom-made individualized printed models allow a new patient-oriented perspective that may improve the communication strategy from the ophthalmologist to the patient, easing patient’s understanding of their asymmetric disease and its later treatment.
Plane geometry drawing tutorial Gutierrez de Rave, Eduardo; Jimenez-Hornero, Francisco J; Ariza-Villaverde, Ana B
Dyna (Medellín, Colombia),
01/2014, Volume:
81, Issue:
188
Journal Article
Peer reviewed
Open access
A tutorial has been developed with the aim of making geometry drawing teaching easier. It arises as a helpful tool for lecturers and engineering undergraduate students, with the objective of giving ...support to theoretical and practical lessons in plane geometry drawing. This easy-to-use tutorial provides users with interactivity, practical videos, self-evaluation, fundamental lessons, and "step by step" teaching due to the different levels of conceptual complexity included in its contents.
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