اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCharacterisation of rational and NURBS developable surfaces in Computer Aided Design
207
0
0.0
(
0
)
نشر من قبل
Leonardo Fernandez-Jambrina
تاريخ النشر
2020
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions $Lambda$, $M$, $ u$. Properties of developable surfaces are revised in this framework. In particular, a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions $Lambda$, $M$, $ u$, which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative. It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant $Lambda$, $M$, $ u$ . The results are readily extended to rational spline developable surfaces.
قيم البحث
اقرأ أيضاً
In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. T
he reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are Bezier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.
In this paper we address the issue of designing developable surfaces with Bezier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumanns algorithm. We a
lso obtain the set of polynomial developable surfaces which can be constructed using general polynomial curves. The conclusions can be extended to spline surfaces as well.
This work suggests a new variational approach to the task of computer aided restoration of incomplete characters, residing in a highly noisy document. We model character strokes as the movement of a pen with a varying radius. Following this model, a
cubic spline representation is being utilized to perform gradient descent steps, while maintaining interpolation at some initial (manually sampled) points. The proposed algorithm was utilized in the process of restoring approximately 1000 ancient Hebrew characters (dating to ca. 8th-7th century BCE), some of which are presented herein and show that the algorithm yields plausible results when applied on deteriorated documents.
Computer-Aided Design (CAD) applications are used in manufacturing to model everything from coffee mugs to sports cars. These programs are complex and require years of training and experience to master. A component of all CAD models particularly diff
icult to make are the highly structured 2D sketches that lie at the heart of every 3D construction. In this work, we propose a machine learning model capable of automatically generating such sketches. Through this, we pave the way for developing intelligent tools that would help engineers create better designs with less effort. Our method is a combination of a general-purpose language modeling technique alongside an off-the-shelf data serialization protocol. We show that our approach has enough flexibility to accommodate the complexity of the domain and performs well for both unconditional synthesis and image-to-sketch translation.
Engineering sketches form the 2D basis of parametric Computer-Aided Design (CAD), the foremost modeling paradigm for manufactured objects. In this paper we tackle the problem of learning based engineering sketch generation as a first step towards syn
thesis and composition of parametric CAD models. We propose two generative models, CurveGen and TurtleGen, for engineering sketch generation. Both models generate curve primitives without the need for a sketch constraint solver and explicitly consider topology for downstream use with constraints and 3D CAD modeling operations. We find in our perceptual evaluation using human subjects that both CurveGen and TurtleGen produce more realistic engineering sketches when compared with the current state-of-the-art for engineering sketch generation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
