The Logarithmic Curvature Graphs of Generalised Cornu Spirals
نویسندگان
چکیده
The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [2]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature Graph (LCG) as proposed by Kanaya et al.[10]. The analysis of LCG supports the claim that GCS is indeed a generalized aesthetic curve.
منابع مشابه
The Logarithmic Curvature Graphs of Generalized Cornu Spirals
The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [1, 9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [12]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature G...
متن کاملThe generalised Cornu spiral and its application to span generation
A Cornu spiral is a plane curve having a linear curvature pro le. This paper considers plane curves having rational linear curvature pro les. These curves are de ned to be generalised Cornu spirals (GCS) and are quality curves in the sense that they are continuous and smooth, can contain one in ection at most, and have a bounded and monotonic curvature pro le. In addition, the GCS has an extra ...
متن کاملA rational cubic trigonometric approximation scheme of the generalized Cornu spirals
The [Formula: see text] and [Formula: see text]-approximation schemes are introduced to approximate the popular generalized Cornu spirals with the help of the parametric rational cubic trigonometric Bézier curves. The [Formula: see text]-approximation scheme has two free parameters whereas [Formula: see text]-approximation scheme has four free parameters. To approximate the generalized Cornu sp...
متن کاملLogarithmic Curvature and Torsion Graphs
This paper introduces logarithmic curvature and torsion graphs for analyzing planar and space curves. We present a method for drawing these graphs from any differentiable parametric curves and clarify the characteristics of these graphs. We show several examples of theses graphs drawn from planar and 3D Bézier curves. From the graphs, we can see some interesting properties of curves that cannot...
متن کاملEfficient robust approximation of the generalised Cornu spiral
A Generalised Cornu Spiral (GCS) is a planar curve defined to have a monotonic rational linear curvature profile and as such these curves are considered fair. However, their implementation in current CAD systems is not straight forward partly due to not being in the usual polynomial form. A GCS cannot be expressed exactly using a finite polynomial and so a compromise can be achieved by instead ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1304.7842 شماره
صفحات -
تاریخ انتشار 2013