Designing fair curves using monotone curvature pieces

Designing aesthetically appealing models is vital for the marketing success of industrial products. In this paper, we propose quasi-Aesthetic Curves that can be used in CAD systems for aesthetic shape design. Quasi-Aesthetic Curves represented in rational cubic Bézier Forms are curves whose logarithmic curvature histograms (LCHs) become nearly straight lines. The monotonicity of curvature of quasi-Aesthetic Curves is checked by the proposed method. We generate quasiAesthetic Curves by approximating the Aesthetic Curves whose LCHs are strictly represented by straight lines. We show that one Aesthetic Curve segment whose change of tangential angle is less than 90 deg. can be replaced by one quasi-Aesthetic Curve segment guaranteeing the monotonicity of the curvature in most of practical situations.

Section: Related Workmentioning

confidence: 98%

“…We briefly describe our method for checking the monotonicity of the curvature based on Wang et al's approach [14].…”

Section: The Monotonicity Of the Curvature Of Rational Cubic Bézier Cmentioning

confidence: 99%

Quasi-Aesthetic Curves in Rational Cubic Bézier Forms

Yoshida¹,

Saito²

2007

“…Higashi et al has proposed to use an evolute to control the curvature variation for generating aesthetic curves [6]. Wang et al proposed to use the monotone curvature condition to design fair curves [17]. Farin proposed class A Bézier curves to generate 3D curves with monotone curvature and torsion [4], which was inspired by Mineur's typical curves [9].…”

Section: Interactive Generation Of 3d Class a Bézier Curve Segmentsmentioning

confidence: 99%

Interactive Generation of 3D Class A Bézier Curve Segments

Yoshida

Fukuda

Saito

2010

This paper presents a method for interactively generating a 3D class A Bézier curve segment by specifying two endpoints and their tangents. We clarify geometric properties of 3D class A Bézier curves and use them for efficiently generating 3D class A Bézier curve segments satisfying the specified positional and tangential constraints. The characteristics of typical 3D class A Bézier curves are also clarified. 164 segments [14] can be interactive controlled with user-specified endpoint constraints. However, the curve is not compatible with free-form curves, such as Bézier curves or NURBS curves.

“…Diez and Piper used precomputed tables so that polynomial cubic Bézier curves have monotonically varying curvature [2]. Wang et al presented sufficient monotone curvature conditions for polynomial Bézier and B-spline curves of degree n [13]. More recently, Farin has proposed class A Bézier curves [4].…”

Section: Related Workmentioning

confidence: 99%

Interactive Control of Planar Class A Bézier Curves using Logarithmic Curvature Graphs

Yoshida¹,

Hiraiwa²,

Saito³

2008

We present a method for interactively drawing a planar class A Bézier curve segment. First, we present a method for interactively drawing a typical class A Bézier curve segment by specifying three points like a quadratic Bézier curve segment. We show that as the degree of a typical class A Bézier curve segment is elevated, the curve converges to a logarithmic spiral segment. At the limit of infinite degree, the curve segment becomes a logarithmic spiral segment. We also present a method for drawing a general class A Bézier curve segment by perturbing the elements of the typical class A matrix so that the endpoint constraints are satisfied. To see the characteristics of the generated curves, we propose to use logarithmic curvature graphs.