Quasi-Aesthetic Curves in Rational Cubic Bézier Forms

Abstract

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.

Interactive Generation of 3D Class A Bézier Curve Segments

“…In general, the simultaneous control of the monotonicity of the curvature (and torsion for space curves) and the endpoint constraints (two endpoints and their tangents) is not easy. The papers [11,12,13,14] have addressed the problem. In case of space curves, log-aesthetic space curve In this paper, we extend our previous work of interactively controlling 2D class A Bézier curves [13] to 3D class A Bézier curves.…”

Quasi-Log-Aesthetic Curves in Polynomial Bézier Form

“…This paper proposes quasi-log-aesthetic curves in polynomial Bézier form and compares them with the curves generated by Miura's method [6] and quasi-log-aesthetic curves in rational cubic Bézier form [10]. We show that quasi-log-aesthetic curves are better approximation than the curves generated by Miura's method.…”

“…Both of these methods have only dealt with the specific cases logaesthetic curves. Yoshida and Saito have proposed a method for approximating log-aesthetic curves by rational cubic Bézier curves [10]. They showed that the linearity of the logarithmic curvature graph is wellpreserved by the approximation except when log-aesthetic curves include nearby point of 0 r = or ¥ .…”

Logarithmic Curvature and Torsion Graphs

“…LCGs and LTGs offer the information related to the curvature and torsion variations that the curvature and torsion plots do not offer. For planar curves, LCGs are already introduced in [12,13]. In this paper, however, we draw LCGs and LTGs from space curves and derive more detailed characteristics.…”