Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae

In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler-Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae

Some results on p-shape curvatures of non-lightlike space curves

In this paper, we obtain some findings for a non-null curve parameterized by spherical arc length. We investigate the relationship between a non-null curve with p-shape curvatures and pseudospherical curves on S21 and H2(−1). We introduce the concept of similar helix in Minkowski 3-space E31. Besides, we explicitly determine the parametrizations of all non-lightlike self-similar curves by using the pseudo-spherical curves in E31.No sponso

Similar and self-similar curves in minkowski n-space

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of nonnull curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of En1. We determine the parametrizations of non-null self-similar curves in En1. .No sponso

On Similarity-Invariant Fairness Measures

Abstract. After introducing the basic principles behind the similarityinvariant smoothness measures for curves and surfaces, with references to the relevant literature, we discuss the ramifications of scale-invariance in various problems of image processing and analysis, and point out some unanswered questions.