Abstract
Curves are the building blocks of shapes and designs in computer aided geometric design (CAGD). It is important to ensure these curves are both visually and geometrically aesthetic to meet the high aesthetic need for successful product marketing. Recently, magnetic curves that have been proposed for computer graphics purposes are a particle tracing technique that generates a wide variety of curves and spirals under the influence of a magnetic field. The contributions of this paper are threefold, where the first part reformulates magnetic curves in the form of log-aesthetic curve (LAC) denoting it as log-aesthetic magnetic curves (LMC) and log-aesthetic magnetic space curves (LMSC), the second part elucidates vital properties of LMCs, and the final part proposes G2LMC design for CAD applications. The final section shows two examples of LMC surface generation along with its zebra maps. LMC holds great potential in overcoming the weaknesses found in current interactive LAC mechanism where matching a single segment with G2Hermite data is still a cumbersome task.
Highlights
Curves are widely used in various fields, most commonly in art and designs
Both curves mentioned have great potential for Mathematical Problems in Engineering magnetic space curves (LMSC) for CAD applications; the third part proposes an algorithm for developing G2 continuous log-aesthetic magnetic curves (LMC)
This section discusses that the properties which are roundness, monotone curvature and torsion, extensionality, and locality hold for LMC or log-aesthetic magnetic space curves (LMSC)
Summary
Curves are widely used in various fields, most commonly in art and designs. The fairness of a curve dictates the product’s quality and, in turn, its sales. The definition of a beautiful curve in the eye of an artist is a curve which exhibits constant variation of curvature monotonically and no part of the curve is a circular arc, as expressed by Ruskin [1] It is the same for aesthetic designs in CAGD. The definition of a fair curve still remains subjective and unclear, which makes the condition required for ending a fairing process seems rather ambiguous Conventional curves such as NURBS and Bezier have obvious oscillation in their curvature profile making it less visually pleasing. GLAC extends the family of LAC to include generalized cornu spiral [8] Both curves mentioned have great potential for Mathematical Problems in Engineering magnetic space curves (LMSC) for CAD applications; the third part proposes an algorithm for developing G2 continuous LMC
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