Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

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 G2 LMC 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 G2 Hermite data is still a cumbersome task

Analysis of Drag Coefficients around Objects Created Using Log-Aesthetic Curves

A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α of LAC on the drag generated in an incompressible fluid flow, simulated using a semi-implicit backward difference formula coupled with P2−P1 Taylor–Hood finite elements. An algorithm was developed to create LAC hydrofoils that were used in this study. We analyzed the drag coefficients of 47 LAC hydrofoils of three sizes with various shapes in fluid flows with Reynolds numbers of 30, 40, and 100, respectively. We found that streamlined LAC shapes with negative α values, of which curvature with respect to turning angle are almost linear, produce the lowest drag in the incompressible flow simulations. It also found that the thickness of LAC objects can be varied to obtain similar drag coefficients for different Reynolds numbers. Via cluster analysis, it is found that the distribution of drag coefficients does not rely solely on the Reynolds number, but also on the thickness of the hydrofoil

Analysis of Drag Coefficients around Objects Created Using Log-Aesthetic Curves

A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α of LAC on the drag generated in an incompressible fluid flow, simulated using a semi-implicit backward difference formula coupled with P2−P1 Taylor–Hood finite elements. An algorithm was developed to create LAC hydrofoils that were used in this study. We analyzed the drag coefficients of 47 LAC hydrofoils of three sizes with various shapes in fluid flows with Reynolds numbers of 30, 40, and 100, respectively. We found that streamlined LAC shapes with negative α values, of which curvature with respect to turning angle are almost linear, produce the lowest drag in the incompressible flow simulations. It also found that the thickness of LAC objects can be varied to obtain similar drag coefficients for different Reynolds numbers. Via cluster analysis, it is found that the distribution of drag coefficients does not rely solely on the Reynolds number, but also on the thickness of the hydrofoil