Casey Reas and Ben Fry are to be congratulated on two counts. I have grappled with many programming books over the years in an effort to teach myself programming and none come close to Processing: A Programming Handbook for Visual Designers and Artists. Why did we have to wait so long for this marvelous gem? It is, indeed, rare to find a technical book of such clarity and insight and especially so in books concerning computer programming. Second, the references come from many directions, from quantum to astronomy, from mechanical design to nano-optics, and from pure math to algorithms for the best buy. With this number of references this puts the paper in the top 1,5 % of all papers published. First, 70-80 % of all papers receive less than 10 citations (almost half of the papers are never cited). The number of references marks the paper as extremely highly cited. Given this wide diversity and citations, the database aims researchers are in finding work in similar or distant areas.
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This overview also includes a full list of these publications, in Endnote and in Excel format. In total close close to 500 references are returned by Googlescholar, and in total over 500 have been used to build the database. This is also testimony to the unifying power. The Science category is subdivided in biology, psychology and physics, and for Technology six categories are defined, namely 1) antennas, electronics and metamaterials, 2) nanotechnology, 3) applied physics, 4) mechanics and mechanotronics, 5) computer graphics and modeling, and 6) computer vision and datamining. Using bibliometric data and citation indices, the use of the formula is divided into three categories, namely Mathematics, Science and Technology. It is the purpose of this article to give an updated overview and list of such applications and publications. In the past two decades a variety of papers, books and book chapters, theses and patents were published using this transformation, in the fields of mathematics, physics, biology, technology and education. Its origin is in the description of botanical shapes, but it is a fundamental equation that finds applications in many directions. The former was used in the article, as generalization of Lamé curves, also known as supercircles and superellipses. In the literature one finds names like Superformula, Gielis Superformula or Gielis curves, surfaces and (sub-) manifolds and Gielis transformations. The paper A generic geometric transformation that unifies a wide range of natural and abstract shapes introduced the Superformula, a generalization of circles and the Pythagorean Theorem, based on work of the French mathematician Gabriel Lamé (1795-1860).
We also found that the proposed VR widgets provide a quick overview of the main supershapes, and users can easily reach the desired solution without having to perform fine-grain handle manipulations. We conducted a user study (N = 18) and found that VR shape widgets are effective, more efficient, and natural than conventional VR 1-D sliders while also usable for users without prior knowledge on supershapes. Our designs take leverage on thumbnails, mini-maps, haptic feedback and spatial interaction, while supporting 1-D, 2-D and 3-D supershape parameter spaces.
In this work, we propose VR shape widgets that allow users to probe and select supershapes from a multitude of solutions.
VR appears as a promising setting for Parametric Design with supershapes since it empowers users with more natural visual inspection and shape browsing techniques, with multiple solutions being displayed at once and the possibility to design more interest-* ing forms of slider interaction. Some of the formula's parameters are non-linear in nature, making them particularly difficult to grasp with conventional 1-D sliders alone. However, users are left to probe such a rich yet dense collection of supershapes using a set of independent 1-D sliders. Supershapes are used in Parametric Design to model, literally, thousands of natural and man-made shapes with a single 6 parameter formula.
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