Sánchez-Reyes, Javier; Chacón, Jesús M. Anamorphic free-form deformation. (English) Zbl 1418.68230 Comput. Aided Geom. Des. 46, 30-42 (2016). Summary: In an optical anamorphosis, an object is seen distorted unless the viewer is positioned at a specific point, where the object appears normal. We describe how to endow a rational Free-Form Deformation with an anamorphic character in a simple manner, obtaining an AFFD (Anamorphic Free-Form Deformation). Given a (planar or 3D) initial object, which will appear normal from the desired viewpoint, we deform the object with a rational Bézier surface or volume as deformation tool. To achieve the desired deformation, the user input amounts to displacing the control points of the deformation tool along radial directions through the viewpoint, whereas the weights come as a byproduct. Mathematically, the deformation means changing the last homogeneous coordinate of the control points. An AFFD defined by a linear Bézier tetrahedron can be regarded as a user-friendly way to construct a perspective collineation. In this case, or when the deformation tool is a Bézier triangle of degree one, the AFFD transforms NURBS to NURBS keeping the original degree. With a deformation tool of higher degree, the rational composition required to obtain the exact result yields NURBS also of higher degree. For a quadratic Bézier triangle as deformation tool, our AFFD coincides with the inverse of a stereographic projection. Cited in 1 Document MSC: 68U07 Computer science aspects of computer-aided design 65D17 Computer-aided design (modeling of curves and surfaces) 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) Keywords:anamorphosis; free-form deformation; NURBS; perspective collineation; rational Bézier volume; stereographic projection Software:Stanford 3D Scanning Repository PDFBibTeX XMLCite \textit{J. Sánchez-Reyes} and \textit{J. M. 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