Anamorphic 3D geometry

Hansford, Dianne; Collins, Dan

doi:10.1007/s00607-006-0199-6

Cited by 13 publications

(12 citation statements)

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“…In our work, following the initial ideas by Hansford and Collins (2007), we develop more general anamorphic transformations for true perspective projection, in terms of a rational FFD. Thus, we give a modern interpretation of anamorphosis, more accessible for implementation in CAGD and a NURBS setting.…”

Section: Anamorphosis Via Ffd (Free-form Deformation)mentioning

confidence: 99%

“…Indeed, for creating anamorphic 3D geometry, Hansford and Collins (2007) advocate the use of a collineation, a certain linear map in projective space that can be regarded as a rational linear FFD. Sela and Elber (2007) also employ a FFD (in this case, a polynomial B-spline FFD) to generate deceiving geometry.…”

Section: Anamorphosis Via Ffd (Free-form Deformation)mentioning

confidence: 99%

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Anamorphic Free-Form Deformation

Sánchez-Reyes

Chacón

2016

Computer Aided Geometric Design

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Highlights• We reinterpret optical anamorphosis in a CAGD setting, as a rational FFD.• The key idea is to use homogeneous coordinates with centre at the viewpoint O.• The control points of the deformation tool move along radial directions through O.• With a linear Bézier tetrahedron as tool, the FFD yields a perspective collineation.• In general, NURBS transform to NURBS of higher degree via rational composition. 22 June 16 J. Sánchez-Reyes, J.M. Chacón AbstractIn 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 FreeForm 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.

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Section: Anamorphosis Via Ffd (Free-form Deformation)mentioning

confidence: 99%

Section: Anamorphosis Via Ffd (Free-form Deformation)mentioning

confidence: 99%

Anamorphic Free-Form Deformation

Sánchez-Reyes

Chacón

2016

Computer Aided Geometric Design

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“…138-155;García-Salgado 2003, pp. 22-48;Hansford andCollins 2007, 2012;Hunt et al 2000, pp. 232-237).…”

Section: Development Of Plane Anamorphic Picturesunclassified

Distortion Minimization: A Framework for the Design of Plane Geometric Anamorphosis

Stojaković

Tepavčević

2016

Nexus Netw J

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Anamorphosis, as a drawing, represents shapes on a surface such that they appear in their natural form only under specific viewing conditions. Although anamorphoses are mainly studied in a historical context, they are currently experiencing a revival. Plane geometric anamorphoses are a specific sub-type of anamorphic drawings. Some practical problems may arise during the design and realization of plane geometric anamorphosis causing the 3D illusionistic effect to be impaired. The aim of this paper is to identify and analyze these problems. In the paper we use parametric analysis to quantify the distortion that may appear because the point of view is offset from the preferred point of view, and to simulate the deviations that can appear because of the errors in onsite realization. The analysis leads to a framework for the design of plane geometric anamorphosis that minimizes the impairment of the anamorphic illusion.

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“…Anamorphosis is a deformed projection or representation of a picture on a curved surface, which, when seen from a point or reflected in a curved mirror, appears regular and in proportion 9. This geometrical deformation has been used from the early 15th century by numerous artists for aesthetic purposes 10.…”

Section: Introductionmentioning

confidence: 99%