2018
DOI: 10.1016/j.cagd.2018.06.006
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Contour curves and isophotes on rational ruled surfaces

Abstract: The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the field of applied geometry. An isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. Choosing an angle equal to =2 we obtain a special instance of a isophotethe so called contour curve. While contours on rational ruled surfaces are rational curves, this is no longer true for the isophotes. Hence we will provide a formula for their genus. Moreover… Show more

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Cited by 5 publications
(3 citation statements)
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“…Lines in this projective plane correspond by the central projection to planes through o. Tangent lines to T ′ correspond to tangent planes to T through o. This implies that the dual T ′ * of T ′ is the intersection of the dual T * of the torus with the plane o * ⊂ (P 2 ) * (see also [5]). We call T ′ * the dual picture of the torus.…”
Section: The Torusmentioning
confidence: 97%
“…Lines in this projective plane correspond by the central projection to planes through o. Tangent lines to T ′ correspond to tangent planes to T through o. This implies that the dual T ′ * of T ′ is the intersection of the dual T * of the torus with the plane o * ⊂ (P 2 ) * (see also [5]). We call T ′ * the dual picture of the torus.…”
Section: The Torusmentioning
confidence: 97%
“…Hence the isophote consists of the points where the surface normals enclose the angle α or −α with the given direction. Let us stress that choosing the angle α = π/2 would lead to a special instance of the isophotes, i.e., to the so called contour curves (mentioned for canal surfaces in the previous subsection), see also Vršek (2016) for more details about contour curves and isophotes on ruled surfaces.…”
Section: Intersection Of Ruled Surfaces With Quadricsmentioning
confidence: 99%
“…Isophotic and silhouette curves ( contour generators ) play an important role in differential geometry of curves and surfaces. Such curves are significant not only in the vision theory and visual psychophysics [1–3] but also in Computer Aided Geometric Design (CAGD) [4–6]. Isophotic curves lying on a regular surface in Euclidean 3‐space have a property that the surface normal restricted to those curves makes a non‐zero constant angle with a fixed direction, which is called an axis [7].…”
Section: Introductionmentioning
confidence: 99%