TAILIEUCHUNG - On isophote curves and their characterizations

An isophote curve comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. The main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about the isophote curve and its axis in Euclidean 3-space. | Turk J Math (2015) 39: 650 – 664 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article On isophote curves and their characterizations 1,∗ ˘ Fatih DOGAN , Yusuf YAYLI2 Department of Mathematics, Faculty of Science, Bartın University, Bartın, Turkey 2 Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey 1 Received: • Accepted/Published Online: • Printed: Abstract: An isophote curve comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. The main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about the isophote curve and its axis in Euclidean 3-space. Particularly, for isophote curves lying on a canal surface other characterizations are obtained. Key words: Isophote curve, silhouette curve, geodesic, general helix, slant helix, canal surface 1. Introduction An isophote curve is one of the characteristic curves on a surface such as parameter, geodesic, and asymptotic curves or lines of curvature. An isophote curve on a surface is a nice consequence of Lambert’s cosine law in the optics branch of physics. Lambert’s law states that the intensity of illumination on a diffuse surface is proportional to the cosine of the angle generated between the surface normal vector N and the light vector d. According to this law the intensity is irrespective of the actual viewpoint; hence the illumination is the same when viewed from any direction [9] . In other words, isophotes of a surface are curves with the property that their points have the same light intensity from a given source (curves of constant illumination intensity). When the source light is at infinity, we may consider that the light flow consists of parallel lines. Hence, we can give a geometric description of isophote curves on surfaces, namely, .

• Toán học
• Isophote curve
• Silhouette curve
• General helix
• Slant helix
• Canal surface
• Hydraulic particulars
• Surface water
• Nagarjuna sagar right canal
• Assessment of water resources
• Branch wise discharge data
• Trace element
• Rice field
• Surface water quality
• Paddy rice fields
• Graphite Furnace Atomic Adsorption Spectroscopy