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In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. At such points the normal curvatures in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction .
The horopter as a special set of points of single vision was first mentioned in the eleventh century by Ibn al-Haytham, known to the west as "Alhazen". [3] He built on the binocular vision work of Ptolemy [4] and discovered that objects lying on a horizontal line passing through the fixation point resulted in single images, while objects a reasonable distance from this line resulted in double ...
Having two eyes allows the brain to determine the depth and distance of an object, called stereovision, and gives the sense of three-dimensionality to the vision. Both eyes must point accurately enough that the object of regard falls on corresponding points of the two retinas to stimulate stereovision; otherwise, double vision might occur.
The shape also has a single external face. A cross section of the surface forms a deltoid. The umbilic torus occurs in the mathematical subject of singularity theory, in particular in the classification of umbilical points which are determined by real cubic forms + + +. The equivalence classes of such cubics form a three-dimensional real ...
Away from umbilical points, these two points of the focal surface are distinct; at umbilical points the two sheets come together. When the surface has a ridge the focal surface has a cuspidal edge, three such edges pass through an elliptical umbilic and only one through a hyperbolic umbilic. [3] At points where the Gaussian curvature is zero ...
When an eye focuses light correctly on to the retina when viewing distant objects, this is called emmetropia or being emmetropic. This means that the refractive power of the eye matches what is needed to focus parallel rays of light onto the retina. A distant object is defined as an object located beyond 6 meters (20 feet) from the eye.
The conjecture claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points.In the sense of the conjecture, the spheroid with only two umbilic points and the sphere, all points of which are umbilic, are examples of surfaces with minimal and maximal numbers of the umbilicus.
The macula (/ˈmakjʊlə/) [1] or macula lutea is an oval-shaped pigmented area in the center of the retina of the human eye and in other animals. The macula in humans has a diameter of around 5.5 mm (0.22 in) and is subdivided into the umbo, foveola, foveal avascular zone, fovea, parafovea, and perifovea areas.