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A point p in a Riemannian submanifold is umbilical if, at p, the (vector-valued) Second fundamental form is some normal vector tensor the induced metric (First fundamental form). Equivalently, for all vectors U , V at p , II( U , V ) = g p ( U , V ) ν {\displaystyle \nu } , where ν {\displaystyle \nu } is the mean curvature vector at p .
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 ...
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 ...
The set of ridge points form curves on the surface called ridges. The ridges of a given surface fall into two families, typically designated red and blue, depending on which of the two principal curvatures has an extremum. At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines ...
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.
Apposition eyes work by gathering a number of images, one from each eye, and combining them in the brain, with each eye typically contributing a single point of information. The typical apposition eye has a lens focusing light from one direction on the rhabdom, while light from other directions is absorbed by the dark wall of the ommatidium .