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Distance from the origin O to the line E calculated with the Hesse normal form. Normal vector in red, line in green, point O shown in blue. In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane, a plane in Euclidean space, or a hyperplane in higher dimensions.
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.
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The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane. [1] [2] [3] The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures.
The attitude of a lattice plane is the orientation of the line normal to the plane, [12] and is described by the plane's Miller indices. In three-space a family of planes (a series of parallel planes) can be denoted by its Miller indices ( hkl ), [ 13 ] [ 14 ] so the family of planes has an attitude common to all its constituent planes.
Fig.5: A second, horizontal plane of projection is added, perpendicular to the first. Fig.6: Projectors emanate parallel from all points of the object perpendicular to the second plane of projection. Fig.7: An image is created thereby. Fig.8: The third plane of projection is added, perpendicular to the previous two.
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In normal aspect, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels. Conic In normal aspect, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles. Pseudoconical
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