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A texture map (left). The corresponding normal map in tangent space (center). The normal map applied to a sphere in object space (right). Normal map reuse is made possible by encoding maps in tangent space. The tangent space is a vector space, which is tangent to the model's surface. The coordinate system varies smoothly (based on the ...
The other method is to specify a normal map which contains the modified normal for each point on the surface directly. Since the normal is specified directly instead of derived from a height map this method usually leads to more predictable results. This makes it easier for artists to work with, making it the most common method of bump mapping ...
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
The Mercator projection in normal aspect maps trajectories of constant bearing (called rhumb lines or loxodromes) on a sphere to straight lines on the map, and is thus uniquely suited to marine navigation: courses and bearings are measured using a compass rose or protractor, and the corresponding directions are easily transferred from point to ...
Normal coordinates exist on a normal neighborhood of a point p in M. A normal neighborhood U is an open subset of M such that there is a proper neighborhood V of the origin in the tangent space T p M, and exp p acts as a diffeomorphism between U and V. On a normal neighborhood U of p in M, the chart is given by:
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.
The ending of the BBC adaptation left us with one big question...
Actual printed maps are produced from the projection map by a constant scaling denoted by a ratio such as 1:100M (for whole world maps) or 1:10000 (for such as town plans). To avoid confusion in the use of the word 'scale' this constant scale fraction is called the representative fraction (RF) of the printed map and it is to be identified with ...