Developable surfaces have several applications. Many cartographic projections involve projecting the Earth to a developable surface and then unrolling the surface into a region in the plane.
developable surface -- a surface that can be flattened to form a plane without compressing or stretching any part of it. Examples include cones and cylinders.
Developable surfaces
1. Planar or azimuthal
2. Conic
3. Cylindrical
4. Non-Geometric (Mathematical) projections ...
Which developable surface is used?
Is it a tangential or a secant projection?
What is the position of the developable surface?
Describe some of the scale distortion characteristics.
Are areas correctly represented?
Next, is a discussion of developable surfaces which introduces the notion of the changing light source to create different projections. Campbell then includes distortion diagrams which leads to a discussion of several specific projections.
Most projections are derived from mathematical formulas, but some are easier to visualize as projected on to a developable surface.
A plane, cone, or cylinder (known as a developable surface) is placed outside the sphere. Shadows are cast upon the surface. The surface is opened flat, and the geographic features are displayed on a flat plane.
" They consist of three basic developable surfaces: a plane above or below the spherical surface; a cone tangent to the spherical surface, and a cylinder wrapped around the spherical surface.
Mathematical map projections are not based on developable surface, but often specify a direct mathematical projection from a spheroid onto a flat surface.
Referenced by: WYSIWYG; Shape analysis; Vector graphics; Vectorization (computer graphics); Tessellation; Developable surface; Delaunay triangulation; Computer-aided design; Computational geometry; Geomatics engineering; Geovisualization; World file.
surfaces in blue (just a few of infinitely many possible oblique maps are presented). Some projections may actually be derived via perspective geometry; for most, however, surfaces are only illustrative: the map may be laid on a developable surface, ...
Methods for projecting the spherical coordinates of lattitude and longitude to orthoganal coordinates, may be thought of as metaphorical projections of light through a transparent globe onto a developable surface such as a flat piece of paper.
Projections can be based on a developable surface (such as a plane, cylinder, or cone) or on a mathematical function. proportional symbols p. 13 a thematic mapping technique that displays a quantitative attribute by varying the size of a symbol.
Developable Surface The surface onto which a map projection is projected. This may be a plane, cylinder or cone.
 See also: Surface, Projection, Latitude, Area, Map
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