What are the three types of developable surfaces?

A developable surface (Figure 2) is a surface that can be flattened to a plane without introducing distortion from compression or stretching. There are three developable surfaces: planes, cones, and cylinders.

How do you make a surface developable?

Developable surfaces are surfaces that can be formed by rolling a flat sheet of material such that the material does not stretch, tear, or wrinkle. Examples of this type of shape are cylinders, cones, and some steel ship hulls.

How many types of developable surfaces are there?

three types
There are three types of developable surfaces: cones, cylinders (including planes), and tangent surfaces formed by the tangents of a space curve, which is called the cuspidal edge, or the edge of regression. Cylinders do not contain singular points. The only singular point of a cone is its vertex.

What are some common examples of a developable surface?

Developable surfaces therefore include the cone, cylinder, elliptic cone, hyperbolic cylinder, and plane. Other examples include the tangent developable, generalized cone, and generalized cylinder.

What is the difference between developable and non developable surface?

Developable Surface : A developable surface is that which can be cut or unfold into a flat sheet or paper e.g., cylinder or cone. Non-developable Surface : A non-developable surface is that which cannot be cut or folded into flat sheet paper, e.g. globe.

What is meant by a developable surface?

developable surface. [map projections] A geometric shape such as a cone, cylinder, or plane that can be flattened without being distorted.

Are all ruled surfaces developable?

One consequence of this is that all “developable” surfaces embedded in 3D-space are ruled surfaces (though hyperboloids are examples of ruled surfaces which are not developable). Because of this, many developable surfaces can be visualised as the surface formed by moving a straight line in space.

What is developable surface GIS?

developable surface. [map projections] A geometric shape such as a cone, cylinder, or plane that can be flattened without being distorted. Many map projections are classified in terms of these shapes.

What is a developable surface in surveying?

Developable surfaces are a special kind of ruled surfaces: they have a Gaussian f curvature equal to 0,1 and can be mapped onto the plane surface without distortion of curves: any curve from such a surface drawn onto the flat plane remains the same.

How do I know if my surface is developable?

Just orient the surface in space until you get a clear view straight down one isocurve. The surface edges at both ends of an isocurve on a developable surface will appear to be parallel, at that location, which means that they lie in the same plane.

What are developable surface in GIS?