What do you mean by developable surface?
Definition of developable surface : a surface that may be imagined flattened out upon a plane without stretching any element.
What is developable surface in differential geometry?
A developable surface is a special ruled surface which has the same tangent plane at all points along a generator [13,222,120,32,326,252,329]. Since surface normals are orthogonal to the tangent plane and the tangent plane along a generator is constant, all normal vectors along a generator are parallel.
What are developable and non-developable surfaces?
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 the developable surface on a map?
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.
What is non developable surface?
A non-developable surface is one, which cannot be flattened without shrinking, breaking or creasing. Example. A cylinder, a cone and a plane have the property of developable surface. A globe or spherical surface has the property of non-developable surface.
Which of the following is developable surface?
Developable surfaces therefore include the cone, cylinder, elliptic cone, hyperbolic cylinder, and plane.
What is non-developable surface?
Non-developable surfaces are variously referred to as having “double curvature”, “doubly curved”, “compound curvature”, “non-zero Gaussian curvature”, etc. Some of the most often-used non-developable surfaces are: Spheres are not developable surfaces under any metric as they cannot be unrolled onto a plane.
What is a non-developable surface in geography?
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 is a developable surface and what common shapes are used to represent them?
Developable Surfaces: A developable surface is a geometric surface on which the curved surface of the earth is projected; the end result being what we know as a map. Geometric forms that are commonly used as developable surfaces are planes, cylinders, cones, and mathematical surfaces.
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 is a developable surface What are the most common shapes for a developable surface?
What is a developable surface?
In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. “stretching” or “compressing”). Conversely, it is a surface which can be made by transforming a plane (i.e.
What are geodesics?
Geodesics: the curves that develop into straight lines (and therefore, in particular, the generatrices). A developable surface (or torse) is a ruled surface that can roll without slipping on a plane, the contact being along a line, similarly to a cylinder or a cone.
Can a developable surface be made from sheet metal?
A developable surface has the property that it can be made out of sheet metal, since such a surface must be obtainable by transformation from a plane (which has Gaussian curvature 0) and every point on such a surface lies on at least one straight line.
Which of the following surfaces are developable in three dimensional space?
The developable surfaces which can be realized in three-dimensional space include: Cylinders and, more generally, the “generalized” cylinder; its cross-section may be any smooth curve. Frenet Ribbons are developable. Cones and, more generally, conical surfaces; away from the apex.