In mathematics, a developable surface is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion. Conversely, it is a surface which can be made by transforming a plane. In three dimensions all developable surfaces are ruled surfaces.

What has an undevelopable surface?

An undevelopable surface is any surface that cannot be flattened into a map without stretching, tearing, or compressing itself, as for example the surface of a sphere.

What do you mean by developable surface?

: a surface that may be imagined flattened out upon a plane without stretching any element.

Is Undevelopable a word?

Definition of "undevelopable" [undevelopable]

"Because they basicaly bought land that was undevelopable on one side, but the only thing making it undevelopable is cost."

What is an example 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.

Map Projections: Developable Surfaces - GIS Fundamentals and Mapping (20)

43 related questions found

What is 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.

How many types of developable surfaces are there?

A developable surface is a geometric shape that can be laid out into a flat surface without stretching or tearing. The three types of developable surfaces are cylinder, cone and plane, and their corresponding projections are called cylindrical, conical and planar.

Are all ruled surfaces developable?

In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. ... In three dimensions all developable surfaces are ruled surfaces (but not vice versa).

Is a cone a developable surface?

A developable surface is a special type of ruled surfaces with zero Gaussian curvature which can be flattened on to a plane without distortion [1], [2]. Examples include simple surfaces such as cones and cylinders, as well as tangent or rectifying developables derived from spatial curves.

What are the three elementary types of developable surfaces provide a brief description?

Provide a brief description. (Maximum 100 words) Three elemental types of developable surfaces are cylinders, cones, and tangent surfaces of space curves. ... Tangent surfaces of space curves involve a three-dimensional curve and surfaces based on the tangents of the curve.

Which of the following is not an example of a developable surface?

The cylinder, cone and the plane are all developable surfaces. The sphere and ellipsoid do not have developable surfaces, so any projection of them onto a plane will have to distort the image.

What is a developable surface in map projection?

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 developable 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]. ... A developable surface has following differential geometry properties [412]: A developable surface can be mapped isometrically onto a plane.

What is the necessary and sufficient condition for a surface to be a developable?

2. A necessary and sufficient condition that a surface be developable is that, for every point P on the surface, there is a neighbouring point P' on the surface. such that the normals at P and P' are parallel.

What are the most common three shapes for a developable surface?

Map projections are based on developable surfaces, and the three traditional families consist of cylinders, cones, and planes. They are used to classify the majority of projections, including some that are not analytically (geometrically) constructed.

What are the types of surfaces?

List of surfaces

• Minimal surfaces.
• Ruled surfaces.
• Non-orientable surfaces.
• Quadrics.
• Pseudospherical surfaces.
• Algebraic surfaces.
• Miscellaneous surfaces.

Which of the following is an example of a developable surface that can be used to project a map?

These are called developable surfaces. Some common examples are cones, cylinders, and planes. A map projection systematically projects locations from the surface of a spheroid to representative positions on a flat surface using mathematical algorithms.

What are the primary developable surfaces used to create various map projections?

The primary developable surfaces used to create various map projections include planes, cylinders, and cones.

What is area distortion?

In cartography, a distortion is the misrepresentation of the area or shape of a feature. There are no map projections that can maintain a perfect scale throughout the entire projection because they are taking a sphereoid and forcing it onto a flat surface.

Why is the understanding of developable surface critical in the understanding of architectural geometry?

(Maximum 100 words) Understanding of developable surface is critical in the understanding of architectural geometry because then architects can understand the limitation and use of possible geometries to include in their work.

Which quadric surfaces are ruled surfaces?

Of the non-degenerate quadratic surfaces, the elliptic (and usual) cylinder, hyperbolic cylinder, elliptic (and usual) cone are ruled surfaces, while the one-sheeted hyperboloid and hyperbolic paraboloid are doubly ruled surfaces.

What is a single curved surface?

Single Curved Surface – only one of two curves is actually curved, making this shape developable (in mathematics, a developable surface is a smooth surcafe with zero Gaussian curvature, meaning it could be flattened on plane without distortion). Double Curved Surface – non-developable surface.

What is edge of regression in differential geometry?

The original curve forms a boundary of the tangent developable, and is called its directrix or edge of regression. ... Intuitively, it is a curve along which the surface needs to be folded during the process of developing into the plane.

What is minimum surface area?

In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint.

What is the practical use of development of surface?

The development of a surface is that surface laid out on a plane. Practical applications of developments occur in sheetmetal work, stone cutting, pattern making, packaging, and package design. Single-curved surfaces and the surfaces of polyhedra can he developed.