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cone. In Fig. 6.30, let the vertex of the cone be placed at Π 1, and one element of the cone coincide
with plane. The length of this element is taken from the frontal projection, of either contour
element. All of the elements of the cone are of the same length, so that when the cone is rolled, each
point of the base as it touches the plane will be at the same distance from the vertex. From this it
follows that in the development of the base, the circumference will become the arc of a circle of
radius equal to the length of an element, and of a length equal to the distance around the base. To
find this length divide the circumference of the base in the plan into any number of equal parts, say
twelve, and lay off twelve such spaces I, II, III, etc. along an arc drawn with radius equal to S 2I 2
(S 2VII 2); join I and I with S, and the resulting sector is the development of the cone from vertex to
base.

Figure 6.30 Plan, Elevation of Cone and Development of Cone.

Approximate Development
An approximate development is one in which stretching or distortion occurs in the process of
creating the development.
The resulting flat surfaces are not the same size and shape as the corresponding surfaces on the
3-D object.
Warped surfaces do not produce true developments, because pairs of consecutive straight-line
elements do not form a plane.
Double-curved surfaces such as spheres do not produce true developments.
There are two methods for construction of sphere development.
Zone Method: Development of sphere using frustum of cones (polyconic). Fig. 6.31 represents
half of sphere development.

Figure 6.31

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