Descriptive Geometry: Developments and Intersections — CSEC Technical Drawing

This topic covers the surface developments of solids and the lines formed where solids intersect.

Developments

A development is the surface of a solid "unrolled" or opened out flat into a single pattern. Each surface is shown at its true size and shape so the flat pattern can be folded or rolled to form the solid. Developments are essential in sheet-metal work (ducts, hoppers, cans).

Examples:

The development of a cylinder is a rectangle whose length equals the circumference (πd) and whose height equals the cylinder height.
The development of a cone is a sector of a circle with radius equal to the slant height.
The development of a cube is a net of six squares.

Methods of development

Parallel-line development — used for prisms and cylinders (edges are parallel).
Radial-line development — used for cones and pyramids (edges radiate from the apex).
Triangulation — used for transition pieces (e.g. square to round).

Intersections (interpenetrations)

When two solids meet or pass through each other, a curve or line of intersection is formed (for example, where two cylinders join in a pipe tee). These are found by projecting common points between the views.

Method (prism development)

Draw the orthographic views of the prism.
Divide the base into equal parts.
Project the height of each edge across.
Join the points to complete the flat pattern.

Exam tips

A development shows every surface at its true size, ready to fold/roll.
Cylinder → rectangle (length = circumference); cone → sector.
Use parallel-line development for prisms/cylinders, radial-line for cones/pyramids.
An intersection is the line where two solids meet or penetrate.