CHAPTER 3
Engineering Geometry
INTRODUCTION
Graphics is used to represent complex objects and structures that are created from simple geometric
elements, such as lines, circles, and planes. Current 3-D CAD programs use these simple geometric forms
to create more complex ones, through such processes as extrusion, sweeping, and solid modeling Boolean
operations. Therefore, to fully exploit the use of CAD, you must understand geometry and be able to
construct 2-D and 3-D geometric forms.
3.1 ENGINEERING GEOMETRY
Geometry provides the building blocks for the engineering design process.
Engineering geometry
is
the basic geometric elements and forms used in engineering design.
Engineering and technical graphics are
concerned with the descriptions of shape, size, and operation of engineered products. The shape description
of an object relates to the positions of its component geometric elements in space. To be able to describe
the shape of an object, you must understand all of the geometric forms, as well as how they are graphically
produced.
Complex engineering geometry is found in many engineered products, structures, and
systems.
3.2 SHAPE DESCRIPTION
Shape description of an object relates the positions of its component geometric elements (e.g., vertices,
edges, faces) in space.
Nomenclature of the component elements, the larger geometric configurations (e.g.,
hexagons, cubes, prisms, etc.), and the coordinate systems which describe their spatial locations are all
important concepts in learning about technical graphics.
3.3 COORDINATE SPACE
In order to locate points, lines, planes, or other geometric forms, their positions must first be referenced
to some known position, called a
reference point
or origin of measurement. The
Cartesian coordinate
system
, commonly used in mathematics and graphics, locates the positions of geometric forms in 2-D and
3-D space.
A 2-D coordinate system establishes an
origin
at the intersection of two mutually
perpendicular axes, labeled X (horizontal) and Y (vertical).
The origin is assigned the
coordinate values of 0,0. Values to the right of the origin are considered positive, and those to
the left are negative. Similarly, values above the origin are positive, and those below are
negative.
The numbers assigned to each point are called coordinates where the first number is
the X coordinate and the second number is the Y coordinate.
A rectangle is created by using coordinate values for each corner and then drawing the
connecting lines.
In a 3-D coordinate system, the origin is established at the point where three mutually
perpendicular axes (X, Y, and Z) meet.
The origin is assigned the coordinate values of 0,0,0.
A rectangular prism is created using the 3-D coordinate system by establishing coordinate
values for each corner.