Single-curved surfaces
are generated by moving a straight line along a curved path such that
any two consecutive positions of the generatrix are either parallel (cylinder), intersecting
(cone), or tangent to a double-curved line (convolute).
A
cone
is a single-curved-surface primitive formed by a line (generatrix) moving along a
curved path such that the line always passes through a fixed point, called the vertex. Each
position of the generatrix is called an element of the surface.
There are three basic classifications of cones:
■
If the axis is perpendicular to the base, the axis is called the altitude and the cone is
called a
right con
e.
■
If the axis is not perpendicular to the base, the cone is called an
oblique cone
.
■
If the cone is cut off, it is called a
truncated
cone or a
frustum
of a
cone.
There are many applications for cones in engineering design, including: the nose cone of
rockets; transition pieces for heating, ventilating, and air-conditioning systems; conical roof
sections; and construction cones used to alert people to construction areas. Cones are
represented in multiview drawings by drawing the base curve, vertex, axis, and limiting
elements in each view.
Conic sections
are 2-D plane figures produced by passing an imaginary plane at various
angles through a solid (3-D) right circular cone.
A
cylinder
is a single-curved ruled surface formed by a vertical, finite, straight-line element
(generatrix) revolved parallel to a vertical or oblique axis directrix and tangent to a horizontal
circular or elliptical directrix. The line that connects the center of the base and the top of a
cylinder is called the axis.
If the axis is perpendicular to the base, the cylinder is a
right cylinder
.
If the axis is not perpendicular to the base, the cylinder is an
oblique cylinder
.
A multiview drawing of a right circular cylinder shows the base curve (a circle), the extreme
elements, and the axis.
A
convolute
is a single-curved surface generated by a straight line moving such that it is
always tangent to a double-curved line.
A tangent plane generation convolute is formed by the path taken by a plane tangent to two
curved lines.
A
polyhedron
is a symmetrical or asymmetrical 3-D geometric surface or solid object with
multiple polygonal sides. The sides are plane ruled surfaces, and are called faces, and the lines
of intersection of the faces are called the edges.
Regular polyhedra
have regular polygons for
faces. There are five regular polyhedrons: tetrahedron, hexahedron, octahedron,
dodecahedron, and icosahedron. As solids, these are known as the five platonic solids.
Regular polyhedra are classified by the shape and number of faces, as follows:
Tetrahedron
. A symmetrical or asymmetrical 3-D surface or solid object with four
equilateral triangular sides.
Hexahedron
. A symmetrical or asymmetrical 3-D surface or solid object with six
quadrilateral sides.

Octahedron
. A symmetrical or asymmetrical surface or solid object with eight equilateral
triangular sides.

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- Fall '09
- Cartesian Coordinate System, Euclidean geometry