DESCRIPTIVE GEOMETRY
Descriptive Geometry is the science of
graphic representation and solution of space problems.
Coordinate Systems:
World Coordinates: world axes move
coincident with the created part
Construction Plane Coordinates: relative to
the current construction plane
The lines of intersection of the
perpendicular projection planes are called folding lines
(H/F and F/P)
POINT
Theoretically a point has location only and
no dimensions.
Point in space is represented by a capital
letter (eg. A)
A (x,y,z) , A (80,100,120)
In views of point, identified with
lowercase letter plus the appropriate superscript a^{F}, a^{H},
a^{P}
LINE
In geometry a line theoretically has no
width. The position of a straight line is established by locating any two
noncoincident points on the line.
PLANE
 3 points
 2 intersecting lines
 2 parallel lines
 a point and a line
all the above will represent a plane.
3D OBJECT
intersecting planes form an object. Surface
of objects are limited planes.
INTERSECTION
 Intersection of lines
 intersecting lines (have a common point)
 nonintersecting lines (do not have common
point)
 parallel lines
 skew lines (nonintersecting and nonparallel lines
never form a plane)
 Intersection of planes
 nonintersecing (parallel) planes
 intersecting planes (intersection will be line
of intersection (LI), can be limited or unlimited)
 Intersection of line and plane
(unless a line is in or parallel to a
plane, it must intersect the plane)
The intersection point is called piercing
point.
 Intersection of object and line
 intersecting (piercing points)
 nonintersecting
 tangent (1 piercing point)
 Intersection of object and plane
 intersecting (intersection will be line (LI))
 nonintersecting
 tangent (point or line)
VISIBILITY
An essential step in drawing an
orthographic view is the correct determination of the visibility of the lines
that make up the view. The outline of a view will always be visible, but the
lines within the outline may be visible or hidden, depending on the relative
positions of those lines with respect to the line of sight.
VIEW OF LINE
 True length of a line: A line is shown in true
length, TL, when the line of sight is normal (perpendicular) to the
line.
 Any line of sight not normal to a line results
in a view that is shorter than true length.
POINTS ON LINES
 Any two successive views of a point must lie on
a projection line perpendicular to the folding line between the two
views.
 A point may be said to be above or below, in
front of or behind, or to the right or to the left of another point.
VIEW OF PLANE
 Edge view: The edge view of a plane is seen
when all lines of the plane appear to coincide in a single line (EV)
 Normal view: The normal view (true surface) of
a plane is seen when the line of sight is perpendicular to the plane
(TS)
POINTS AND LINES IN
PLANES
 If a line is known to be in plane then any
point on that line is in the plane.
 A line may be drawn in a plane by keeping it in
contact with (intersecting) any two given lines in the plane.
LOCUS
 A locus is the path of all possible positions
of a moving point, line, or curve.
 The locus of points in a plane and at a
specified distance from a given point is a circle.
 The locus of points in space at a specified
distance from a given point is a sphere.
PIERCING POINTS
 Intersection of lineplane is called a piercing
point.
INTERSECTION OF
PLANES
 The intersection of two planes is a straight
line common to the planes and its position is therefore determined by
any two points common to both planes.
 If a given plane is bounded by a closed figure
then the line of intersection will be limited.
ANGLE BETWEEN PLANES
 The angle formed by two intersecting planes is
called a dihedral angle.
 The true size of the dihedral angle is observed
in a view in which each of the given planes appears in edge view.
 A view showing a point view of a line common to
two planes, the line of intersection (LI), produces an edge view (EV) of
each of the planes.
ANGLE BETWEEN LINE
AND PLANE
 In order to show true magnitude of the angle
between a line and a plane it is necessary to show the line in true
length (TL) and plane in edge view.
COMMON
PERPENDICULAR
 Connecting two skew (nonintersecting and
nonparallel) lines there is only one line which is perpendicular to
both lines.
 Common perpendicular gives the shortest distance
between the lines.
PARALLELISM
Parallel Lines
 Any two lines in a plane must either intersect
or be parallel.
 Lines parallel in space project as parallel
lines in any view except in those views in which they coincide or appear
as points.
 Oblique lines that appear parallel in two or
more principle views are parallel in space.
 Two horizontal, two frontal, or two profile
lines that appear to be parallel in two principal views may or may not
be actually parallel in space.
 The true distance between two parallel lines
may be obtained either by constructing a view showing the lines as
points or by obtaining a normal view of the plane of the two lines.
Parallel Planes
 If two intersecting lines in one plane are
parallel respectively to two intersecting lines in a second plane, the
planes are parallel in space.
 If two planes are parallel, any line in one
plane is parallel to the other plane, since it cannot intersect the
other plane.
 If two planes are parallel, any view showing
one of the planes in edge view must also show the other plane as a
parallel edge view.
Lines Parallel to Planes
 If two lines are parallel, any plane containing
one of the lines is parallel to the other line.
 If two planes are parallel, any line in one
plane is parallel to the other plane, since it cannot intersect the
other plane.
PERPENDICULARITY
 If a line is perpendicular to a plane it is
perpendicular to any line in the plane
Plane perpendicular to line
 A plane is perpendicular to a line if the plane
contains two intersecting lines each of which is perpendicular to the
given lines.
Copyright © 2006 , Middle East Technical University
