Orthographic Projection of Lines

1
Orthographic Projection of Lines

• Definition A line may be defined as the path
  or locus of a point moving through space.
• A straight line segment is the shortest distance
  between its end points.

2
Classification of Lines

• Lines are classified according to the plane or
  planes of projection to which they are parallel.
• The classifications are Horizontal, Front,
  Profile, Vertical, and Oblique, lines.

3
Classification of Lines

• A Horizontal line is parallel to the Horizontal
  plane of projection.

4
Classification of Lines

• A Front line is parallel to the Frontal plane of
  projection.

5
Classification of Lines

• A Profile line is parallel to the Profile plane
  of projection.

6
Classification of Lines

• A Vertical line is parallel to the Frontal and
  Profile planes of projection.

7
Classification of Lines

• A Oblique line is not parallel to any of the
  principal planes of projection.

8
True Length of a line

• An Oblique line can not be measured in either of
  the given views because it is not true length.

9
True length of a line

• The true length of any line in space is found
  only upon a plane of projection parallel to the
  line.
• We must locate a hinge line parallel to one of
  the oblique lines and project it into that plane.

10
True Length of a line

• Place the hinge line parallel to FH and GH.

11
True Length of a line

• Project perpendicular to the Auxiliary 1 plane.

12
True Length of a line

• Locate F1 and G1 in the auxiliary plane.

13
Point View of a Line

• The Point View of a line is found on a plane that
  is perpendicular to the true length image of the
  line.

14
Point View of a Line

• Construct a hinge line perpendicular to the TL
  line and project into that plane.

15
Point View of a Line

• Project perpendicular to the hinge line.

16
Point View of a Line

• Measure distance from a Related Plane.

17
Bearing of a Line

• Bearing is the deviation of a line from the
  North-South direction.
• We will define the bearing as the acute angle
  between the line and a North-South line through
  the origin of the line.
• The bearing of a straight line can be measured
  only in the horizontal projection of the line.
• We will select the origin point of a line
  alphabetically. For example, given line AF,
  BFAF would be the origin because it comes first
  in the alphabet.

18
Bearing of a Line
19
Bearing of a Line
N 30 E
Origin
20
Bearing of a Line
N 72 W
Origin
21
Bearing of a Line
S 14 E
Origin
22
Bearing of a Line
S 51 W
Origin
23
Angle of a line.

• Inclination is the deviation of a line from the
  horizontal.
• The inclination of a line may be measured only in
  an ELEVATION view which shows the line in TRUE
  LENGTH.
• The elevation views are F, P, and any auxiliary
  view hinged to the Horizontal plane.
• Inclination is expressed as slope angle, slope,
  and percent grade.

24
Angle of a line.

• The angle is positive () if inclined upward or
  negative (-) if inclined downward from its
  origin.
• The Slope Angle of a line is the acute angle
  formed between the TL image and a horizontal
  plane through its origin.

25
Angle of a line.

• The angle is positive () if inclined upward or
  negative (-) if inclined downward from its origin.

26
Angle of a line.

• The angle is positive () if inclined upward or
  negative (-) if inclined downward from its origin.

27
Angle of a line.

• Can the angle of line D,C be obtained from the
  given views?

28
Angle of a line.

• ANSWER No. The line is in an elevation plane
  but is not from a TL line.

29
Angle of a line.

• The true angle of a line can only be measure from
  an elevation plane and a TL line.

NOT TL
30
Angle of a line.

• An Oblique line can not be measured in either of
  the given views because it is not true length.

31
Angle of a line.

• Find TL in auxiliary plane 1. Measure from a
  horizontal line.

32
Slope of a line.

• SLOPERISE RUN
• Slope is the tangent of the slope angle

33
Slope of a line.

• Find TL in auxiliary plane 1. Measure from a
  horizontal line.