Chapter Two Points and Lines

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Chapter Two Points and Lines
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Objectives

• Upon completion of this chapter the student will
  be able to
• Define the following terms point, line, bearing,
  foreshortened line, oblique line, inclined line,
  bearing, azimuth, locus, longitude and latitude.
• Determine the equivalent distance in statute
  miles and feet for a given degree of latitude.
• Determine the equivalent in hours of a given
  degree of longitude.
• Use the AutoCAD commands list, id, and properties
  to determine the location of a point.
• Describe the difference between a bearing and an
  azimuth.
• Determine the bearing and azimuth of a given
  line.
• Convert from bearings to azimuths and from
  azimuths to bearings.
• Use AutoCAD to determine the bearing and azimuth
  of a line.

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Introduction to Points and Lines

• All objects, whether they are man-made or the
  result of natural conditions and/or forces,
  contain points and lines.
• They are the basic building blocks for all two-
  and three-dimensional objects.
• Both points and lines have been widely studied in
  almost every technical field.

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Latitude and Longitude

• This grid network provides worldwide coverage and
  consists of a system of meridians and parallels
  known as lines of longitude and latitude.
• Meridians are lines of longitude that run
  north-south
• The meridian passing through Greenwich, England,
  is 0 longitude or the prime meridian.
• Measurements can be made east or west of the
  prime meridian and range from 0 to 180.
• Lines of longitude west of the prime meridian are
  designated by the letter W, or prefaced with a
  negative () sign.

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Latitude and Longitude

• Longitude and latitude are measured in degrees,
  minutes, seconds (DMS).
• Each degree is made up of 60 minutes, and each
  minute contains 60 seconds.

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Latitude and Longitude
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Bearings

• Angles will vary from 0 to 90.
• Require a reference plane at the beginning and
  end.
• Are measured from either a clockwise or counter
  clockwise direction.

The bearing in the above figure is N60E
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Azimuths

• Angles will vary from 0 - 360.
• Require only a numeric value, they are assumed to
  be referenced from due north unless otherwise
  specified.
• Are measured only in the clockwise direction.

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Converting from Bearing to Azimuths
Using North as a Reference

• For all lines in the first quadrant the angle
  associated with the bearing will be the same for
  the azimuth.
• For all lines in the second quadrant the azimuth
  is calculated by subtracting the bearing from
  360.
• For all lines in the third quadrant the azimuth
  is calculated by adding the bearing to 180.
• For all lines in the fourth quadrant the azimuth
  is calculated by subtracting the bearing from
  180.

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Converting from Bearing to Azimuths
Using South as a Reference

• For all lines in the first quadrant the azimuth
  is calculated by adding the bearing to 180.
• For all lines in the second quadrant the azimuth
  is calculated by subtracting the bearing from
  180.
• For all lines in the third quadrant the angle
  associated with the bearing will be the same for
  the azimuth.
• For all lines in the fourth quadrant the azimuth
  is calculated by subtracting the bearing from
  360.

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Grade

• Is the percentage of inclination between a line
  and the horizontal plane. It is defined as the
  vertical rise of a line divided by its horizontal
  run with the quotient multiplied by 100

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Slope

• Is an angle created between a line and the
  horizontal plane. It is always measured in
  degrees.