Geometric Construction
& Modeling Basics
Points
• A point represents a
location in space or on
a drawing. It has no
width, height or depth.
• Sketch points by a
short crossbar on a
line, or by a small
cross.
Lines
• A straight line is the
shortest distance
between two points.
• Parallel lines
• Intersecting lines
• Perpendicular lines
Drawing Straight Lines
• Always use some sort of straight edge (Triangle,
ruler, credit card, etc.)
• Line weights must be consistent. Rotating the
pencil as you draw the line keeps the lead tip
width consistent.
• Lines need to begin and end crisply.
• Line intersections must connect and not overshoot.
• Good Lighting is essential to seeing where to draw
lines when using mechanical tools.
Drawing Parallel &
Perpendicular Lines
• Parallel lines are drawn using a straight
edge (can be a triangle) and a triangle. See
Figure 12.19 (pg 146) of text. Straight edge
must not move.
• Perpendicular lines are drawn with same
instruments.
Practice!
• Draw 3 parallel lines 6” long and 1.5” apart, p146
• Construct a perpendicular bisector to the bottom
line using a compass, p144
• Connect them at the ends and midpoint with a
perpendicular line using a triangle
• Draw a random angle 30 – 170 degrees and
construct its bisector, p145
• Do Worksheet 7, parts 1, 2, 5, 6
Drawing Lines at Angles that
are a Multiple of 15 degrees
• Using a horizontal reference and the two
basic triangles, any angle that is a multiple
of 15 degrees can be drawn.
• The angles are the sum or difference of 30,
45, or 60 degrees which can be obtained by
the combination use of the two standard
triangles.
• A protractor may be used to assist in
constructing lines at other angles.
Drawing
Curved Lines
• General curves are
drawn by plotting
points along a line
then using an
irregular curve
(normally a French
curve) or a Spline to
connect the points.
Scales
• Scales are used to measure distances.
• Drawings are often not done at the same
size, or “scale”, as the object being drawn.
• There are many types of scales available.
• The text (p123-128) has a good discussion
(with illustrations) on how to read a scale.
Polygons
• A polygon is any plane
figure bounded by
straight lines.
A Pentagon
Regular Polygons
• Regular polygons have equal angles and
equal sides.
• They are often created and described by
inscribing them in a circle, or
circumscribing them about a circle.
• Hex head bolts are a typical example
Circles
• A circle is a closed curve, all points of which are
equally distant from the center.
• Circumference equals pi times the diameter
pd
C=
Practice!
•
•
•
•
Do Worksheet 6 (see p143, 144)
Do Worksheet 8 (see p147-149)
Do Worksheet 9 (see p150-151)
Do Worksheet 10 (see p152)
Solids
Extruded Solid
• CAD construction for
a 3D part having a
uniform cross section.
• Named for the
manufacturing process
of forming material by
forcing it through a
shaped opening.
Revolved Solid
• construction by
revolving a uniform
cross-section along a
circular path.
Boolean Operators
• Venn diagrams can be
used to show Boolean
operations.
• Union (addition)
• Difference (subtraction)
• Intersection
Boolean Operations
of Solids
Summary
• Points, lines, and circles are the basic geometric
elements used to make 2D sketches.
• Using CAD you can create 3D models.
• Understanding geometric solids can help you
create CAD models and interpret and visualize
from 2D sketches and drawings.