fundamentals of descriptive geometry

Fundamentals of Descriptive Geometry

Department of Applied Technology And Technology Management

September 9, 2013

Point View of a Line

• What you see when you look down the length of a line.

• Experiment:– Take a pencil and

look at it from various directions, keeping in mind the rotations between line of sight directions.

Principles of Descriptive Geometry Rule #2

If the line of sight is parallel to a true-length line, the line will appear as a

point view in the adjacent view.

CorollaryAny adjacent view of a point of view of

a line will show the true length of the line.

Points on a Line

• If a point is on a line, it will appear on the line in all views and be at the same location on the line.

Not All Points that APPEAR to be on a Line actually are!

• Two orthographic views are required to see where any given point lies.

Planes

• Planes are surfaces that can be uniquely defined by:– Three non-linear points in space,– Two non-parallel intersecting vectors,– Two parallel vectors, or– A line and point not on the line.

Plane Definitions

Plane Classifications

• Planes are classified as– Horizontal– Vertical

• Profile• Frontal

– Inclined (perpendicular to a principle plane)– Oblique (not perpendicular to a principle

plane)• Horizontal and Vertical planes are principle

planes.

Examples

• Orthographic representations of planes as they appear in the principle views

Principles of Descriptive Geometry Rule #3

Planar surfaces of any shape always appear either as

edges or as surfaces of similar

configuration

Principles of Descriptive Geometry Rule #4

If a line in a plane appears as a point, the plane appears as

an edge

Principles of Descriptive Geometry Rule #5

A true-size plane must be perpendicular to the line of sight and must appear as an edge in all adjacent views.

Drawing a Plane in Edge View

A Corollary to Rule #5

If a plane is true-size then all lines in the plane are true

length and all angles are true.

Finding the Angle Between Two Intersecting Planes

• The key is to create a view where BOTH planes are in edge view.– The common line between the planes is the

intersecting line. – Create a view where the intersecting line

appears as a point.• Start by drawing a view of the line in true length• Then draw the desired view.

Finding an Angle