Fundamentals of Descriptive Geometry

1. Fundamentals of Descriptive Geometry Department of Applied Technology And Technology Management September 9, 2013

2. 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.

3. 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. Corollary Any adjacent view of a point of view of a line will show the true length of the line.

4. 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.

5. Not All Points that APPEAR to be on a Line actually are! • Two orthographic views are required to see where any given point lies.

6. 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.

7. Plane Definitions

8. 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.

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

10. Principles of Descriptive Geometry Rule #3 Planar surfaces of any shape always appear either as edges or as surfaces of similar configuration

11. Principles of Descriptive Geometry Rule #4 If a line in a plane appears as a point, the plane appears as an edge

12. 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.

13. Drawing a Plane in Edge View

14. 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.

15. 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.

16. Finding an Angle