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Transcript
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 truelength 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. 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