Orthographic Projection of Points, Lines and Planes
This domain tests first-angle orthographic projection of points, straight lines and plane surfaces. The exam asks you to place views correctly relative to XY, find true lengths and inclinations, and locate traces.
Points
In first-angle projection the object sits between observer and plane: the front view is above XY and the top view below XY. A point is fixed by its height above HP and distance in front of VP. If A is 20 mm above HP and 30 mm in front of VP, its front view a′ is 20 mm above XY and its top view a is 30 mm below XY. A point on HP has its front view on XY; a point in VP has its top view on XY.
Lines
- Line parallel to both HP and VP: both views true length, parallel to XY.
- Line parallel to HP, inclined to VP: top view true length and shows true inclination; front view parallel to XY.
- Line inclined to both: neither view shows true length. Use the rotating-line or auxiliary-plane method; the true length appears when the line is made parallel to one plane.
- Traces: HT where the line meets HP, VT where it meets VP; extend the views to XY to locate them.
Planes
A plane surface appears true shape when parallel to the plane of projection and as an edge when perpendicular. An inclined plane needs an auxiliary view to show true shape.
Worked example
A line AB, 60 mm long, is parallel to VP and inclined 30° to HP. Because it is parallel to VP, the front view is true length: draw a′b′ 60 mm at 30° to XY. Project down to the top view; since the line is parallel to VP, ab is parallel to XY and its length is 60 cos 30° = 52.0 mm. The reasoning is that the top view foreshortens by the cosine of the inclination to HP.
Traps
Putting the top view above XY is third-angle, not first-angle. Do not mark a view as true length unless the line is parallel to that plane. A line's inclination to VP must not be written in the front view unless the line is parallel to VP.