Orthographic Projections of Points, Lines and Planes
Reference planes and notation
In first-angle projection, the IS 10714 convention used in India, the object lies between the observer and the plane: the view on VP is the elevation and on HP the plan, with the plan appearing below the elevation when the planes are rotated open. A point above HP has its elevation above XY; a point in front of VP has its plan below XY. Primes mark elevations (a′), plain letters mark plans (a).
Lines
A line has a true length TL, true inclinations θ to HP and φ to VP, and apparent angles α (in the elevation) and β (in the plan) that are always greater than the true ones. A line parallel to HP shows true length in plan; parallel to VP shows true length in elevation; perpendicular to a plane appears as a point in the view on that plane. The horizontal trace HT is where the line meets HP, the vertical trace VT where it meets VP, and for a line inclined to both planes both traces lie on XY produced. The auxiliary-plane and trapezoid methods recover true length from given projections.
Planes (laminae)
A plane figure is drawn true shape in the view where it is parallel to a plane, then given its inclination; when inclined to both planes it needs two stages - edge view first, true shape second.
Worked example
A 70 mm line makes 30° with HP, so its elevation measures 70 cos 30° = 60.6 mm. If it also makes 45° with VP, the plan measures 70 cos 45° = 49.5 mm. Conversely, a 60 mm line whose elevation is 50 mm has cos θ = 50/60, giving θ = 33.6°.
Traps
Quoting the apparent angle α as θ; drawing the plan above XY; assuming HT and VT always lie on XY produced; giving a point in the second quadrant the wrong sign for its distance from VP.