Descriptive Geometry: Orthographic and Auxiliary Projection
Descriptive Geometry: Orthographic and Auxiliary Projection
This domain tests spatial reasoning: finding true lengths, true shapes, inclinations, traces and intersections that are foreshortened in the principal views. Auxiliary projection is the main tool for solving these problems without calculation.
Core rules
- Start with the reference line XY separating plan and elevation. Project every point perpendicularly between views.
- An auxiliary plane is chosen perpendicular to one principal plane and inclined to the other. Its reference line is parallel or perpendicular to the relevant feature in the view it is derived from.
- A line shows true length when the viewing plane is parallel to it. Its inclination to a principal plane appears only in a view where that plane is seen as an edge.
- Transfer heights from the elevation, or depths from the plan, perpendicular to the new reference line; never scale them by eye.
- Mark traces where a line or plane meets HP or VP, and label all projected points consistently.
Worked example
Line AB is inclined to both HP and VP. Its plan is ab and elevation is a′b′. To find true length and inclination to HP, draw X1Y1 parallel to ab. Project from a and b perpendicular to X1Y1. Transfer the height of a′ above XY onto the projector from a, and the height of b′ above XY onto the projector from b. Join the new points: this auxiliary view shows AB true length because the auxiliary plane is parallel to the line. The angle between the true-length line and X1Y1 is the inclination to HP.
Traps that cost marks
Treating the plan length as true length, drawing the auxiliary reference line at the wrong angle, transferring heights from the plan instead of the elevation, projecting in the wrong direction, and omitting traces or labels.