Projection of Solids and Sections
Positions of solids
Polyhedra (prisms, pyramids) and solids of revolution (cylinder, cone, sphere) are started with the axis perpendicular to one reference plane and the base parallel to the other. The standard resting positions are: on HP on its base; on HP on a base edge or corner; on HP on a generator (cylinder and cone); and freely suspended. When the axis is inclined to one plane and parallel to the other, one tilt is enough; when inclined to both, the change-of-position method is used - tilt the elevation, project the new plan, then rotate that plan.
Sections
A section plane perpendicular to VP and inclined to HP cuts a prism in a polygon whose true shape is found by projecting the cut points onto an auxiliary plane parallel to the cutting plane, or by rotating them. The cutting plane is drawn in the view where it appears edge-on: chain line, thickened at the ends, arrows showing the direction of sight, letters A–A. For a cone, a cutting plane inclined more steeply than the generators gives an ellipse, parallel to one generator a parabola, steeper still a hyperbola.
Worked example
A pentagonal prism of side 30 mm and axis 60 mm rests on HP with its axis inclined 45° to HP and parallel to VP. Draw the plan first with the axis perpendicular to HP (regular pentagon, one side parallel to XY) and the elevation as a 60 mm rectangle. Tilt the elevation about the base corner until the axis is at 45°, project down to a new plan, then finish the elevation with visible and hidden edges.
Traps
Tilting in the plan when the axis is parallel to VP; losing the base-corner pivot and floating the solid; drawing hidden edges as visible after tilting; placing the section plane parallel to HP when a true shape perpendicular to VP is required.