2D Geometric Construction and Sketching
Construction logic
Every sketch should be built from a small number of constraints: coincident, horizontal/vertical, parallel, perpendicular, tangent, equal, concentric and symmetric. Use construction geometry and object snaps (endpoint, midpoint, intersection, tangent, perpendicular, centre) instead of eyeballing. Offset, trim, extend and fillet are the main editing tools; a fillet is a tangent arc of known radius, not an approximate curve.
Standard constructions
- Perpendicular bisector: equal-radius arcs from both endpoints; the line through their intersections is the bisector.
- Angle bisector: equal arcs from the vertex, then equal arcs from the two intersection points.
- Tangent arc between two lines: offset both lines inward by R; the intersection is the arc centre; trim to the tangent points.
- Regular polygon: use inscribed (vertices on the circle) or circumscribed (sides tangent) construction; the exam will state which.
- Ellipse: the four-centre approximation is acceptable for pictorial work but not for a true ellipse dimensioned by major and minor axes.
Worked example
Two lines meet at 60° and must be joined by a tangent arc of R20. Offset each line 20 mm toward the angle's interior. The offsets meet at the centre, 40 mm from the vertex along the angle bisector, because the perpendicular distance from the centre to each line must equal R and the half-angle is 30°, so distance = R/sin 30° = 40 mm. Draw the arc between the two perpendicular foot points and trim the lines. Check tangency by confirming the centre-to-line distance is exactly 20 mm.
Traps
Over-constraining a sketch so it cannot rebuild, leaving stray construction lines on the outline layer, using a polyline arc that is not tangent, and rounding coordinates instead of applying a constraint.