Surveying

A rising (ascending) curve indicates cut (excavation), while a falling curve indicates fill (embankment).

A point where the cumulative curve crosses the balance line (zero ordinate), meaning cut equals fill between that and the previous balance point.

Volume = L × (A1 + A2)/2, where A1 and A2 are cross-sectional areas at two stations a distance L apart.

A bearing is an acute angle (0–90°) from north or south toward east or west (e.g., N45°E); an azimuth is a clockwise angle (0–360°) measured from north.

S45°E. Since 135° is between 90° and 180°, bearing = 180° − 135° = 45° in the southeast quadrant.

The back bearing has the same angle but opposite quadrant letters (N↔S and E↔W); equivalently the back azimuth differs by 180°.