The lines plan (lines drawing) consist of projections of the intersection of the hull with a series of planes. The planes are equally spaced in each of the three dimensions. These set of planes are mutually perpendicular or orthogonal in nature.
The point of intersection of these planes with the hull results in a series of lines that are projected onto a single plane located on the front, top, or side of the ship. This results in three separate projections, or views, called the Body Plan, the Half-Breadth Plan, and the Sheer Plan.
To visualize, place the ship in an imaginary rectangular box whose sides touch the keel and sides of the ship. The bottom, side and front of the box will serve as the basis for three orthogonal projection screens on which lines will be projected onto. The lines to be projected result from the intersection of the hull with planes that are parallel to each of the three orthogonal planes mentioned.
Planes parallel to the front and back of the imaginary box are called stations. There are three important stations. The intersection of the stem of the ship at the design water line is called Forward Perpendicular (FP). The intersection of the stern at design waterline(immersed transom) or the rudder stock is called the Aft Perpendicular (AP). The station midway between the perpendiculars is called the midships stations.
Each station plane will intersect the ship's hull and form a curved line at the points of intersection. These lines are called sectional lines and are all projected onto a single plane called the Body Plan.
The body plan takes advantage of the ship's symmetry. Hence only half the section is show; the sections forward of amidships are drawn on the right side, and the sections aft of the amidships are drawn on the left side. The amidships section is generally shown on both sides of the body plan. The vertical line in the center separating the left and right half of the ship is called the centerline.
The bottom of the box is a reference plane called the base plane. The base plane is usually level with the keel. A series of planes parallel and above the base plan are imagined at regular intervals, usually at every meter. Each plane will intersect the ship's hull and form a line at the points of intersection. These lines are called waterlines and are all projected onto a single plane called the Half-Breadth Plan.
Each waterlines shows the true shape of the hull from the top view for some elevation above the base plane.
The water lines referred to here has nothing to do with where the ship actually floats. There waterlines are the intersection of the ship's hull with some imaginary plane above the base plane.
Since ships are symmetric about their centerline they only need be drawn for the starboard or port side, thus the name Half-Breadth Plan.
A plane that runs from bow to stern directly through the center of the ship and parallel to the sides of the imaginary box is called the centerline plane. A series of planes parallel to one side of the centerline plane are imagined at regular intervals from the centerline. Each plane will intersect the ship's hull and form a curved line at the points of intersection. These lines are called buttock or butt lines and are projected onto a single plane called the Sheer Plan.
Each buttock line shows the true shape of the hull from the side view for some distance from the centerline of the ship. The centerline plane shows a special butt line called the profile of the ship.