# Easter egg or the final stage of smoothing the ship's hull.

In one of the latest releases of Shape Maker, it became possible to visualize lines of equal angles of inclination of a surface to a vector perpendicular to the projection plane. The number of lines calculated on the surface is specified as the number of sectors dividing a right angle. So if the number of lines is 90, this means that all lines will be shown in one degree increments. This is somewhat similar to rendering a zebra on a surface, but in our case it is rendering lines, not a painted surface. What does this give us and how can it be used to control the quality of our surface? The next picture shows a hemisphere with a radius of 10 meters with the visualization of lines of equal angle.

Accordingly, the lines are concentric circles. Shown below is the same sphere, but one of the points of the control polygon is shifted 10 mm from its original position.

The shape of the lines of equal angle in the region of this point is distorted. That is, on a 10-meter sphere, this allows you to detect a surface roughness of 0.01%. Note also that the movement of the control polygon point is always greater than the movement of the corresponding surface point. This means that the sensitivity of this method is even higher. That is, it is a kind of microscope for studying the smoothness of the surface. Of course, the shape of the ship's hull surface is usually far from spherical, but for controlling the shape of the ship's surface, equal angle lines are very useful. For example, in the area of the bilge radius, the surface of the hull is close to cylindrical and the lines of equal angle should be parallel to each other and evenly distributed over the surface of the bilge. Typically this area is difficult to control using frame curvature plots. The bilge frames differ little from each other and the curvature graphs are superimposed on each other, forming a mess of lines. For a more visual representation of the real shape of these curves, you can use a compressed image along the longitudinal axis.

After a few experiments with lines of equal surface angle, the following can be said:

- to study the shape of the surface along the lines of equal angle, it is necessary that the shape of the surface of the hull is already sufficiently accurately determined,

- lines of equal angle do not define the surface shape as unambiguously as orthogonal sections, but give a good idea of local surface defects,

- surfaces smoothed along lines of equal angle, as a rule, have a smooth change in the curvature of cross-sections,

- the most informative projections for smoothing along lines of equal angle are side and plan,

- for local smoothing, it is better to use the mode of modifying one control point in combination with the mode of moving the cursor into the depth of the projection,

- for better visualization, it is more convenient to disable the lines connecting the points of the control polygon,

- it is not necessary to modify the points of the control polygon, modification of an arbitrary point on the surface is also a very effective method of changing the shape of the surface in this case,

- since this method has a very high sensitivity to changing the shape of the surface, it is necessary to use the mode of scaled movement of the cursor with a division value of 1mm or even 0.1mm.

This will allow very slight changes to the surface shape while still achieving the required smoothness. A close analogue of equal slope lines is a method of surface quality control based on reflections on the surface of parallel stripes with equal steps. This control method is also used in modeling the surface of cars. You can try to use this method to control the quality of yacht surfaces. Of course, it would be naive to believe that the mathematical model will be exactly replicated in the steel hull of a new yacht, without distortion and deformation. I am of the opinion that a correctly smoothed surface will still significantly reduce the work of manually smoothing, sanding and painting the yacht's hull. I think that for the hulls of large ships this method will help to improve the quality of the hull surface.