# Fore ship surface approximation.

**Smoothing surfaces is the most difficult task** when modeling the surface of the ship’s hull. The very name of the sculptural surface suggests that modeling of such surfaces takes a lot of time and effort. It is mostly manual work on changing the position of control points and boundary lines to get required result.

Before proceeding directly to smoothing, let us dwell on the properties of the surface shape depending on the shape of the control polyhedron:

- the tangents to the boundary curves depend on the position of the control points adjacent to the boundary. - the location of the area of points on the plane defines a flat area of the surface. - a convex polyhedron guarantees a convex surface without dents. - coincidence of a row of three control points gives a knuckle line on the surface. - the shape of the surface at the corners strongly depends on the tangent boundary curves in this area. In the future, this will be the subject of separate consideration.

The most complex surface of the hull is the fore ship. Smoothing is recommended to start with this surface. Let us consider this on the example of the fore ship of a fishing vessel with bulbous bow.

As a prototype, we choose a preliminary surface defined by a set of frame lines and a large number of patches of the Bezier surface.

Let us select the following lines as the boundaries of the fore ship surface: the bilge radius line, the flat bottom line, the stem line, the upper deck line, passing into the flat side line. The last line is set so due to the restriction on the number of surface boundary curves.

It is recommended to use the minimum set of control points at the initial stage of surface definition. Since the number of points on the surface depends on the number of points on the boundary curves, it is not necessary to add many points on the curves and approach the desired result before the surface is set. A large number of points on the surface will make the work on the initial smoothing very time consuming.

The very first approximation is 4 control points on each curve.

We form a bilge radius curve more or less precisely because the shape is very simple. The flat bottom line also usually has a simple form for definition by the four control points. The line of the stem can be defined very approximately at the initial stage. Do not pay much attention to this yet. It only makes sense to set the tangent of the stem to the bottom. The same applies to the flat board line. It is necessary to set the tangent to the midship frame.

After making the lines, the surface is defined by specifying the boundary lines along the contour. The control surface polyhedron has only four control points.

Pay attention to the number of points of the polyhedron closest to the line of the bilge radius. It is necessary to set a number of control points strictly vertically position. The next row of points should look like something between the previous row and the stem. This is achieved by changing the position of the corresponding control points of the flat side line and the flat bottom line. Then a series of control points of the surface can be simply straightened, preserving the shape of the projection “Front”.

The correct location of control points is very important at the initial stage of work. Subsequently, when adding new control rows of control points, the system will take into account the previous location of control points. This will significantly speed up the smoothing process in subsequent stages.

After that, you can increase the number of control points on the stem curve to 5. This will give more degrees of freedom to approach the desired shape of the curve and accordingly increase the number of points on the surface. An important property of the surface should be noted - when adding a control point on the boundary line, the shape of the line and the shape of the surface remain unchanged. When modifying the shape of the curve, it is better to use the mode without surface modification. In this case, the points of the control polyhedron remain unchanged.

As shown above, even with the use of five control points on the curve, it is possible to fairly accurately describe the shape of the stem contour. It is recommended to use “magic” numbers when adding control points, as described in the section “Useful Tips on Surface Modeling.” This will significantly reduce the complexity of the process of smoothing the surface.

When editing the position of surface control points, try to position them evenly with respect to neighboring points. A beautiful and even distribution of control points will also help to quickly achieve the desired result. Never increase the number of control points on a surface before all the possibilities have been used to achieve the desired result with the existing set of control points. The next step is to increase the number of control points to 5 on the flat side line and, as far as possible, bring the shape of the boundary curve to the prototype. Additional control points on the surface can be used to more closely approximate the prototype.

This process is repeated several times with a successive increase in the number of points and the refinement of the shape of the boundary curves and the surface.

The whole process of smoothing the surface can be divided into three parts:

- approximation to the desired shape of the body. This may be an approximation to the prototype or to other source data. At this stage it is necessary to control not only the deviations from the prototype and the shape of the surface, but also the location of the points of the control polygon. A uniform and natural distribution of control points will give advantages in smoothing at subsequent stages. It is recommended to use a smooth distribution of lines of control points along the hull approximately repeating conventional streamlines around the hull. In the cross-section of the rows of control points is better to try to put in the planes of the frames. At the same time try to avoid the diamond cells of the network of the control polygon. As a rule, such a network configuration is very difficult to smooth. Increasing control points at subsequent stages will increase the complexity of smoothing, if the control polygon is initially set incorrectly.

- the correct distribution of the inflection lines on the surface. Despite the fact that the surface representation of the ship hull has long been a standard, the shape of the hull is traditionally controlled on the basis of the shape of orthogonal sections - frames, waterlines and buttocks. The system provides the ability to visualize inflection in plane of orthogonal sections. Along the inflection lines one can see if, for example, the waterline intersects with the inflection line along the waterlines several times - this means that there are waves on the waterlines in this region. The same with other lines of the hull. The inflection lines clearly show the irregularities of the ship's surface. In contrast to the Gaussian curvature and other methods of studying the shape of the surface of the inflection line, the most informative in our case since almost all the hull structures lie in planes of orthogonal sections.

- smoothing the surface sections along the curvature. Uniform distribution of the surface curvature graphs gives a smoother surface. Often a significant change in the curvature of the surface depends on a very small change in the position of the corresponding control point of the polygon. It is recommended to use the scalable movement of control points. Note also that this helps to maintain minimal changes in the shape of the surface and deviations from the prototype.

Each of the above steps can be repeated with an increase in the number of control points on the surface.

As you can see the definition of the shape of the surface is a sequential, iterative and rather time-consuming process. In the system there are several methods to automate this process:

- editing a group of control points,

- interpolation of the area of control points,

- smoothing the surface area,

- approximation of the surface to the prototype,

- straightening a number of control points.

Despite the various methods, the process of forming the surface still remains largely labor-intensive and manual. The system only simplifies this work and, finally decision is left to the engineer.

The above method is the most common when designing sculptural surfaces. For simpler surfaces like extruding or rotation surfaces, you can use the drivers. If you explode the driver, it becomes possible to edit the driver's surface, like any other surface. As an example, you can use an extruding driver to build the bilge surface of the aft ship. The line of the bilge is pulled out along the line of the flat side. Once the driver is unmounted, you can change the shape of the transom line. The shape of the surface will change according to the specified mode of transformation of lines and surfaces. We will focus on ways to transform the surface later.