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# 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.

Initial set of boundary lines -red color. Prototype surafaces shown by grey color.

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.

Initilal bondary lines apprimation (four control points).

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.

Initial itteration surface based on boundary lines.

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.

Initial distribution of the surface control points.

Corrected control points position.

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.

Increase number of points on stem line.

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.

Distribution of surface control points after adding five points to stem line.

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.

Distribution of surface control points after addin five points on flat side line.