The process of editing the shape of a surface patches is similar to editing a curve. The difference is that the surface case is a two-dimensional case. The points of the control polyhedron affect a certain region of surface variation and are somewhat farther from the surface than in the case of the line. In the case when there is a sufficiently large number of control points on the surface, a change in the position of one control point leads to a local change in the shape of the surface.
To edit a surface, just click inside the surface contour formed by the boundary lines. After selecting the surface for editing, the points of the control polyhedron will appear. Modification of the position of the points of the control polyhedron is the main method of smoothing the surface. Only internal points of the control polyhedron are available for editing. The corner points of the control polyhedron can only be modified by changing the position of the corner point of the surface contour. The same can be said about the boundary points of the control polyhedron. Their position depends on the shape of the boundary curve and changes only when the boundary curve changes.
Change the position of the corner points of the surface.
As was shown in the case of editing the line, the points of the line and the surface form a single topological system. Therefore, as in the case of editing the end point of a line, editing the corner point of the surface will change the shape of the boundary lines and the surface. Changing the shape of the surface in this case depends on the mode of changing the shape. So the figure below shows the change in shape in the mode:
In this case, only the position of the end point of the lines and the corner point of the surface changes.
If the following form editing mode is selected:
The position of all control points adjacent to a given point of the lines and all control points of the surface, except for opposing boundaries, will be recalculated according to a linear law.
In the case of the following editing mode:
The tangents at the end points of the boundary curves and the tangents at the modified surface boundaries will be unchanged. All intermediate points of the curves and the surface area will be recalculated linearly.
This mode is convenient to use if you need to change the position of the corner point, but at the same time keep the tangents of the surfaces in connection to this point.
Also, as in the case of line modification for a surface, you can set the modification mode of part of the surface.
The following settings will result in partial surface modification.
As can be seen from this example, only part of the control points of the surface changes.
Changing the shape of the boundary line of the surface.
A change in the shape of the boundary curve affects the change in the position of the points of the control surface polyhedron similarly to the change in the corner point. So with the same editing mode settings as in the previous case, the result will be like this.
It is important to note that when changing the shape of the boundary curve, all surfaces based on this curve will be changed in accordance with the selected editing mode. In this case gaps at the boundary of two surfaces does not occur.
Changing the position of the points of the control surface polyhedron.
In order to start editing the surface, just click by the mouse inside the contour formed by the boundary lines of the surface. Changing the position of the points of the control polyhedron will lead to a change in the shape of the surface.
The control surface polyhedron is similar to the control line polygon and has similar properties. Let's consider some of them:
- Locality of surface changes. In the case of a sufficiently large number of points of the control polyhedron, a change in the position of one of them will lead to a local change in the surface shape.
- Tangent to surface boundaries. The surface shape near the boundary, the tangents, and the slope angles are determined by the points of the control polyhedron closest to the boundary.
- The planes. If all points of the control polyhedron belong to the same plane, then the surface is a plane.
- Cylindrical and conical surfaces. And if all the rows of control points in one direction are on a straight line, then the surface will be a cylinder or a cone depending on the shape of the opposite borders.
- Properties of the convexity of the control polyhedron. The convex control polyhedron defines a convex surface area without dents or kinks.
As well as for the points of the control line polygon, for the surface there are several different ways to modify the control polyhedron. The simplest is to change the position of one control point. In this case, the editing mode should be set as follows:
The following shows editing one control point.
If the surface has a sufficiently large number of control points and is already smoothed, you can edit the group of control points. In this case, the changes will affect not only the point selected for editing, but also the group of points around this point.The position of these points is calculated from the condition of maintaining maximum surface smoothness. To edit a group of points, select the following mode:
As in the case of editing a group of points on a line, the S: 1 parameter means how many rows of points around the selected point will change during editing. So, in our example, this is one row of points.For the convenience of the user, the lines connecting the editable points are highlighted in a different color.
It is also important to note another feature of this surface editing method. Often, when editing a group of points, it is possible to erroneously change the coordinates of points adjacent to the boundary of the surface and determining the tangentcy in connection with another surface. If the following mode is enabled when editing a group of surfaces, the points adjacent to the surface boundary will not be edited.
Changing the shape of the surface when changing the position of the points of the control polygon is dynamically displayed on the screen. As mentioned earlier, the surface shape can be represented as lines of equal parameter, orthogonal sections, and painted surfaces. Each of these views changes dynamically. In addition, for the editable surface, the graphs of curvature of the orthogonal sections and the inflection line along the frames, waterlines and buttocks can be visualized. The curvature plots and the inflection lines also dynamically change when the position of the control points changes. This allows you to quickly control the shape of the surface.
You can display a graph of the radii of curvature and inflection lines using the following command:
Or from the Modify toolbar:
In the Options menu, enable the following options.
If these options are enabled, inflection lines and curves of curvature will appear for each surface that is currently being edited.
Below is an example of visualization of inflection lines and a graph of the curvature of the sections.
The program provides a fairly wide set of commands for operations with points of the control surface polyhedron. Commands for smoothing the surface, editing the area of control points or straightening the series of control points of the surface are described in the User Guide. Here, we will look at these commands as needed.
Smooth connections of surface patches.
Sometimes, in the process of surface modeling, it is required to smoothly join the patches together. The example below shows that the surface section of the aft end of the hull should be smoothly connected with the surface of the fore ship along the midsection frame. Before joining surfaces, it is necessary to make a smooth connection of the longitudinal lines to each other. In our case, these are the lines of a flat side and a flat keel bottom. Commands for smoothly connecting lines to each other were described in the here. Another necessary condition for smooth joining of two surfaces is the common boundary line.
For smooth joining of surfaces along a common border, we use the following command.
Or from the Modify toolbar:
In the dialog box that appears, select the following option.
After this, it is necessary to indicate the common boundary lines of the surface and the abutting surface. After that, the control points closest to the common border will be set in such a way as to ensure smooth joining of these surfaces.
Straightening a number of surface control points.
One of the most common problems when modeling flat or ruled surfaces is the problem of straightening a series of control points in one direction.The example below shows the location of surface control points before straightening.
To straighten the series of control points, we use the following command.
Or from the Modify toolbar:
Select the appropriate options in the dialog box that appears.
After that, you need to click on the lines connecting the two control points in order to show the direction of straightening. The location of the control points after straightening in the longitudinal direction is shown below.
As mentioned earlier, the condition for constructing a ruled surface is straight parametric lines in one direction. The straightening of the series of control points allows us to achieve this. If you want to quickly straighten a series or part of control points only on the current projection, you can click on one of the points with the mouse and hold the Ctrl key, then click on the second point. After that, a series of points between the selected points will be rectified on this projection.
Smooth mating surfaces with orthogonal planes.
In the practice of modeling ship surfaces, it is often required to smoothly join curved surfaces, for example, the nasal extremity, with the surface of a flat side and a flat bottom. To do this, you can use the method of joining two surfaces that was described earlier. The example below shows a flat side area on a hull projection. The image is compressed 10 times along the vertical axis. In order to smoothly dock the surface of the nasal extremity with a flat side, it is necessary to set the vertical tangents to the flat side line. The easiest way is to click the mouse with the Ctrl key pressed on each line between the boundary point and the surface control point closest to it. At this position, the control point will be changed so that the tangent in this area of the surface will be vertical.
The result after editing control points of the surface in the area of a flat side.The image is compressed 10 times along the vertical axis.
Smoothing surfaces.
Smoothing surfaces is the most time-consuming process, which consists in distributing points of the control surface polyhedron in such a way as to satisfy the conditions for approaching the starting points or lines and, at the same time, maintain the required smoothness and manufacturability. For the most part, the smoothing process is manual movement of control points. The program also provides several different teams that automate this work, where possible.
Most of these commands are showed when the next command is called.
Or from the Modify toolbar:
As you can see from the dialog box that appeared when you clicked this command, there is a fairly large set of functions for smoothing the control surface polyhedron. The system allows you to smooth out the area of control points, as well as a series or rows of control points.However, in some cases, you can save one of the projections without changing. All these methods will be discussed in more detail later.
For now, we restrict ourselves to the smoothing methods available by hot buttons. If you click on one of the control points of the surface while holding down the Ctrl button and then select the area for changing control points, the system will recalculate the position of the control points inside the selected area as interpolation from the borders of the selected area. If you click on one of the control points of the surface with the Shift button pressed and then select the area for changing the control points, the system will try to find the position of the control points at which the deformation energy is minimal. It should be noted that this method of smoothing does not apply to control points closest to the boundaries of the surface. This method works better if a sufficiently large number of control points are selected.
Visualization of the graph of the curvature of cross sections and inflection lines.
Controlling the shape of a surface during editing is very important. To do this, the system provides visualization of the graphs of the curvature of the cross sections and the bend line of the surface with an orthogonal section. This information provides a visual indication of surface quality. As well as sections, the curves of curvature and the inflection lines dynamically change when the position of the control points of the surface changes. This gives a clear idea of the correct direction of movement of the control point of the surface. Enabling this mode can also be performed by the following command:
Or from the Modify toolbar:
And by selecting the appropriate mode in the dialog box.
Let's see how this works with the side projection as an example.
The inflection line of the buttocks surface is the red line. On the side projection shown above, any buttocks intersects the inflection line only once. This suggests that none of the buttocks on this surface will have more than one inflection point. The case is shown below when the buttocks have several inflection points in a very small area of the surface. This means that the surface in this area is defective.
You can remove such a surface defect by changing the position of the control points in this area as shown below.
Note that on any of the projections, all the inflection lines are shown along the frames, along the waterlines and along the buttocks. This allows you to control the shape of the sections across all three projections. It should be noted that, in general, the inflection lines are not smooth. This is because the system uses third-degree B-spline surfaces, for which the smoothness condition of only the first and second derivatives (the angle of inclination and curvature at each point on the surface) is satisfied. The inflection lines are a representation of the third derivative for which the smoothness condition is not satisfied. But, as experience shows, the smoother the inflection lines - the higher the smoothness of the surface. A significant change in the shape of the inflection line can be achieved even with a slight change in the position of the control points. Therefore, when modifying the position of control points, it is recommended to use scaled cursor movement. Often moving the control point a few millimeters is enough to change the shape of the inflection line. Kink lines are a simple and reliable means of controlling surface quality. The correct location of the inflection lines on the surface guarantees the absence of undulation on any sections of this surface. Work with kink lines will be discussed in more detail later. The following is an example of visualization of the curvature of the frames and the inflection line for frames, waterlines and buttocks.
