# Developable Plate Ruling Line Example

Stephen M. Hollister

New Wave Systems, Inc.

www.newavesys.com

This example or tutorial covers the following topics: reverse engineering (getting existing geometry data into the program), fairing or smoothing curves, creating developable surfaces using our unique dynamic ruling line capability, and plate layout or development. If you are new to computers or new to computer-aided design, you should really start with another of our tutorials, called “CreateBoat”. The CreateBoat tutorial covers the easiest way to start a boat design process using the principal dimensions of the boat. This tutorial covers most all of the other ways of defining your shape.

This tutorial describes how I recreated a traditional rowing dory whose offsets (defining data points) were taken from Skene’s Elements of Yacht Design, by Francis S. Kinney (Eighth Edition, 1973, pg 47). This rowing dory is 12 feet long and consists of three surfaces or panels and four edge curves: the sheer or deck edge, the upper chine, the lower chine, and the keel line. Each edge curve is defined by a series of [X,Y,Z] points (offsets). X is a measurement along the length of the boat (starting at the bow or the forward end of the waterline and increasing towards the stern), Y is the half breadth or width measurement, and Z is the height measurement. It was designed (before computers) to use plywood for construction.

## Reverse Engineering or Geometry Input

These are the things you can do if you have an existing shape (or idea of a shape) that you wish to get into the program.

First, you can read in the geometry data from another program using a standard transfer file format. Our programs accept DXF, IGES, and TXT file input. The TXT or text file input can be used to transfer geometry from a spreadsheet to our program. Also, if you have one of our boat design programs (ProSurf , ProBasic, or ProChine), you can read various standard hull offsets files, like GHS, NWS, OFF, and SHCP. These files use offsets to define a series of stations or sections along the length of the hull.

The DXF file is one that is defined by Autodesk for their AutoCAD program. It has become a standard way to transfer simple geometry like points, lines, polylines (a polyline is a series of points connected by straight lines), and curves. The IGES (Initial Graphics Exchange Specification) file format is more complete than the DXF format and can be used to transfer more complex geometry like NURB surfaces.

If you have your geometry in another program and you want to get it into one of our programs, look to see if your program can output your geometry into an IGES or DXF format file. If so, then try one of those formats to see if you can read it into our program. You can check our manual in the “Help” section of the program under “File” to find out all about each of these formats. Call us if you need further help.

If your geometry data is in a spreadsheet or if you have your own special application that creates the geometry, then you want to look at our own TXT file format that is easy enough for anyone to understand and use. [See also our article called: Reverse Engineering 3D Computer Hull Shapes From 2D Lines Drawings and Offsets Tables, which includes an example of transferring geometry from a spreadsheet to our program.]

For example, the following picture shows the partial contents of a TXT file (in our format) that defines two polylines (connected points) in three dimensions (using X,Y,Z]. The first line of the file has the label “PLINE3D”. The second line states the number of points as: “Npts= “. The following lines contain each of the X,Y,Z points of the polyline, one point per line using blanks to separate the numbers. Blank lines are ignored and you can put as few or as many geometry definitions in the file as you want. The “Help” command in the program under File explains all of the input and output file formats in detail.

### Example of our TXT file for geometry input

Second, you can input the data directly by typing in the numbers. Whenever the program is asking for you to pick the left mouse button to define a point (a point entity, a curve or polyline point, or a point on a surface), you can instead type in the [X,Y,Z]  coordinate with the keyboard using the following format:

X,Y,Z

For example:

2.5,3.732,1.5

… to define a point at X=2.5, Y=3.732, and Z=1.5

As you type in these numbers they will appear on the status line at the bottom of the screen and the program will use that point when you press the enter key. This method is useful if you have a limited set of coordinates or offsets that you want to get into the program. You could do many input points this way, but you might find it easier to use a text editor, like NotePad or a spreadsheet, like Excel.

A variation of this technique is to first define the curve using the number of points for which you have offsets or coordinates. Then you can pick each point using the right mouse button and a dialog box will appear (see below) showing the current X,Y,Z values for the point and allowing you to change or set the new, desired value.

This dialog box appears when you right click on an edit point.

If you have a lot of points to enter, then typing them into a text file with NotePad using our TXT format is probably the fastest method.

Third, you can input the geometry using a 2D digitizer tablet if you have a paper drawing that defines the geometry. 2D digitizers come in all sizes, but the most common one is approximately 12” X 12”. You tape your drawing to the digitizer and enter the curve shape into our program using your drawing as a template.

Fourth, you can use a 3D digitizer arm (MicroScribe, Faro Arm, etc.) to directly get the shape into our program. Most of these 3D digitizers can generate a text form of the digitized point that can be passed to our program. Our program will treat the point values exactly the same as if you typed in the values.

Fifth, you can use 3D scanners (laser or otherwise) to generate a cloud set of points that define the shape of the object. The problem is that these techniques usually generate hundreds, thousands, or even millions of points on the object. Our program can read these points, but you still have to fit the curves and surfaces to these points manually. This can be done by snapping cross-section curves to some areas of the cloud of points and then fitting a surface to these curves. This is more tedious than automatic surface fitting techniques, but you end up with surfaces that you can use to do fairing, smoothing, or other shape alterations.

## Starting the Program

Double click the program icon on your desktop. The default display shows four screens for four different views of the model. Although this was recommended to me as being the common CAD approach, I like to work with one large view at a time. That is why I always delete 3 of the 4 windows and maximize the last one. (Actually, you can set this one window display as the default display by changing the “Set4Views” parameter in the program’s “INI” file to “n”. Many programs have “INI” files for setting default program values. Look for the ProSurf.ini, the ProBasic.ini, or the ProChine.ini file in your Windows folder.

This is what the program looks like with only one (empty) view on the screen.

The data that I need to get into the program is from an offsets (coordinates) table in the eighth edition of Skene’s Elements of Yacht Design (1973), on page 47. Unfortunately, the coordinate values are defined using feet-inches-eighths and I had to convert them all to decimal feet. I have a simple program to do that, but I still had to type them all in by hand. The end result is the TXT file shown above containing the 4 chine curves for the boat. These curves define the edges of each of the panels that will be used to create the boat. This boat was designed to use developed plates, so we will see what the program says about the developability of these panels.

## Reading in the Geometry Data

I used the File-Data File Input-TXT File Input to read the TXT file. The result of this file read is shown below.

### Section, Right, or Bodyplan View of Curves

Remember that the TXT file contained polylines, which are a series of coordinate points that are connected by straight lines.

NOTE - Our program uses the term “curves” to refer to any combination of curve and polyline. Most CAD or drawing programs define separate entities or geometry types for polylines and curves. This makes it difficult to deal with shapes that are a combination of smooth, curved portions and hard, knuckle points. It also means that you have to create, edit, and delete these entities separately. Our program assigns a special indicator for each edit or defining point that tells the program whether the line passes through the point like a smooth curve (or batten) or as a hard knuckle point. If all of the points are defined as hard knuckle points, then the “curve” is a polyline. If all of the points are defined as smooth curve points, then the “curve” is a smooth curve.

It is very simple for the user to change the smoothness indicator value of any curve defining point with just one command. This is done with the Curve-Knuckle Pnt command. If you use this command to “click” on an edit point, it will toggle the status of that point back and forth between being a smooth curve point and a hard polyline point. When you use the Curve-Add Curve command, the points will be entered as smooth curve points. You can override this by using the ‘k’ (knuckle) key to “pick” a point rather than using the mouse button. If you use the Curve-Add Polyline command, the points will be entered as hard knuckle points. You can override this by using the ‘c’ (curve) key to “pick” a point rather than using the mouse button. After you create the curve, you can still change the smoothness status of any point using the Curve-Knuckle Pnt command. You are not stuck with the values you used when you created the curve. Often, users will define a rough shape of an object using a simple polyline. Afterwards, the user will selectively convert some of the hard, knuckle points to smooth curve points while doing the final shaping and fairing. There is no need to deal with more than one geometric entity as in most other CAD programs.

## Editing and Fairing the Curves’ Shapes

As shown below, try moving one of the points (see the Move Pnt command on the toolbar) to see that everything is connected by straight lines; not curves. This is something you always have to watch out for, since many programs transfer the shape of curves (via DXF, IGES, etc.) as polylines defined with very many points. It looks smooth like a curve, but it isn’t.  You can check for this by moving a point and seeing if it looks like the picture below.

Move a Point to See if the Curve is Really a Polyline.

Use the Undo command to undo this change in curve shape.

Before we can check the smoothness of these curves, we first have to convert them to real curves with smoothness. This is done using the Curve-CurveFit command. After applying this command to each of the curves (use the bottom or right view), try moving a point to see what happens, as shown below.

Move a Point to See That the Curve is Now a Smooth Curve.

Now you can see that each of the curves is a true, smooth curve and not just a connected set of lines. The next step is to use the program’s curvature overlay curve to check on the fairness or smoothness of these curves.  Use the Undo command to eliminate this shape change.

The big problem with the computer screen and smooth curves and surfaces is that you cannot tell (by looking) whether a curve or surface is smooth enough for your application. That is why our program uses a unique overlay curvature (in orange) that magnifies all minor little bumps, wiggles, and inflection points.

Profile View Showing Orange Curvature Curve Overlay.

The orange curvature (or K-curve) in this view was drawn using the Curve-K_Curve Toggle command (which is the same as picking the ‘K’ icon on the toolbar). This command acts like a toggle or on/off switch. One click on the curve and the K-curve turns on and another click on the curve and the K-curve turns off. When you move a point on the curve, the shape of the curve and K-curve both change shape. The K-curve is designed to change shape dramatically when the curve is moved just a little bit. This allows you to “see” very small changes in curve shape even on a small computer screen. What this also means is that if the K-curve looks smooth, then the curve it relates to must be very smooth. Remember that smoothness or fairness is human judgment and you will have to decide when the curve or surface is smooth enough. This will discussed in more detail later.

If you use the regular Edit-Move Point command for one of the edit points, you will see that the K-curve changes dramatically with just a small change in curve shape. That is why the program has a fine-tune command called the Edit-Move Point % command (see also the % sign with the 4 arrows on the toolbar). This command works exactly like the regular Move Point command, except that the point is moved only 1/100th (1 percent) of the distance in the direction of the cursor. When you use this command, you may not see the curve move much, but you will see the K-curve move. That is the whole idea of how this fine-tune fairing or smoothing works.

Try using the regular and fine-tune Move Point commands on a curve with the K-curve turned on and watch how the orange K-curve changes shape. You should see that the Move Point % command gives you the required fine-tune shape control over the curve. This allows you to fair the curve without having to zoom in on the curve.

K-Curve showing Unfairness and Inflection Points.

This picture (profile view of the dory curves) shows you how much the orange K-curve changes shape with just a small change in curve shape. Another thing to notice is that whenever the K-curve crosses the curve, it defines an inflection point in the curve – a place where the curve changes from convex to concave in shape. Remember, for fairing or smoothing, the goal is to make the K-curve smooth without a lot of up and down jagginess of the K-curve. However, you will find that there are many ways to make the K-curve smooth. You have to decide how to fair the curve. As one of my professors used to say in the days of hand drafting with splines and battens: “Don’t let the batten design your boat”. Therefore, I will say: “Don’t let the K-curve design your boat”.

K-Curve Shown in the Plan or Top View.

This picture shows you the curves and K-curve in the plan (or top or bottom) view of the boat. You have to fair or smooth the curves in all views. For these curves, that run the length of the boat, you really just want to fair them in the profile and the plan views. If you display the section or bodyplan view of the boat, then the K-curve will be exaggerated too much due to the foreshortening of the curves. Generally speaking, you want to fair the longitudinal curves in the plan and profile views and you want to fair the sections (transverse curves) in the section or bodyplan view.

K-Curve Shown With Reduced Magnification.

How do you know if the curve is fair enough? It is a judgment call, but there are a few rules to follow. First, the K-curve is relative. You can increase or decrease its magnification using the K-up arrow or the K-down arrow buttons on the toolbar. The shape of the K-curve will not change – just it’s magnification. These two buttons turn up or down the magnification of the K-curves by a certain amount. You can keep clicking on the button to keep increasing or decreasing their magnitudes. The picture above shows what happens to the K-curve in the plan view when you use the K-down arrow button a few times. When you turn the K-curve down too much, it does not change shape much and it is less sensitive to the changes using the Move Point % command. When you turn the K-curve up too much, it changes too much even with a tiny change to the shape of the curve. What you want to do is to magnify or reduce the K-curve until it changes a little bit if you change the shape of the curve by the building tolerance.

For example, if you are building a boat and the best accuracy you need is about 1/32nd of an inch, then you want to adjust the sensitivity of the K-curve until you can see changes in the K-curve when you move the curve by 1/32nd of an inch. If you lower the magnification any more than this, you will no longer be able to smooth the curve to within the building tolerances. You can look at the status line when you are using the Move Point % command to see how much you are moving an edit point. When you move an edit point by the building tolerance, you should be able to see a slight change in the K-curve. On the other hand, if you magnify the K-curve too much, you will see wild changes in shape of the curve even when you move an edit point by the building tolerance.

Most of the time, the default magnification works fine and that is what you should use. Try increasing and decreasing the K-curve magnification using the K-Up and K-Down toolbar buttons and test it out with the Move Point % command.

K-Curve Shape When the Curve is Finally Faired.

This is the same curve after it has been faired. Notice that the K-curve is fairly smooth. It doesn’t have to be perfectly smooth. Remember that the K-curve is a large magnification of the smoothness of the curve. If you do try to make the K-curve perfect, then you might end up spending a lot of time smoothing the curve to within a 1/100th or 1/1000th of an inch.

Profile View Showing all K-Curves at Once.

This picture shows the K-curves for all four chine curves on the dory. You might want to do this to compare the shapes of the consecutive curves. The calculations of the K-curves are independent of each other, but they should all have somewhat the same shape.

### Plan View Showing All K-Curve Lines

This picture shows the same K-curves in the top (bottom) or plan view. All of the curves (using the offsets from the book) have been faired to within the building tolerances

## Checking Plate Developability

Let’s check to see how developable the plates or panels are using the program’s ruling line calculations. Remember that a surface is perfectly developable if it can be created with absolutely no twisting or stretching of the plate material. In real life, however, a small amount of twist or double curvature is perfectly acceptable.

First, let’s get some background information on ruling lines. What is a ruling line? I will use an example that perhaps you can visualize. Imagine that you are building the dory in this example upside down and you have several frames set up along the length of the boat. Also, imagine that these frames are notched at the chines and sheer and that you have longitudinal chine and sheer bars or battens that define these curves. Your job is to lay a piece of plywood across from one chine curve to another and wrap the plywood to fit the chines and frames.

When you take the flat sheet of plywood and first lay it down between two neighboring chine curves, you will notice that the plywood touches the chine curves at only one spot (assuming that the curves are not flat). If you connect those two chine touching spots with a line, that line would be a ruling line. If you continue this process over the entire length of the hull, then you will have a large number of ruling lines that span the two chine curves. If any of these ruling lines cross or if you can’t find any ruling lines for a particular section of the surface, then the surface is considered to be non-developable. Either you cannot build the surface out of flat material or you might have to stretch (torture?) the material quite a bit.

Our program tries to account for different amounts of twist in different materials by allowing for a certain amount of twist (in degrees) along each ruling line. Let’s go back to the ruling line example. This time, imagine that you and your helper are on opposite sides of the sheet of plywood that you laid down across the chine curves. Both of you go to the spots on the plywood that touch each chine. These are the ends of the ruling line. At each end of the imaginary ruling line on the plywood, you both glue a pencil perpendicular to the plywood on top of the plywood. Now there is a pencil pointing straight out from the plywood at each end of the imaginary ruling line. Next, you both bend down and look along the ruling line from one pencil to the other. Since you haven’t bent the plywood yet, the two pencils should line up exactly – there is zero twist in the ruling line or in the plywood.

Next, each of you should grab the plywood on each side of the ruling line and twist the plywood in opposite directions so that the pencils start to point in opposite directions. You are introducing twist into the plywood. If you now sight down the ruling line at the pencils (assuming that you can twist and look down the ruling line at the same time), you should see that the pencils do not line up. We define twist as the angle (in degrees) between the two pencils when you sight down the ruling line. You can tell the program how much of this twist is allowable when it looks for ruling lines between any two curves. [See the help manual for more complete details about how the ruling line calculation is done.] The program will find a set of ruling lines between two curves and draw them using a color that is related to how much twist is found to be in that ruling line. Dark blue is used for perfectly developable hull with no twist. As the color changes to light blue, green, then to yellow and red, the twist gets larger and larger. If the twist gets larger than some angle limit that you define, the program will not draw the ruling line. See the article on Plate Development and Expansion for more details on the difficulties of surfaces with double curvature and twist.

The program automatically recalculates and draws the ruling lines as you edit (drag) the shape of the chine curves. The goal is to get a nice spread of ruling lines that are as close to dark blue in color as possible.

There are two purposes for ruling lines. The first is to check for developability of the plate and the second is to define the shape of the surface, since the hull is only defined by chine curves at this point. To “turn on” the ruling lines between any two surfaces, use the Develop-Set Ruling Lines for Curves command and you will be prompted with:

“Pick the first of two curves”

After picking one of the two curves (in any order), you will be prompted with:

“Pick the second curve”

Since ruling lines are calculated and drawn between any two curves, you need to pick both curves to tell the program which surface or plate you want to work on. You can’t pick just one curve because each curve can be the edge for more than one surface. If you use this command for all three dory surfaces, you should see something like the following.

### Plan View Showing Ruling Lines Between All Chines

This is the plan or bottom (bow pointing to the right) view of the dory showing all of the ruling lines. Remember that the dark blue ruling lines indicate no double curvature or twist and the areas of green to yellow to red show increasing amounts of twist. We don’t know yet whether this is going to make the hull unbuildable with plywood. Since the hull was in Skene’s, I would assume that the developability is close enough. We will study this later.

### Profile View Showing Ruling Lines Between All Chines

This is the profile or back (bow pointing to the right) view of the hull showing the same ruling lines.

If you display the bodyplan, section, or right view of the hull, you will notice that the starboard side of the hull is displayed all on one side. What we want to do (this is not required) is to tell the program where the middle of the boat is so that the program can “flip” the aft geometry over to the port side for the section view. This is standard naval architecture practice because it allows you to see the aft sections without having the forward sections get in the way. This value can be set using the Options-Display Options dialog box, as shown below.

### Display Options Dialog Box

Notice that the “X-Flip Position” is now set to 5, which is in the middle of the boat. When you pick the OK button, you should see the following for the section view.

### Section View With Split View of the Hull

Notice how the forward sections (ruling lines) are on the right and the aft lines are on the left. This may take some getting used to, but you will see this layout in all books about naval architecture. If it really bothers you, then you can change the “flip” value to some large number, like 2000, to get all of the lines back on the right.

OK, back to the problem of deciding what is wrong with this hull. You can see some red ruling lines that indicate twist. But, how much twist is OK? Let’s try a test. Display the hull in plan (bottom) view and use the Move Pont % command to move a point on the middle chine in the red region. As you drag the point, see how the ruling lines change shape. You may see something like what is shown below.

[Note – We probably shouldn’t have spent much time on fairing the original curves if we expected to change the shape of the curves to fix developability problems. I would say that since it is quick to fair the curves, I would initially fair them a little bit, but I wouldn’t spend a lot of time on it. The assumption is that this is an existing design that has already been successfully built out of plywood.]

### Change in Ruling Lines Due to a Change in the Chine

Notice how things start to go bad very quickly, even for small changes in shape. This would seem to indicate that the allowable twist settings are very strict and that maybe this hull is pretty close to being developable just as it is. [Use the Undo command to go back to the original shape.] How can we check this out? Let’s look at the ruling line options for one of the surfaces. The following Ruling Line Options dialog box can be displayed using the Develop-Ruling Line Options command. When it is selected, the program asks you to pick the two edge curves of the surface that you are interested in. When you do that, you should see the dialog box shown below.

### Ruling Line Options Dialog Box

This dialog box allows you to change a number of options related to one or all of the ruling line surfaces. The field that we are interested in is the “Desired Twist Angle” field, which is set to ¼ of a degree. If you remember the description above about the plywood, the pencils, and the twist angle, then this angle is the angle between the two pencils. As you can see, ¼ of a degree is pretty strict. This is the twist angle that the program tries to meet for each ruling line. If it can’t, then it will find the best ruling line that it can and mark it with another color, depending on how close it is to the desired twist angle. If the best twist angle that it can find is greater than the “Maximum Twist Angle” then the program will not draw the ruling line. This value is set very high since most people want to see the ruling line anyway and it will be colored red.

What we can do is to change the “Desired Twist Angle” to something higher to see what happens to the ruling lines. Remember, this angle is the twist in the material defined by the angle between the two pencils. Most people can twist material quite a bit if they really work at it. However, this twist angle tells the program how much twist is allowed for all ruling lines. Just because you can locally put a lot of twist in a surface doesn’t mean that you can do it over the entire surface. You should be a little bit careful about increasing this angle. If you increase it too much, then all surfaces will be marked as developable, but the surface won’t be buildable!

For this dory example, I think that a 1 or 2 degree twist angle should be fine. Change the “Desired Twist Angle” field to 2 and pick the OK button.

### Ruling Lines With a Desired Twist Angle of 2 Degrees

Notice how the ruling lines look better and that more of the ruling lines are dark blue. If we increase the twist angle to 3 or 4 degrees, you should see something like what is shown below.

## Creating Surfaces From Ruling Lines

It is not necessary to eliminate all of the ruling lines that are not dark blue. What you do want is a clean set of ruling lines that don’t wiggle back and forth. This is because we want to fit a NURB surface across all of the ruling lines. This is done with the Develop-Fit Surf to Ruling Lines command. When you select this command, you will have to (like before) select a surface by picking its two edge curves. If the ruling lines look OK, then go ahead and fit the surfaces to the ruling lines, as shown below.

Note – There is no exact answer here about how much twist is allowed in a surface. As you increase the “Desired Twist Angle”, the program will be able to calculate better and better ruling lines. HOWEVER, this does not mean that the program says that the surface is buildable. Just because the program can create the ruling lines and flatten out a surface, it doesn’t mean that you can take that 2D shape and wrap, twist, and distort that shape onto the frames without problems. Ultimately, it is your responsibility to determine if a surface is close enough to true developability to be buildable. If you have to, print out scale drawings of the 2D patterns and build a little mock up out of paper or cardboard.  Remember, this is only for surfaces with twist or double curvature. If you have a perfectly developable hull (within a very small twist angle), then there shouldn’t be any problems at all. Well, I shouldn’t say that exactly. As described more in the paper on “Plate Development and Expansion”, even if the hull surfaces are perfectly developable, you still have to be very careful. One problem is if you wrap the pre-cut plate onto just a few frames. The plate might not assume the same shape as in the computer program. As you wrap the plate onto the frames, you might think that everything is wrong. You have to make sure that you have “enough” frames (even if you have to use temporary frames) to get the plate to take on the same shape as in the computer. Another problem happens if you cut out the frames and plates exactly (by CNC) but someone in the yard sets up a frame slightly canted or in the wrong location. If everything is cut out exactly, then you have to make sure that everything is set up exactly. A small error or misalignment in the middle of the boat can translate to a large error at the ends. There is no more cut and fit.

### Plan View Showing NURB Surfaces Fit to All Ruling Lines

After you fit the NURB surfaces to each set of ruling lines, this is what you should see. Now we can look at the surfaces themselves to see if they are developable. This is done with the Surf-K_Patch-Kpat All command. This command colors in the surfaces based on the amount of double curvature (Gaussian curvature) there is in the surface. The colors are “sort-of” the same as for the ruling lines: dark blue is for developable surfaces and the colors progress to red for surfaces with a lot of double curvature. However, the two sets of colors are not calibrated the same, so the colors only give you a relative idea about the developability of the surfaces. When you select the command, you should see something like what is shown below.

### Bodyplan View Showing Gaussian Curvature Colors

The default coloring fills in just every other pixel on the screen. If you want to see what is shown above, you need to adjust some options using the Surf-K_Patch-Kpat Options dialog box, shown below. To get the full saturation of color, you need to change the Row and Col Density values to 1 and 1. If you pick the OK button, then you should see the view above.

### K_Patch Options Dialog Box

Well, the colors look awful! How can the ruling line method show that the hull is developable (buildable, anyway) and this display shows lots of non-blue colors. The problem is that the sensitivity of the Gaussian curvature is not the same as that used by the ruling lines. If you go back to the above dialog box and change the “Curvature Gap” value from 0.015 to a larger number and select OK, then you will see something like the picture below.

### Gaussian Curvature With Lower Curvature Sensitivity

Just by changing the sensitivity of the calculation, you can show that the surfaces are nearly developable. Again, if you change the sensitivity up a lot, then anything will look developable. It is up to you to judge how much twist is allowed before the surface becomes unbuildable. Generally, I like to use the ruling line twist angle to judge developability since it seems to have a more real-world or physical understanding. Gaussian curvature looks nice and is good for a second check, but I wouldn’t use it as a primary check of developability.

## Creating a Developable Hull Shape

This tutorial kind of glossed over the problem of how you change the shape of the curves if the ruling lines are not developable. Other programs and an old program of ours calculated ruling lines only after you made an edit change to one of the curves and it was extremely sensitive to the slightest change in shape. You were constantly guessing about what shape change was necessary to get the ruling lines just right. It was often a painstaking process. Our new technique of dynamic ruling lines with color-coded twist information is a lot better, but it isn’t automatic. The sensitivity of the ruling lines can be controlled by the user, but it is still up to you to know what shapes are developable and what shapes are not. However, the dynamic ruling lines allow you to check many different shapes very quickly.

For multi-chine hulls, you should start at the bottom surface and work up (or at the upper surface and work down). Get one surface developable and then move on to the next. Changing the shape of a middle chine (like we did above) is not a great approach, since it is unlikely that you will manage to get both surfaces developable at the same time. You have to work on one surface at a time. Over time, you will begin to get a feel for what shapes are developable and what shapes are not. You will be able to look at the chine curves and see what has to be done. You can also start with existing developable designs, like the dory in this example.

## Flatten Out the Plates

Finally, once you get the hull just the way you want and you are ready to flatten out the plates, you can do so using the Develop-Develop Plate command. It asks you to pick the surface you wish to develop (just pick one of the surface columns) and displays the following dialog box.

### Plate Development Dialog Box

There are a lot of options here, but try it out using the default settings first. Remember that the program uses a finite element type of calculation that can work for both developable and double curvature surfaces. It searches for a reasonable solution, since there are an infinite number of solutions for surfaces with double curvature. Many of the options relate to this search process and you can see the full help manual for all of the details.

When you pick the OK button, the calculation will be done and you should see a result box, as shown below.

## Plate Development Results Box

This result box tells you that it took 2 iterations to find the solution and that the 2D pattern perimeter length is almost exactly the same as the 3D perimeter shape of the surface. (This is a stretch option that can be changed.) It also says that there is no strain (stretch) in the plate. Everything looks good. When you pick the OK button, you will see one of the plates shown below.

This is the developed 2D pattern for the upper side plate.

This is the developed 2D pattern for the lower side plate.

This is the developed 2D pattern for the bottom plate.

## Output of the 2D Patterns

You can use the regular File-Print (see the Print Preview command first) command to print out the pattern. The default output is to scale the picture to fit the printer paper you are using. If you want to print it out at a particular scale factor, then you have to change the settings in the Options-Mod/Doc Definitions dialog box.

If you want to output the pattern to a DXF file to give to someone else for plotting or CNC cutting, you have to follow these steps:

1. Make sure that the pattern you want to output is in the current view on the screen.
2. Select the File-Data File Output-DXF Output command. You should see the dialog box shown below.
3. Change the top “Output” field to “2D View Output” to make sure that you output the 2D pattern rather than the full 3D model of the boat.
4. Since you are outputting the 2D view, the rest of the options really don’t matter. The program will output whatever is in the current view.

### DXF Output File Options

Note that the program does not scale the numbers (geometry) when they are put into the DXF file. If you are using feet, the file will contain feet. If you are using millimeters, the file will contain millimeters. However, the DXF file does NOT contain any units information so the program that reads the DXF file might assume that the units are inches. You need to make sure that the receiving program knows what units you are using.

## Frame Shapes and Patterns

I haven’t said anything about getting the 2D frame shapes of the hull, but now that you have the full NURB surface shapes, you can define and draw all of the frame shapes. This tutorial is long enough, so I will just get you going in the right direction. To get the frame (or station, waterline, buttock, diagonal) shape, you need to use the PlaneCut commands to define a set of frames, waterlines, buttocks, and diagonals. The “Initialize Lines” command allows you to define a group of lines all at once and the Add, Modify, and Delete commands allow you to modify the initial set of lines. Once the lines are defined, you can turn them on or off for display and you can display or plot a traditional lines drawing (View-Lines View) of the hull. Then, you can display and print/plot one or more section or frame shapes full-size or at any scale factor. You can also send the frame shapes to a DXF file just like you did for the plate shapes.

## 3D Views of the Hull

You can also display the hull in 3 dimensions now that you have the full surface shape of the hull. This can be done in wireframe or render modes as shown below.

## Summary

There is much more I could explain about the program. The goal of this tutorial, however, was to get you started with the least amount of pain and head scratching. As with any non-trivial program, it takes some time and patience to master the required skills. I hope this tutorial makes that task a little bit easier.