Creating a Lines Plan with Rhinoceros 3D by Dave Murrin (November 2007) The following document describes a method for creating a lines plan using the commercial software package Rhinoceros 3D. A rudimentary knowledge of ship terminology is assumed. Rhinoceros 3D is a stand-alone, commercial NURBS-based modeling tool developed by Robert McNeel & Associates. It is commonly used for Industrial design, Marine design, Automotive design, CAD / CAM, and rapid prototyping. An evaluation version of the software (that is good for 25 saves) can be downloaded from the Rhino3D website: http://www.rhino3d.com/download.htm
Introduction The process of developing a lines plan is not set in stone. For example, one student may find it easier to start with a shear plan, while others find it easier to develop the lines from a series of sections. In the end, the boat is a three-dimensional object and the lines represent the three-dimensional lines projected onto an orthographic surface. The order is not important, since each of the lines define the shape of the hull. The lines plan consists of projections of the intersection of the hull with a series of mutually perpendicular planes. The points of intersection of these planes with the hull are projected onto the Body Plan, the Half-Breadth Plan, and the Sheer plan, as shown in Illustration 1.
Illustration 1: Boat lines (Source: www.nadn.navy.mil/NAOE/courses/en200/) We will start this tutorial from the general shape of the plan deck and develop the hull in the following sequence: Part One 1. plan deck shape 2. profile of bow and hull bottom 3. sheer line 4. max beam line
5. Rough Surface Part Two: Lines plan Part Three 1. Fairing the lines plan 2. lofting the surface 3. fairing the hull surface Part Four: Hydrostatics We will also be loosely basing our design on a canoe with the following specifications: LWL = 5.0m BWL = 1.2m, Design draft = 0.15m, capacity = 190 kg.
Part One – The Rough Surface Step 1: The plan deck First create the centerline from 0,0,0 out to the right. Use “curve > interpolate points to draw a shearline plan, as shown in Illustration 2 Turn edit points on (in the sidebar) and remove extra points. This smooths out the line. The line can also be approximated using edit > rebuild, and selecting a fewer number of control points. Note that this technique will be used later to fair the surface.
Illustration 2: The shear plan curve Note: for boats with a transom, this line should terminate at some distance away from the centerline, and a separate transom line should be drawn. Step 2 Change to the top view and lift the plan curve created in step 1 to some distance above the assumed
waterline (i.e. the freeboard distance). As shown in Illustration 3, use “curve > interpolate points” again to draw the bow and underbody profile. Smooth the curves as before.
Illustration 3: Raised plan curve
Optional step Create the shear line profile view of the plan curve created in step 1.
Illustration 4: Shear line profile (optional) Use “curve > curve from two objects” and select the plan and profile shear curves. This will interpolate the deck edge. Delete the unwanted curves and keep the deck curve (see Illustration 4)
Illustration 5: Finished shear plan The remainder of this tutorial assumes that the shear line profile view of the plan curve created in step 1 was horizontal. Illustration 5 Shows the finished shear plan. Step 3 As shown in Illustration 6, create a rough hull shape at the maximum beam (and the transom if required) and interpolate using “curve > interpolate points”
Illustration 6: Maximum beam shape
Step 4. Insert lines at the bow and stern, as shown in Illustration 7.
Illustration 7: Midship section curve Step 5 Create a rough surface for the boat. Select “surface > sweep along two rails”. Select the shear and hull bottom as the profile curves, and the max beam, bow, and stern lines as the cross-section curves. As shown in Illustration 8, select the number of control points to rebuild the grid (again, fewer is better), and preview the shape.
Illustration 8: Rough surface Now we have a rough hull shape to take our lines from.
Part Two: Lines Plan Step 1 Change back to a new layer and select the centerline in the top view. As shown in Illustration 9, draw a vertical line from the centerline beyond the extent of the hull. Use “transform > array > array along curve” to duplicate the line at regular intervals (say a spacing of 0.5m)
Illustration 9: Station lines Step 2 In the top view select all of the station lines, and use “Curve > Curve From Objects > Project and select the surface (in the top view as well). As shown in Illustration 10, this will create a set of stations based on the hull form that was created in Part One.
Illustration 10: Projected station lines Step 3. Repeat the previous step to create the buttocks (Illustration 11) and waterlines (Illustration 12).
Illustration 11: Projected buttock lines
Illustration 12: Projected waterlines We now have a rough set of lines. We will discuss fairing these lines in the next section.
Part Three- Fairing The meaning of fair is much debated in the marine industry, and there is no mathematical definition of fairness. This does not mean that everyone would disagree on the fairness of a curve or that there are no mathematical tools to use to check for bumps and wiggles. It just means that there are no good ways to automatically fair a curve or surface by computer without some form of human input. Most hull design and fairing programs provide ways to check the fairness of a hull by using some form of second derivative or curvature curve, and by using some form of surface curvature color mapping. The designer interactively changes the shape of the hull to obtain a smooth derivative or curvature curve. As you can see, the designer is actively involved with the fairing process. Characteristics of Fairness In Rhino, the first cue for fairness in a surface is the spacing of the rows (u) and columns (v) that make up the surface mesh (the isoparms). These are shown in Illustration 13. Unevenly spaced isoparms are often an indication that the surface has little chance of being fair.
Patch
Surface Normal Isoparm
U
V
Illustration 13: Surface terminology (Source: http://Source: http://www2.tech.purdue.edu/) The following figures show two surfaces that are very close in shape. Illustration 14 shows isoparms that bunch up in some areas and spread out in others, while Illustration 15 has much fewer isoparms, spaced evenly across the surface. For reasons we will discuss in this tutorial, the second figure is much better.
Illustration 14: Poorly spaced isoparms (Source: www.rhino3d.com)
Illustration 15: Well spaced isoparms (Source: www.rhino3d.com) The guidelines for creating a fair surface include: ➢ Use the fewest possible control points to get the curve shape. The shapes defined in a boat a generally subtle, and should not require a large number of control points to define them. The larger the number of points used to create the line, the more difficult the line will be to fair ➢ Use the fewest possible curves to get the surface shape. Similarly to points in curves, a fair surface is most easily obtained by using the fewest number of curves. This does no imply that you have to sacrifice the shape of the surface; just try to use only the amount of data you really need. ➢ Reflect curvature tendencies in one station to neighbouring station lines. Station lines are taken off of a fair surface, and their shapes should transition consistently from one station to the next. For example, if a station at the bow has a lot of flare and the stations amidships have no flare, each station in between should have progressively less flare. Fairing our hull A good strategy for a surface with subtle curvature (like our canoe) is to use a few of the station lines, make them simple curves in Rhino, and then loft a surface through them. The general steps to follow are: 1. Copy the station lines that we need from the initial lines plan, and save the remaining lines to check the final surface against it 2. Automatically fair the curves, and then rebuild them to simple curves 3. manually fair stations and their relationship to other station lines (if required) 4. loft the hull surface 5. edit the surface for fairness and edge shape Step 1 Create a new layer called “Curves for Surface”. Copy the curves. Change the layer for these curves to the new “Curves for Surface” layer. Turn off the discarded curves layer. There are more curves than needed, so remove station lines where there is little change in shape from one to the next. For this tutorial every second station line was removed, as shown in Illustration 16.
Illustration 16: Removing extra stations Now we are ready to start fairing these lines to simple curves Using the Curvature Graph for Fairing The curvature graph shows the changes in curvature of a curve. If the graph changes smoothly the curve is likely to be smooth (or fair) as well. Jumps in the curvature graph indicate abrupt changes in the derivatives of the curve. The curve graph shows you which way the line is curving, and magnifies the wiggles, bumps, and inflections in the curve. Illustration 17 shows three very similar curves. The curve on the left has many jumps in the curvature graph and is not fair. The middle curve, which has had some fairing done on it, is smooth for the most part and may be considered fair for most applications. The last curve is very smooth and mush simpler than the other curves, although it deviates very little in shape.
Illustration 17: Curvature graphs for curves So our approach in this tutorial is to first fair the curves, then rebuild them into simple curves. Simple curves Curves in Rhino are defined by the number of control points and the degree of the curve. Simple curves are the fairest curves possible, and make surfaces that are easy to edit. To make simple curves in Rhino, you must make curves that have one more control point than the curve's degree. For example, degree 3 curves need four control points. Fairing the curves Select all of the station lines in the “Curves for Surface” layer and fair the curves using the curves > edit tools > fair command. This will give us a good starting point in the fairing process. Use the edit > rebuild command to refine the curves further, and create a simple curve. You normally shouldn't have to go higher than degree 5 (with six control points) to obtain a suitable curve. In fact, in some cases a degree 3 curve will be sufficient. When you rebuild a curve the maximum deviation between the source and rebuilt curve is displayed. The faired (simple) station lines for this boat are shown in Illustration 18. Note: These curves may be further refined by moving points on the curve. To edit a curve, you should turn on its control points (control points on, in the sidebar), and make sure the curvature graph is on. Normally, you should not edit the endpoints of the curve. The nudge feature provides the most control over the position of the points and can be accessed by selecting a point on the curve to edit, holding down the Alt key, and pressing the arrow keys until the curvature graph looks the way you want it.
Illustration 18: Faired simple stations Step Four: Lofting the hull surface As shown in Illustration 19, use the surface > loft command to select all of the stations in order. Simplify the surface if you wish.
Illustration 19: Lofted hull surface We can assess the Surface fairness by using the surface curvature analysis tools select the surface and use the analyze > surface > curvature analysis command. Using the Mean curvature option, you can see areas on the hull that may require more work. The colour in these graphs are not as important as the pattern that the colour creates. Spikes in the graph indicate
that the surface could be improved. Illustration 20 shows the curvature analysis for our canoe. There is a gradual transition in colour across the hull, and no spikes, indicating that the surface is probably close to being fair.
Illustration 20: Surface curvature analysis
Part Four: Hydrostatics We can check the boat's hydrostatics using some of Rhino's analysis tools. First, use the transform>mirror command to mirror your boat surface. Use the join button (on the sidebar) to join the hulls together. Make sure that your scale is correct, and then determine the position of the design waterline. Use the Analyze > mass properties > hydrostatics tool to get the hydrostatics of the ship. Note that if your waterline elevation is not located at 0, you should enter it by typing 'W' when you execute the hydrostatics command, and then set the elevation. Note also that you can simply type 'hydrostatics' at the command prompt to evaluate the hydrostatics at any time. Illustration 21 shows the hydrostatics for the canoe used in this tutorial.
Illustration 21: Canoe hydrostatics Optional: To change the hydrostatic properties of the canoe, we can simply manipulate the hull below the waterline. Delete the hull surface, select all of the curves, and turn on edit points. Select the edit points below the hull, and manipulate as desired. For example, to make the boat a little shallower, select the points and drag them up slightly in the section view, as shown in Illustration 22. Note: this step should be taken with caution, since small changes in the location of the station curves can result in large changes in the hydrostatic properties. It is however, a useful exercise for gaining an appreciation of how the shape of the hull affects the hydrostatics.
Illustration 22: Modifying Hull below waterline Final steps When you are satisfied with the hull, you can now develop the final set of lines. Repeat the procedure described in Part Two to produce a final lines plan. The completed lines plan for the canoe is shown in Illustration 23.
Illustration 23: Final canoe lines
