BetterSpace: Whitestar Tutorial

Lesson 7 part a:
Building the Spline Cage for the Bridge Section

Back from our brief trip into the two-dimensional world, it's back to 3D to build the spline cage for the Whitestar's bridge section.

All the lessons up until now have dealt with creating body parts for the Whitestar based on my Whitestar v3.6, as v4.0 was not even conceived when I started writing this tutorial. However, the v3.6 spline cage for the bridge was an absolute nightmare, and rather than try to talk you through how to build that, this lesson will deal with how to build the bridge from Whitestar v4.0, which is much simpler and more elegant in its construction.

This is a pretty long lesson, and might take a while to download...

Just so you know what we are hoping to achieve, this image shows the completed spine cage. It's pretty complex, but it will soon all make sense... hopefully.

the completed spline cage

Let's start with the main rail curve. In the side view, create a curve like this:

the first rail curve (left view)

As you can see, I have called this rail curve r1, and named the points along it r1p1 to r1p7. All the points on this curve have x=0.

We can now create the second rail, which I will call r2. Again, all points have x=0.

the second rail curve

If you look very closely at the right-edge of the image above, you will see that r1p7 and r2p8 are not the same point. There is a very small gap in-between them, as seen below.

r1 meets r2 with a gap (left view)

You can also see from this image that the curve r2 uses the point r1p6 as a smoothing control point. The reason for my not joining r1 to r2 will become apparent later.

Create a third rail curve, r3, in-between r1 and r2.

a third rail curve: r3

Again, note that r3p7 is not the same point as either r1p7 or r2p8.

This rail must be altered in the top view to form the shape of the side of the bridge. Using the Drag tool in the Top view, move the points of the curve so that they look like this:

dragging r3 in the top view

The following image shows the front view of the same curve.

dragging r3 in the front view

For our fourth and final rail, r4, the composite image below shows top, left and front views.

top, left and front views of r4

As before, r4p7 is not the same point as r1p7, r2p8 or r3p7.

This image shows a close-up perspective view of these four points.

relative positions of r1p7, r2p8, r3p7 and r4p7

That completes the construction of the four main rail curves.

Luckily, the profile curves for this section are remarkably simple.

Change to Points Selection mode and select all of the points that make up r3 and r4.

Pick the Mirror tool (shift + V) and mirror these points across the Z-axis.

mirroring all the points from r3 and r4 across the Z-axis (top view)

As you can see from the image above, I have named the mirrored points with the same name as the points they were mirrored from, but added a * into their name, so the mirrored partner of r4p7 would be r4*p7.

We now have all the points we need to create most of the profile curves. Select the following points in order and make curves from each set (Ctrl+p). Stay in point selection mode, and do not deselect the curves as you create them.

Once you have created all these curves, press the SPACE BAR to change to Polygon selection mode. You should see that all the new profile curves are selected. (If they aren't, then select them now).

the new profile curves

We are going to toggle start and end control points for all the curves here, so with all the profile curves still selected, press Ctrl+B and then press Ctrl+N.

You should be left with something like this.

control points toggled for all profile curves

It should now be apparent why the points r1p7, r2p8, r3p7 and r4p7 do not share the same space. By creating two very small curves here, we avoid having any ugly triangular patches in the forward (and most visible) area.

This approach does leave a hole in the completed mesh, which we will have to fix later on.

We must now build the curves which form the basis of the wing-like extensions which protrude from the sides of the bridge. I will call these the extension curves, as they are not really rails or profiles, but something else. The first two curves will be e1 and e2.

It is probably best to create these curves in the top view, then manipulate the points into their correct positions in the left view.

point positions for curves e1 and e2 (top and left view)

This image shows the two new curves in a new layer, although this is only for clarity in the image, and you should create them in the same layer as the rest of the curves from this lesson.

As you can see from the image, the first three points of these curves are formed from points which already exist, except for r4*p2 and r4*p3 which must be created by mirroring r4p2 and r4p3.

In this table points marked in bold type already exist, and you will need to create the rest.

Once the curves are built, select them both and toggle their control points as in the previous step. You should now be looking at a cage which resembles this one:

cage including curves e1 and e2

The two curves we just built have partners; e3 and e4, which follow approximately the same path as e1 and e2, but a little bit lower.

Again, these curves share points with the rails r2 and r3, and you will need to mirror r3p2 and r3p3 to create r3*p2 and r3*p3.

point positions for e3 and e4

The following table may make things clearer. The points marked in bold type already exist, and you will need to create the rest.

Notice that the curves end by looping aroud e1p9 and e2p9, which is why the two curves appear to be joined in the image above.

Once again, you should build these curves in the same layer as the rest of the splines.

When they are built, select both curves and toggle their control points, to leave you with something like this:

cage including all four extension curves: e1, e2, e3 & e4

The following image shows the ends of the four extension curves close-up so you can see how it all fits together.

close-up showing smoothing

The four extension curves now need some basic profile curves, which I will call extension-profile curves.

extension profile curves

Select the following points and make curves from them:

Curve Name Point 1 Point 2 Point 3 Point 4 Upper Extension Profiles epu1 e1p4 e4p4 e3p4 e2p4 epu2 e1p5 e4p5 e3p5 e2p5 epu3 e1p6 e4p6 e3p6 e2p6 Lower Extension Profiles epl1 e2p4 e1p4 - - - - epl2 e2p5 e1p5 - - - - epl3 e2p6 e1p6 - - - -

point order for extension profiles

Your curves will look like these:

newly created extension profile curves

Select all six new curves and use the Tools \ (Curves) \ Smooth tool to smooth between the pairs of curves.

If all has gone to plan, your profile curves now look like this...

extension profiles smoothed into one another

... and the whole cage looks like this:

cage including extension profile curves

We now need two small fix-it curves, f1 and f2. These curves are made from existing points as shown in the table below.

When the curves are built, toggle their control points to end up with this:

f1 and f2, fix-it curves

At the rear of the bridge section are two supports which (appear to) join into the upper hull and the gravity drive fins.

We will create the first pair of curves for these now. I will call these the support curves, and give them an s prefix.

The first two curves will be called s1 and s2, and will be formed partly from points on the extension curves e1, e2, e3 and e4.

The following image shows their structure...

this image took bloody ages to put together...

... and this table gives you the order to join the points. Again, point names marked in bold type already exist, and the others must be created by you.

When your curves are built, toggle their Start control points (only) by pressing Ctrl+B.

curves s1 & s2 (front & perspective view)

Does you cage look like this? Good.

So, we've built the forward curves for the supports, now for the rear curves.

Yet again, they mostly use existing points, but each curve will need two new points as well. Refer to the table below for the point order.

curves s3 and s4 (top and left view)

Once again, bold type indicates an existing point.

After you've created these curves, toggle their Start control point with Ctrl+B and you'll be left with this:

curves s3 and s4 (top and left view)

Time for two really simple profile curves now. These will define the bottom of the supports, so I will call them support profiles, and name them with an sp prefix.

support profiles sp1 & sp2

These curves use only points that already exist, so just join the points shown in the table below.

Use the Tools \ (Curves) \ Smooth tool to smooth between the newly created pair of curves.

sp1 & sp2 smoothed together

Resting atop the supports are a pair of mini-wings, and those are what we will build next.

These will be the wing (w) curves, and the first of them will be w1.

the new curve w1 (top & left view)

This table shows the point order. Note that the first two points are taken from curves e2 and e1.

Create the curve in the top view and then use the Drag tool to modify its shape in the left view so that it matches the image above.

Finally, toggle the curves end control point with Ctrl+N.

When your curve is correct, select it and copy it into a new layer. Put the layer with all the rest of the curves into the background so that you have this sort of arrangement:

the copy of curve in a new foreground layer

Once this is done, move the curve down in the front view until you have something resembling this:

copied curve w1 becomes curve w2

This curve is now w2, and has its own list of points, as shown in the image above.

The two points x1 and x2 are so called because they are only temporary, and will soon be eliminated, as you will see.

Cut this curve out of this layer and Paste it back into the layer that contains the rest of the splines.

Select the two temporary points x1 and x2 and zoom-in to them. You will see that they are remarkably close to the points e3p7 and e4p7. (At least, they are supposed to be!) We will now weld the point x1 to the point e3p7, and x2 to e4p7.

To do this, deselect everything and ensure that you are in Points selection mode. Then select x1, followed by e3p7 and press Ctrl+W to Weld them together. Deselect everything again and select x2, and then e4p7, and weld these two together. As you can see, the points x1 and x2 no longer exist, as they have merged with e3p7 and e4p7.

You now need to perform some very slight modifications to the curve w2 using the Drag tool to make it look like the image below.

dragging points from curve w2 (left view)

The eight curves which define the back of this wing section require us to add only two new points. These two new points are shown below, labelled w3p3 and w4p3.

new points w3p3 and w4p3

The image above also shows two new curves in place: w3 and w4. The table below shows the point order for these new curves.

Now toggle the Start and End control points (Ctrl+B, Ctrl+N) for curve w4 and toggle the Start control point for curve w3.

You should now have curves that look like these:

curves after control point toggling

Now there's only six more curves needed to complete this cage.

We will deal with two fiddly little fix-it curves first. These will be called wF1 and wF2. The table below gives you the point order.

When you have joined these points up and made the curves, toggle their control points so that you have this:

fix-it curves wF1 & wF2 after control point toggling

The last four curves are profile curves for the wing sections, so they'll be called wP1, wP2, wP3 and wp4.

When you have put together these splines, select wP1 and wP2 by themselves and toggle their Start and End control points, so that they look like the image below.

wing profile curves wP1 & wP2

Next, deselect wP1 and wP2, and select wP3 and wP4 together and smooth them using the Tools \ (Curves) \ Smooth tool. You should be left with this:

wing profile curves wP3 & wP4

Do a final Merge Points just to be sure that there are no offending points lying around. If you have followed this lesson precisely, you should have eighty-one points in the cage (I think...)

Save the cage as ws_bridge_main_splines.lwo.

looks good, doesn't it?

Just for fun, mirror the entire cage across the Z-axis (but don't save this object). Now zoom your view out to fit the whole cage into the display, and admire what is sitting there.

Do you have any comments of questions regarding this lesson?