6. Pushing for G3 continuity conditions

The CV positioning and layout is the key to G3 continuity. In general, we are aiming for a most simplistic and even CV layout within all surfaces of an object.

6.1 CV layout and manipulation

To explore the CV layout and the possibilities to manipulate the CVs more in depth, we first go back to the roof surfaces and push them from G2 to G3 maintaining a most even CV layout as described in Chapter 5.5. Then we move to the most difficult part of the car: the rear wheel arch.

We learn how to use the Planarize Hull tool and the CV Move Functions together with the Surface Continuity Check tool, the Stripe Shader and the Cross Section tool at the same time to get the surfaces of these areas into the right conditions. The exact workflow is shown in Chapter 7.

6.1.1 Planarize Hull

The Planarize Hull tool straightens CVs of the Hulls between the first and the last CV of each of Hull, so that the footprint of the patch is not affected but the internal condition of the patch is more even.

6.1.2 CV move functions

Here we have a very efficient and easy to use tool to manipulate CVs in a wide range of different ways. It is an almost self-explanatory tool.
You can choose via the Mode options the direction in which the CVs are going to be moved and if you wish to move individual CVs or a complete u or v direction row of CVs as a Hull.
There are just a few things to mention.

I recommend to create a range of different Step sizes for each mode to be dragged into your Shelf-set. That way you have direct access to this tool for each work step, which will speed up your Class-A surfacing workflow.

6.1.3 Surface continuity check tool

Same recommendations as for the CV move functions, drag it three times with different settings for direct access to G2, G1 and the positional check option into the Shelf-set.

6.1.4 Proportional modification

Proportional modification enables us to move a selected range of CVs of one surface with a pre-selected dependency and in proportion to each other.The application of this tool was already demonstrated on a surface earlier in chapter 5.5 direct history – rebuilding fillets.

6.2 Evaluating the surface continuity

6.2.1 EVALUATION Shader

We assess the surface quality of our model by using various diagnostic shader methods.
The most commonly used is the Stripe Shader. It simulates a tunnel of linear white light stripes which are reflected by the surfaces of our object.The orientation of the stripes can be changed from horizontal to vertical which may be necessary to review certain parts of the model.
The Stripe Shader can also be set to an adjustable transparency. In transparent mode one can select and modify CVs or Hulls of surfaces while assessing their surface flow at the same time. With transparency it is also easy to compare final surfaces with the original surfaces that were rebuilt.
As already mentioned, the final surfaces displayed in Stripe Shader mode should appear without any jags, dots or kinks.
The Sky Shader projects an abstract horizon with diffused light direction onto the surfaces of the object. This allows a much better assessment of the overall shape of the object compared to the Stripe Shader.
The Double Horizon Shader gives an extra dimension of evaluation potential of the surface flow because it combines the advantages of the Stripe Shader (having „one stripe“) with the overall shape assessment properties of the Sky Shader.

6.2.2 Cross Section Curvature Plot

The Cross Section tool with the enabled option Curvature Scale is the most important tool to evaluate G3 continuity of surface transitions. All primary and secondary surfaces need to have G3 conditions for Class-A quality. Curvature combs should show a smooth transition of curvature acceleration between surfaces (see the example in chapter 5.5 Working with direct history-achieving G3 continuity).

7. Complex workflow examples

7.1 Rebuild the Secondary Bonnet Surface

Take the primary bonnet surfaces plus the front fender and the bonnet piece of the mesh.
Then use the Fillet tool with the Advanced settings as shown in the Surface Fillet Control box (see chap. 5.5.2) and increase the surface fillet size until the cross sections through mesh and fillet are nearly congruent.
Even if you turn off Explicit Control we can't get curvature conditions for this fillet.

Therefore, in the next step we rebuild the borders of the fillet via very simple curves, which will then be projected onto the primary surfaces to trim these surfaces again. Build the two curves as shown in the animation. Set the start point of the first curve to the patch end of the fender. This is helpful later on, when the sidewall transition into the wheel arch has to be done.
Give the curves a bit more shape. Hide away the original fillet and "untrim" the primary surfaces. Throw away the two old "curve-on-surfs" and project the new curves back onto the primary surfaces. Then trim them, again.

Create a 5 degree curve between the primary bonnet surfaces at the side of the fender and align the curve with curvature conditions to bot, , , , h surfaces.
Create another 5 degree curve at the other side of the sur, faces. Start at the end of the, surface that runs through the windscreen and run it in the shortest possible way to the opposite surface and align the new curve with curvature conditions to both surfaces using the Project Tangent or the Blend Curves tool.
Create a square with the curvature conditions to the primary surfaces. Leave Explicit Control on to find the lowest possible complexity of the square by increasing the number of spans until you achieve curvature conditions to the primary surfaces. To enhance the surface quality from a NURBS structure to a Bezier structure, using the Square tool again with Explicit Control 5-5 degree or max 7 degree. In order to do this use some of the spans of the NURBS fillet underneath as new patch borders with the aim to replace the NURBS fillet in the end. You may have to repeat this procedure a few times until you have found the best distribution of single span patches to replace the NURBS patch.

For the last patch add another 5 degree curve with the curvature conditions to the inner corner of the front sweep of the bonnet and the inner edge of the upper surface. Create a square with curvature conditions at the front sweep and the fillet and the set Continuity Conditions for the square to Tangent.
If you measure this connection with the Surface Continuity check too, it shows you curvature Flat conditions which is acceptable at this point.

7.2 Generate the Rear Fender Sweep

We start with the same method we used to rebuild the bonnet fillet. Create a chordal fillet as big as possible between wheel arch and sidewall. Review the result.
• Point one: the fillet is much too small to follow the contour of the scan data.
• Point two: the area where we want a simple patch to connect to the roofline already looks difficult. Therefore, we need a different strategy.

To get a nice patch layout of the transition from the side wall to the wheel arch, we create new surfaces that connect directly to wheel arch and side wall.
In order to keep the direction of the fender we extend the front part of it using Extend Unmerge.
We then get a clean surface edge with the correct direction to connect the new transitional surfaces to. Because we want to achieve a nice and even patch layout, we need to define the opposite edge of the side wall to connect these surfaces to. Therefore, we rebuild the edge of the extended wheel arch using Duplicate Curve as a 5 degree curve. In side view Offset this curve until it touches the gap line of the door we see in the scan data.

The upper part of the curve is now running above the roofline. Take this end of the curve down below the roomline and smooth the curve out to achieve a nice continuously accelerating curvature comb. Switch to the Perspective window, put the fillet and the front part of the fender on a separate layer and hide it.

The Extend/unmerge the upper sidewall part until it touches the point where the projected line ends at the lower surface. Do it as precisely as possible.
It is very important to match this point exactly.

Connect a 2 degree line to the lower end of the upper sidewall surface precisely at this point again and extend it over the middle of the rear wheel. Use this line to project it with Project normal onto the rear fender. Create another 5 degree curve with the curvature conditions between the beginning of the projected curve on the rear fender and the lower end of the upper sidewall.

Then build a 5/5 square between the shortened upper sidewall and the rear fender with the curvature conditions to both surfaces.
The square might not achieve curvature conditions to the upper sidewall.

Check it with the Surface continuity checker with Show comb option ticked. Then correct the curvature using CV move/NUV/Step size 0.001 and move the lowest CV of the second row until the continuity achieves curvature.

Now using Project/normal, project the fillet edge line in side view onto this surface and trim the lower part away. Hide the curves, original sidewall and the front part of the rear fender. Project a line in side view, starting at the mid point of the rear wheel arch, running over the point where the sidewall surfaces cross and project it onto the wheel arch and the corner of the upper sidewall surface. Create a curve between these projected curves and align them with curvature conditions to both sides. Correct the curvature plot for a most even acceleration. Now do the same at the lower end of the wheel arch and the lower sidewall. Try to create squares with the curvature conditions as few spans as possible joining the sidewall and wheel arch. Analyze the result (CV layout, spans, cross sections, mesh etc.)

It's very obvious to see the Hulls of the two squares do not run continuously, but have a kink where the squares connect.

Before we rework the squares to get rid of their spans we have to bring the Hulls in line. To do this we make use of the direct history again.
Activate CV mode/slide/step size 0.1 and move the CVs of the curves used to build the squares until the Hulls of the squares run continuously and almost parallel to the wheel arch and the sidewall cut out.

Back in the side view, project two more curves through the centre of the just corrected squares onto the wheel arch and the sidewall. Now rebuild the projected curves of the squares as 5 degree curves and align them with curvature conditions to the previously projected curves of sidewall and wheel arch. Hide the two squares and replace them with four new squares without spans but curvature conditions to the sidewall and wheel arch surfaces.
Look at their CV layout and correct it at their connections in the same way as you did earlier with the two big NURBS squares containing spans.

Display the continuity conditions of all edges of these four squares with the Curvature (G2) check the Surface continuity check tool. Try reduce of the combs that show G2 breaks where the squares are connected to each other even more using the CV move/slide/step size 0.01 function and manipulating the CVs of the original curves (direct history).

Then use the CV move/NUV/step size 0.001 to get G2 continuity by moving the CVs of the second and thrid row of the squares slightly. Be aware not to mess up the continuity conditions of the squares to the sidewall and wheel arch surfaces.

The last mismatch to correct is the connection of the upper sidewall to the upper transitional square where there is a gap. Use the CV move tool again to correct the positional error.

With a bit of luck all your surfaces now have achieved curvature conditions to each other and you have fulfilled a very difficult task.

If not, don't despair and practice until you get all surfaces right.

Good luck!

8. Data validation checks

To ensure the delivery of a proper and clean data file to your client, it is absolutely essential to check the final data for errors and insufficiencies.

8.1 Check model tool

The options on the left are not only good for Class-A surfaces, but also for a general data check of all other surfacing quality standards.
The tick Normal Consistency check is necessary if your file is used for visualization purposes.
Short Edges sometimes have to be checked by hand if parts of your model are very small.

In general, all positional and continuity checks measure the objects to the construction tolerances used.

8.2 STITCH Check

For rapid prototyping parts a closed model has to be achieved.
The Surface Stitch tool “sews together” and immediately highlights all gaps, unclosed regions and other problems of your completed model.
In general, it is a good and quick tool to do a fast check of the entire model.