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1 Tutorials Rhino 3D Surface Continuity (Part One) em Qua Jan 26, 2011 1:33 am


September 8, 2010
Category: 3D Modeling

3D is one of the few 3D modelling CAD package that can create accurate
and precise surfaces with curvature (G2 & higher) continuity.
Because of that, it is especially suited for product and industrial
design surfacing.
There are a few points to take note when creating adjacent surfaces
with good level of continuity to each other. Traditionally, position
(G0) and tangent (G1) level continuity are not sufficient for smooth
transition and can result in a noticeable break to the ‘flow’ of the
In order to maintain surface continuity with neighbouring (adjacent)
surfaces, the curves to be used for surfacing MUST likewise attain the
required continuity as well.
That is,
1. Construction curves must be tangent to each other in order for the corresponding surfaces to maintain tangency continuity.
2. Construction curves must be curvature to each other in order for the corresponding surfaces to maintain curves continuity.
It must be noted that in order to create a curve with a certain
degree, the minimum number of control points required is ‘Degree + 1′.
That means, a degree 3 curve will require a minimum of 4 control
points. In Alias Studio, Control Points are call CVs. A good practice
is to use the minimal amount of control points (CVs) to get the curve
created. This is because we will want to minimise the necessary
undulations that can result from excessive amount of manually-created
control points.
Additionally, we can also investigate the continuity changes and
dynamics along curves and surface. This can be done using the Curvature
Graph. This is as shown below.

To build adjacent curvature curves, one method that I use is to
1. first build a curve that is tangent to the adjacent curve.
2. Use Match tools to rematch the curve to G2 continuity
3. Fine tune the curve with a combination of Curvature Graph and End Bulge command.
To build a tangent curve, I turn on the Control Point Display of the surface to be tangent to. (As shown below)

Next, I start to create the curve using the Control Point Curve.
First, use the point or end osnap to snap the first control point of
the curve to the end of the edge. Next, making sure that the Point
Osnap is enabled, snap (but do not click) the next point to the next
control point of the existing surface edge. This is as shown below.

The directional lock is now activated. Move the cursor to the
opposite end to start clicking to create the curve. As we want to
create a curvature-level curve, the minimum number of control points
(CVs) required is 4 (ie, 3 +1).
Additionally, if we are creating the curve correctly, the 2nd
control points of the surface edge and the newly create curve as well
as the 1st point of the curve should form a straight line. This is as
illustrated below.

Now, turn on the Curvature Graph for the edge as well as the newly created curve. For this illustration purpose, the edge curve is used to display the curvature graph instead of the surface itself. This is as shown below.

As you can see, the Curvature graph shows that the flow is not
continuous and smooth. The break indicates that the match between the
edge and the newly created curve is not G2.
This is the end of part one of the articleIn Part 1, we have created a curve that is tangent to the edge of
the existing surface. Now, we need to proceed to make the curve G2
(curvature) continuous to the edge.
We can use Match Curve to bring the curve to
curvature (G2) continuity with the adjacent surface edge. Match Curve
is within the Curve Tool panel. Select Continuity as Curvature from the
Match Curve option. Note: For curves that have less than 6 control
points, the curvature at the other end of the curve to match may be
modified. The Preserve other end option prevents this modification.

From the screenshot shown above, we can see that the Curvature Graph
displays a better flow with little or no sudden break or transition.
Next, we can bring up the Adjust Curve End Bulge
tool to fine tune the curve. Make sure that the side (as indicated as 1
in the screenshot below) has Continuity = Curvature at the command
line/prompt. For the other end (indicated as 2 in the screenshot
below), in our case here, Continuity = Position is to be set. This is
because we have only created enough control points for curvature to one
end of the curve.

Once we are satisfied with this curve, we can proceed to create the
other curve to match the other surface edge. Use the same method as
described to ensure curve is curvature-matched to the edge as well. See
illustration below of the other curve.

Now, we can use a surface tool with continuity to create the
surface. In this case here, a new curve is created as shown below. The
control point is turned on to adjust the profile to give it a slight

Next, using Surface from Network of curve, create the surface. Remember to set the Edge matching option to Curvature at the Options dialog. In this case, this is indicated as edge D. This is very important as surfaces do not automatically become curvature-matched even though the curves used to create them are.

Use the Zebra tool to evaluate the surface continuity. Zebra strips
can be used to indicate whether surfaces are position, tangent or
curvature to each other. However, we are not going to go into the
details here. Please note that the zebra tool cannot detect higher end
continuity that can be seen by a curvature graph display.

What we have illustrated here is just a simple example. If we have additional adjacent surface edges to match to, the surface from network of curve tool can provide surface continuity matching options for all sides of its boundaries.
Well, that’s all for this article. Thanks for reading
About the Author: Being an industrial designer by
profession, I have done much technical modelling projects for clients
such as Razer and Creative Technology. I am proficient with
Aliasstudio, Pro-Engineer and Rhinoceros 3D.
Disclaimer: We are in no way to be held responsible if the results is not as desired by you..]

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