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

September 8, 2010

Category: 3D Modeling

Rhinoceros

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

form.

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.

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

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.

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

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

bulge.

Next, using

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

Well, that’s all for this article. Thanks for reading

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..]

Category: 3D Modeling

Rhinoceros

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

form.

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 tocurvature (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.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

bulge.

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 byprofession, 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..]