Surfaces > Boundary Surfaces

To build from four boundary curves with continuity

Create surfaces by blending four boundary curves (or curve segments), while maintaining continuity with adjacent surfaces.

To create a new surface by blending four boundary curves (or curve segments)

Double click the Square icon, or choose Surfaces > Boundary Surfaces > Square ❒ from the tool palette.
The Square Control window appears.
Click the first boundary curve
or

Click a point on the curve (to use as a corner) by holding down either the (Windows) or (Mac) key or the and (Windows) or and (Mac) keys.
- You can use free curves, curves on surface, isoparametric curves, and/or trim edges.
- To maintain continuity with another surface, you must pick an isoparametric curve or trim edge on that surface, not a construction curve used to create that surface.
- You can use a segment of a longer curve. The Square tool will use the section of the curve bounded by the other curves you click.
or

Click a grid point (to use as a corner) by holding down the (Windows) or (Mac) key.
Click the remaining curves and/or points (corners) in clockwise or counter-clockwise order.
- You can select either four curves, four corners, one corner and two curves, or two corners and one curve.
- If you select both curves and corners, you must select the curves first.
- You can only use a snapping mode to select the first corner.
- If two adjacent boundary curves do not intersect, the Square tool displays an error in the prompt line. Otherwise, the surface is built.
Move the corner locators (if any) by clicking them and dragging to change the position of the corners.
Use the options in the Square Control window to set the continuity you want at each edge (see below).

To use the tangent angle manipulator

This manipulator appears when you set an edge to Tangent Angle in the Square Control window (see below).

Click an axis line to set the tangent angle to 0, 90, 180, or 270 degrees.
Click an arc, then drag the mouse left and right to change the angle value, or type a number to set the value exactly.
When you are finished, click the Go button.

To edit the construction history of a Square surface

Pick the surface you want to edit.
Click the Square icon, or choose Surfaces > Boundary Surfaces > Square from the tool palette.
The Square Control window appears.
Use the curve modification tools (in the Transform, Curve Edit, and Object Edit palettes) to reshape the curves used to create the surface, and use the Square Control window to change the surface creation options.

Tips and notes

To make sure the boundary curves intersect, use:
- Curve snapping
Use the Project Tangent tool to make sure the curves are already continuous before creating the surface. This will ensure the Square tool can achieve continuity and decrease calculation time.
The first curve you click defines the U direction of the new surface. The second curve defines the V direction.
You can select several boundary curves at a time by dragging a pick box around them, but you cannot control in what order they will be picked.
Curve segments can be ambiguous. In the example at left, it is not clear which part of the U-shaped boundary curve should be used as the left edge of the new surface.

In these cases, the Square tool will guess which segment to use. If it guesses incorrectly, detach the ambiguous curve to create two separate, non-ambiguous curves.
If you know the boundary curves already have matching parameterization and minimum spans, you should turn the Rebuild checkboxes off. Rebuilding can sometimes inhibit continuity.
For the continuity options to work for some edges, the adjacent edges (for example, edges 2 and 4 are adjacent to edge 1) must usually be free.
If you have continuity constraints on all edges, the constraints may sometimes conflict and fail.
If your surface has a bulge or dent, try reducing the Influence slider for the edges whose continuity is Fixed or Free.
The Influence sliders are found in the Square Control window when Blend Type is Cubic.

When you specify the four corners of a Square surface, you must specify the first corner using a snap mode (that is, holding down either the (Windows) or (Mac) key, the (Windows) or (Mac) key, or the Ctrl and (Windows) or and (Mac) keys). However, you can specify the remaining corners with or without using a snap mode.
There are several techniques to try when Square does not produce the intended results:
- Turn Rebld on for all boundaries with trimmed surfaces or curves on surface, and have the system recalculate the surface.
- Adjust the influence sliders to adjust the shape of the resulting surface.
- Set the Blend Type to Linear instead of Cubic.
- If trying to maintain continuity with trim edges or curves on surface, it may be necessary to decrease the curve fit tolerance in the Preferences > Construction Options settings.
- Verify that the square surface doesn’t have a corner where the U and V edges are colinear.

Square Control

Continuity table

The Continuity Table displays one row for each boundary curve involved in the Square operation.

Use the pop-up menu next to each curve to set the level of continuity you want across that curve.

Use the Continuity pop-up menu above the table to set the continuity you want for all of the curves at once.

Click the checkboxes at the end of each row to rebuild the curves to reduce data and improve parameterization.
Use the Rebuild pop-up menu to set rebuild on or off for all the curves at once.

Continuity

Free Boundary – This edge is free to move if required by another edge’s continuity or by the Influence sliders (see below). This is the default.

Fixed Boundary – Keep this edge exactly like the boundary curve that created it. In other words, do not let the edge move as with the Free option. This is equivalent to positional continuity.

Implied Tangent – Try to keep tangency with an implied surface that shares this edge. The implied surface is the surface that would be created by mirroring the new surface. (The way the Square tool tries to keep tangency with an implied surface is by blending the slopes of the boundary curves.)

This is a powerful feature. It lets you model one half of a symmetrical surface (such as a car body), and maintain continuity at the seam. When you duplicate the surface to create the other half, the seam will already be continuous. For this to work across a symmetry plane, you must make sure the ends of the curves are tangent across the symmetry plane (that is, the tangents are perpendicular to the symmetry plane).

Tangent Angle – Try to keep tangency at an angle with a surface that shares this edge.

When you set this continuity type for an edge, a manipulator appears on the edge. Use the manipulator to set the tangent angle.
The two adjacent edges of the new surface should be Free to allow the Tangent Angle edge to move.
Setting the Tangent Angle manipulator to 0 or 180 degrees is the same as using Tangent continuity.
This continuity type can be very slow to calculate.

Tangent – Try to keep tangency with a surface that shares this edge.

Curvature – Try to keep curvature continuity with a surface that shares this edge.

Blend Type

Linear – Create the new surface by blending the free CVs (CVs not controlled by the continuity options) of the four boundary curves.

Cubic – Create the new surface by interpolating the boundaries (as in Linear), plus the tangent and curvature ribbons. The interpolation is cubic (if only tangent continuity is needed) or quintic (if curvature continuity is needed).

Depending on how much the tangent and curvature ribbons change, Cubic blends can be much wavier than Linear blends.

1-3/2-4 Boundary Blend

These sliders control the point of equal influence of opposite boundaries (in other words, the midpoint of the blend between opposite boundaries): that is, between 1 and 3, and between 2 and 4. Values can effectively range from 0.17 to 0.83.

Changing the surface using the Boundary Blend sliders is slow, because continuity must be recalculated. For very complex surfaces, or when using Curvature or Tangent Angle continuity, you may want to turn off the Auto Recalc option.

1-3/2-4 Influence

These sliders control how much each set of boundary curves influences the new surface.

They only appear when Blend Type is Cubic.

For example, if you set the 2-4 Influence slider to 0.0, the new surface will mostly blend between edges 1 and 3, and will have little of the shape of edges 2 and 4.

Changing the surface using the Influence sliders is much faster than with the Boundary Blend sliders, because continuity is not affected.

Explicit Control

Turn on this option to open the Explicit Control Options section that allows you to explicitly specify the degree and number of spans of the surface in both the U and V direction.

Explicit Control Options

These controls are displayed only when Explicit Control is turned on.

U Degree / V Degree: Degree of the square surface in the U and V direction respectively.
U Spans / V Spans: Number of spans on the square surface in the U and V direction respectively.

Continuity Options

The following two options only appear if Explicit Control is turned off.

Max. New Spans: Maximum number of spans the Square tool can insert on each edge of the new surface as it tries to achieve continuity.

If the Square tool cannot achieve tangency without inserting more than the allowed number of spans, it displays an error in the prompt line.

Max. New Spans is not available when Explicit Control is turned on.
Insert at Midpoint: On – Insert extra edit points at the midpoint of the span with the largest continuity deviation. This is the default, and results in a better distribution of the isoparametric curves.

Off – Insert extra edit points at the location of the largest continuity deviation.

Insert at Midpoint is not available when Explicit Control is turned on.

Colinear Options

Boundary 1,2,3,4: Check the boundaries across which you want the isoparametric curves of the new surface to line up with adjacent surfaces.

This is similar to turning off Skews in the Align tool.

Control Options

Create History

Save the history of the new surface for later editing. If you turn Create History on, you can modify the curves that were used to create the surface, and the surface will update.

Auto Recalc

Update the new surface automatically as you change the values in the Square Control window.

Boundary Labels

Label the boundary curves in the view windows. The labels also show

the kind of continuity wanted,
whether the continuity failed,
which tangents are implied or averaged, and
the angle on edges with Tangent Angle continuity.

Continuity Check

Display the surface continuity locator at the boundaries between the square surface and adjacent surfaces. The locator is persistent and will remain after you exit the Square tool. To remove it, use Pick > Locator to pick the locator, then select Delete > Delete Active , or toggle the checkmark off when entering Square again.

See Check the deviation and continuity on surface edges.

Buttons

Recalc: Recalculate the surface with the current values in the Square Control window.
Next: Finish the current surface and prompt for new curves.