Advanced Modeling

12

Blend Curves

In This Section:

• Introduction to Blend Curves 408
• Drawing Blend Curves 411
• Editing Blend Curves 414
• Changing the Type of a Constraint 418
• Changing the Continuity of a Constraint 422
• Changing the Curvature Type of a Constraint 424
• Changing the Degree and Parameterization Type 426

Introduction to Blend Curves

Purpose

Blend curves let you create and edit curves that maintain a large amount of construction history. You manipulate blend curves by placing constraints on the shape of the curve, including continuity with other objects.

Overview

Blend curves provide higher-level, simpler methods for shaping and manipulating curves. They provide a level of abstraction on top of the actual geometry of the curve. Blend curves let you focus on what the curve needs to do, and have the system calculate the right curve to fulfill those requirements.

In another sense, however, blend curves are just normal NURBS curves with more construction history: you can use all the normal curve tools on blend curves, and when you are not using blend curve tools, they look like any other curve.

You can create blend curves to intersect surfaces, other curves, and point clouds. When you move either the intersected objects or the intersecting constraint, the blend curve updates automatically.

Blend curves are controlled by constraints:

You create the curve by interactively setting up all the constraints, such as

• what points in space the curve should pass through,

• which surfaces it should be tangent to,

• which existing curves the blend curve should intersect,

• what direction it should be travelling at a certain point,

and so on. Alias draws the curve to satisfy the constraints, and automatically updates the curve when the constraints, or the objects the curve is constrained to, change.

Types of Constraints

There are three main types of constraint. Each constraint type affects the curve it controls in different ways:

• Location: force the curve to pass through the constraint's location in space.

The location constraint is like the edit points of a standard curve. It is the type of constraint you create when you first draw a blend curve.

• Direction: force the curve to pass through the constraint's location in space travelling in a certain world space direction.

There are two sub-types of direction constraints:

• Directed: you set an actual direction for the curve tangent. Use this type when the specific tangent direction at the point of the constraint is important.

• Parallel: you set a line to which the tangent direction must be parallel. This is easier to enforce and results in better curve continuity.

• Geometry: force the curve to pass through a point on a curve or surface and travel in a tangent direction relative to that curve or surface.

The following table shows the icons used to represent the different constraints:

Type	Not attached	Attached to blend curve	Attached to regular curve
Location
Direction

How To

To show the Blend Curve toolbox:

1

Click the Blend curve toolbox icon, or choose Blend curve toolbox from the Curves palette menu.

2

The Blend Curve window appears, with its own palette of blend curve tools. You can use these tools exactly like the tools in the standard tool palettes.

3

To close the Blend Curve window, click the Blend curve toolbox icon again, or click the window's close box.

Drawing Blend Curves

Purpose

Create new blend curves in the scene by placing location constraints and edit existing blend curves.

You will use the Blend curve create tool to create the initial shape of the curve. Then you can add, edit, or delete the initial constraints using the constraint tools.

How To

To create a blend curve:

1

Click the Blend curve create icon, or choose Blend curve create from the Blend Curves palette menu.

2

Click to place the initial location constraints of the new curve. You can continue to move the constraint while the mouse button is down. When you release the mouse button, the new constraint is added to the curve.

• Click the left mouse button to place a constraint.

• Click the middle mouse button to place a constraint horizontal to the previous one.

• Click the right mouse button to place a constraint vertical to the previous one.

• Click another curve to attach a new constraint to that curve.

• Type a 3D coordinate to place a constraint exactly.

• Use the snapping modifier keys or buttons to snap to the grid or existing parts of the model. (See Snapping to Grids, Curves, and Points on page 35.)

3

You can also go back and edit the current curve as you draw:

• Click the current curve to add another constraint between two previous constraints.

• Double-click and drag a constrain on the current curve to move the constraint.

4

Continue adding constraints to the end of the curve as in Step 2 (see Tips and Notes below).

5

Click the Blend curve create tool again to start another curve, or choose another tool.

To continue adding to or editing an existing blend curve:

1

Click the Blend curve create icon, or choose Blend curve create from the Blend Curves palette menu.

2

Shift-click the previously completed blend curve.

3

You can now continue to add to or edit the curve as described above.

Tips and Notes

• If you insert a constraint in the current curve, then try to add a new constraint, the new constraint will be added to the end closest to the inserted constraint.

For example, if you draw a blend curve by placing three constraints, then insert a constraint between the first and second constraints (that is, near the beginning of the curve), the next constraint you add will be added to the beginning of the curve, rather than at the end.

• You can change a blend curve's knot spacing and degree easily with the Blend curve chord, Blend curve uniform, and Blend curve degree tools. See page 426.

Options

"Knot" is another term for edit point.

Knot Spacing

Chord-the new curve's edit points will be parameterized by the chord length of the curve in current units. The chord length is the cumulative straight line distance between consecutive edit points.The starting point of the curve has the parameter 0.0, and the ending point has the parameter equal to the total chord length of the curve.

See Parameterization on page 10.

Uniform-the new curve's edit points will have integral parameters: the first edit point will be parameter 0.0, the second will be 1.0, and so on.

See Degree on page 12.

Curve Degree

The mathematical degree of the curve created, which control the number of CVs per span: 1 (linear), 2 (quadratic), 3 (cubic), 5 or 7. The default is 5. (For some products the default may be 3.)

See Also

• Drawing Curves on page 128

Editing Blend Curves

Purpose

• Select constraints for use with constraint editing tools.

• Move constraints.

• Attach and detach constraints to/from other objects.

• Delete constraints.

Overview

To edit the constraints on a blend curve, you must first select the blend curve with the Blend curve edit tool. This tool allows you to move constraints and attach them to curves or surfaces.

You also use the Blend curve edit tool to select constraints before using the constraint editing tools (such as Blend curve interp direction) to change their properties. See Changing the Type of a Constraint on page 418.

• To add constraints to an existing curve, use the Blend curve create tool (see page 411).

• To change the type of a constraint (for example, from position to direction), see Changing the Type of a Constraint on page 418.

How To

To begin editing a curve:

1

Click the Blend curve edit icon, or choose Blend curve edit from the Blend Curves palette menu.

2

Click the curve you want to edit.

To move a constraint:

1

Select the curve to edit using the Blend curve edit tool (see above).

2

Double-click and drag the constraint you want to move.

or

Click the constraint and type a 3D coordinate to place the constraint exactly.

To attach a constraint to a curve, surface, or point cloud:

1

Select the curve to edit using the Blend curve edit tool (see above).

2

Click the constraint you want to attach.

3

Click the curve or surface you want to attach the constraint to, or click a point in a point cloud.

4

A dialog box appears asking you to confirm the action. Click Yes to attach the constraint to the object.

The constraint's position is now locked to the curve, surface, or point cloud.

To detach (dissociate) a constraint from a curve or surface:

1

Select the curve to edit using the Blend curve edit tool (see above).

2

Click the constraint you want to detach.

3

Click the Blend constraint dissociate icon, or choose Constraint Edits > Blend constraint dissociate from the Blend Curves palette menu.

The constraint stays in the same place, but is no longer constrained to the curve or surface. It is now a simple location constraint.

To delete a constraint:

1

Select the curve to edit using the Blend curve edit tool (see above).

2

Click the constraint you want to delete.

3

Click the Blend constraint delete icon, or choose Constraint Edits > Blend constraint delete from the Blend Curves palette menu.

The selected constraint point is deleted and the curve is re- interpolated.

To reverse the master-slave relationship between attached blend curves

A master-slave relationship between two blend curves is defined as follow. Imagine that curve A is attached to curve B at constraint C. Moving curve B causes curve A to follow. Hence, curve B is the master, and curve A is the slave at constraint C. To reverse this relationship:

1

Select the slave curve using the Blend curve edit tool (see above).

2

Click the constraint for which you want to change the master-slave relationship.

3

Click the Blend pt make master icon, or choose Constraint Edits > Blend pt make master from the Blend Curves palette menu.

When you use the Blend pt make master tool on constraint C, the tool creates a new constraint attaching curve B to curve A, and dissociates constraint C. Now moving curve A causes curve B to follow (the master/slave relationship is reversed).

Tips and Notes

• To edit a different curve while using the Blend curve edit tool, hold down the Shift key and pick another curve.

See Checking the Continuity Between Curves on page 509.

• To evaluate the curvature of the curve as you edit it, click the Curve curvature tool in the Locators palette, then use Blend curve edit to edit the curve.

See page 418 to learn how to create a direction constraint.

• If you use the Blend constraint dissociate tool to detach a direction constraint that was based on the direction of the curve or surface, the direction information is lost and the constraint reverts to a location constraint.

See Also

• Changing the Type of a Constraint on page 418

Changing the Type of a Constraint

Purpose

Change how a constraint affects the blend curve.

See Types of Constraints on page 409 for information on the different types of constraints.

How To

To constrain the curve to simply pass through the constraint:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the constraint you want to change.

3

Click the B.C. interp location icon, or choose Constraint Interp. Direction > B.C. interp location from the Blend Curves palette menu.

The curve will now pass through the constraint freely.

This is the way constraints are created by default.

To constrain the curve to pass through the constraint in a certain direction:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the constraint you want to change.

3

Click the Blend constraint interp direction icon, or choose Constraint Interpolation Direction > Blend constraint interp direction from the Blend Curves palette menu. (Note: the short icon label for the Blend constraint interp direction tool is "pt xyz").

4

Use the direction manipulator (see page 420) to set the direction of the curve at this point.

The curve will now pass through the constraint in the direction you set with the manipulator.

To change the sub-type of a direction constraint:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the direction constraint you want to change.

3

Click one of the Constraint Direction Type tools:

• To set an actual direction for the tangent, click the Blend constraint directed icon, or choose Constraint Direction Type > Blend constraint directed from the Blend Curves palette menu. (Note: the short icon label for the Blend constraint directed tool is "pt ray"). This is shown as a single ended arrow on the manipulator.

• To set a line to which the tangent must be parallel, click the Blend constraint parallel icon, or choose Constraint Direction Type > Blend constraint parallel from the Blend Curves palette menu. This is shown as a double ended arrow on the manipulator.

To constrain the curve tangent relative to another curve, surface, or point cloud:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the attached constraint you want to change.

See page 415 for information on attaching constraints to geometry.

3

Click the Blend constraint interp geometry icon, or choose Constraint Interpolation Direction > Blend constraint interp geometry from the Blend Curves palette menu.

You can only use this tool with constraints that are attached to other objects.

4

Use the direction manipulator (see page 420) to set the direction of the curve at this point, relative to the object it is attached to.

The curve will now pass through the constraint in the direction you set with the manipulator.

To use the tangent direction manipulator:

• Click an axis line to set the tangent direction.

For direction constraints, the axis lines relate to world space (X, Y, Z). For geometry constraints, the axis lines relate to the curve, surface, or point cloud (U, V, Normal).

• Click the center handle, to move the constraint, or type a 3D coordinate.

• Click the arrow, then drag left or right to move the constraint along the manipulator direction line.

Note that the constraint will not move if it is attached to another curve, surface, or point cloud.

• Click the rotation handle (the small circle on the arrow), then drag with the different mouse buttons to change the rotation freely, or type rotational coordinates.

• Click an arc, then drag left and right to change the rotation in that plane, or type a rotation angle.

• Click the square, then drag left or right to change the tangent magnitude, or type a value.

• Click the large circle, then drag left or right to change the curvature magnitude, or type a value. The default is 1.0.

This handle appears when the constraint's continuity is set to G2 or higher (see Changing the Continuity of a Constraint on page 422).

• Click the small circle, then drag left or right to change the curvature rate of change, or type a value. The default is 1.0.

This handle appears when the constraint's continuity is set to G3 or higher (see Changing the Continuity of a Constraint on page 422).

Tips and Notes

• You can use a direction constraint to ensure tangent continuity with an imaginary reflected half.

In the example at left, the direction constraint ensures the blend curve (on the left) is perpendicular to the centerline (usually a major axis). When you reflect the blend curve to create the other half, the tangent at the centerline will be continuous.

See Also

• Changing the Continuity of a Constraint on page 422

• Changing the Curvature Type of a Constraint on page 424

Changing the Continuity of a Constraint

Purpose

Change the continuity required at a constraint.

Overview

When you first create them, all constraints have G2 (curvature) continuity. Use these tools to require less or more continuity at a constraint.

The names of tools correspond to the mathematical terms for the different types of continuity:

• G0: positional.

• G1: tangent.

• G2: curvature.

• G3: constant rate of change of the curvature.

• G4: constant rate of change of the rate of change of the curvature.

See Continuity on page 23 for explanations of the different types of continuity.

How To

To change the continuity at a constraint:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the attached constraint you want to change.

You can only change the continuity on constraints that are attached to other objects. See page 415 for information on attaching constraints.

3

Click one of the Constraint Continuity icons (G0, G1, G2, G3 or G4), or choose from the Constraint Continuity sub-menu of the Blend Curves palette menu.

Tips and Notes

• Use G4 continuity when you want a blend curve to match an existing curve's shape as much as possible. This level of continuity creates a curve join that is difficult to detect.

• Higher levels of continuity require more flexibility in the curve. If maintaining the continuity is completely reshaping your curve, try increasing the degree of the curve. See Changing the Degree and Parameterization Type on page 426.

See Also

• Continuity on page 23

• Changing the Curvature Type of a Constraint on page 424

Changing the Curvature Type of a Constraint

Purpose

Change how curvature is calculated when a geometry constraint is attached to a surface.

Overview

• Parametric curvature.

Align the curvature to an isoparametric direction of the surface.

This type of curvature is especially useful to achieve curvature continuity with the edge of a surface.

• Geometric curvature.

• Construct a plane from the surface normal and the constraint direction (or the normal and the tangent of the curve at the attach point for location constraints).

• Create a section curve by intersecting this plane with the surface.

• Align the curvature to this section curve.

How To

To change the way curvature continuity is calculated for a constraint:

1

Select the curve to edit using the Blend curve edit tool (see page 414).

2

Click the attached curvature continuous constraint you want to change.

You can only change the curvature type of constraints that are attached to other objects, and have G2 or greater continuity. See page 415 for information on attaching constraints, and page 422 for information on setting continuity.

3

Click one of the Constraint Curvature Type tools (Geometric or Parametric), or choose from the Constraint Curvature Type sub-menu of the Blend Curves palette menu.

Tips and Notes

• You must use geometric curvature if you want the blend curve to be planar (all points on the curve lie in the same plane).

See Also

• Changing the Continuity of a Constraint on page 422

Changing the Degree and Parameterization Type

Purpose

Change the degree or parametrization of a blend curve.

See Parameterization on page 10 and Degree on page 12 for explanations of parameterization and degree.

How To

To change the degree of a blend curve:

1

Select the curve or curves to edit using the Blend curve edit tool (see page 414).

Remember that to pick more than one curve with the Blend curve edit tool, you must hold down the Shift key while you pick the other curves.

2

Click one of the Curve Degree icons (Blend curve degree 1,2,3,5, or 7), or choose from the Curve Degree sub-menu of the Blend Curves palette.

The Blend curve degree tool rebuilds the underlying curve to the new degree.

To change the parameterization type of a blend curve:

1

Select the curve or curves to edit using the Blend curve edit tool (see page 414).

Remember that to pick more than one curve with the Blend curve edit tool, you must hold down the Shift key while you pick the other curves.

2

Click one of the Curve Knot Spacing icons, or choose from the Curve Knot Spacing sub-menu of the Blend Curves palette:

• For uniform edit point spacing, click Blend curve uniform.

• For chord-length edit point spacing, click Blend curve chord.

The Blend curve chord or Blend curve uniform tool rebuilds the underlying curve to the new method of parameterization.

Tips and Notes

• When you change the degree of a blend curve, surfaces constructed from the blend curve are also rebuilt to the new degree, unless they have constraints of their own that prevent regeneration.

• You can set the parameterization and degree of new blend curves by setting the corresponding options in the Blend curve create option box (see page 412).

See Also

• Parameterization on page 10

• Degree on page 12

• Drawing Blend Curves on page 411