form•Z Revolutions and Sweeps

30 Sep, 2002 By: John E. Wilson

We examined form•Z's tools for creating wire objects, such as lines and curves, last month. This month we will examine two of the program's tools for transforming those wire objects into 3D objects.

Both of the tools we will look at--the Revolved Object and the Sweep tools--are initiated from the Parametric Derivatives palette in form•Z's Modeling toolbar, as shown in Figure 1. When the resulting 3D object is completely closed, it is a solid you can modify with form•Z's Boolean operations. When the object has an opening, though, it is a surface you will use trim and stitch operations to modify.

form•Z refers to a wire object that represents an outline, or profile, to be transformed into a 3D object as a source. A source can be either open or closed and is always planar. If you should specify a non-planar object, form•Z automatically projects it onto the reference plane (the current xy plane) as it creates a 3D object.

When you are using a tool that requires a source, form•Z normally issues a prompt for you to specify the source object. If you have used form•Z's Pick tool to preselect any number of objects, though, form•Z automatically accepts them as sources and skips the prompt to select a source. When a source consists of multiple objects, each object creates a separate 3D object, even though they were created simultaneously.

Revolved Objects
The Revolved Objects tool transforms the rotational space of a source object into a 3D object. The rotation axis can be one of the three coordinate system axes, a line, a straight segment of a vector line, or a straight edge on a 3D object. The source object may touch the axis, but it cannot cross it or have a segment that is collinear with or tangent to the axis. See Figure 1 for an example of a source and axis.

Figure 1. form•Z's Revolved Object tool creates a 3D object by revolving a 2D source object fully or partially about an axis. You can specify that the surface of the revolved object be facetted or smooth, as well as the direction and angle of partial revolutions.

Usually, you will use a wire-frame object as a source, but you can also use the faces and edges of existing 3D objects as sources. In the Tool Options palette, which is displayed when you initiate the Revolved Objects tool, select Keep as the Operand Status. Otherwise, the existing 3D object becomes ghosted (and, therefore, unavailable) or is deleted when the new 3D object is created.

You specify, in the Tool Options palette, the number of degrees than the source is to be revolved around the axis. When you specify less that 360 degrees, you can set the revolution direction to clockwise or counterclockwise, as viewed from the positive end of the axis. You can also specify whether the two ends of a partial revolution are to be capped or left open.

The Tool Options palette offers two alternatives in establishing the revolved 3D object's surface type: facetted or smooth. The curved and rounded surfaces of facetted 3D objects are composed of three- and four-sided flat faces, and additional options give you control over the size and extent of the facets. The surfaces of smooth 3D objects, on the other hand, are perfectly rounded. A sub-option of smooth 3D objects is to construct them as nurbz (auto des sys likes to replace the letter s with a z). When you choose this option, the shape of the source is transformed into a NURBS curve as it is revolved. As a result, even a rectangular source object becomes a NURBS curve.

form•Z's Sweep tool uses one or more source objects to define the cross section of a 3D object, and one or more wire-like path objects to define its lengthwise shape. A path can be planar or 3D, and open or closed. Except for Boundary sweeps, which are described later in this section, you can specify that the ends of an open sweep are to be closed or left open. The as-drawn location and orientation of source objects is not important because form•Z automatically positions them at the start--and the end as well for some sweeps--of the path and perpendicular to it. The Sweep tool has four different methods for creating a sweep object: Axial, Two source, Two path, and Boundary.

An Axial Sweep creates a 3D object from one source and one path. You can increase or decrease the size of the source, in either or both its x and y dimensions, as it is swept along the path. You can also rotate the source as it is swept. By default, the source remains perpendicular to the path as it travels, and for some 3D path shapes this may cause the source to rotate. You can, though, select the Perpendicular to Plane option to keep the source perpendicular to the current reference plane. Figure 2 shows an example of this. This option, however, does not give satisfactory results if any portion of the path is perpendicular to the reference plane. The facetted and smooth surface options for axial sweep 3D objects are the same as those of revolved objects.

Figure 2. The source tends to rotate during axial sweeps along a 3D path. To prevent this, activate the Sweep tool's Perpendicular to plane option.

In Two Source sweeps, one source establishes the 3D object's cross-section shape at the beginning of the path, while the second source sets the cross-section shape at the end of the path; in between, the two cross-section shapes gradually blend together. To avoid twisting, the two source objects must have the same direction and their first points must be aligned. (To display wire directions and first points select Display Options from form•Z's Display menu, and then select Wire Frame Options. Use the Reverse Direction and Make First Point tools in the Topologies palette to change the direction and first point location of a source object.) The facetted surface option for Two Source sweeps works the same as for revolved objects. The Smooth surface option, though, always changes source objects into NURBS curves.

In Two Path sweeps the size of a single source object changes to fill the space between two paths as it moves to create a 3D object. As you would expect, the paths must have the same direction. By default the overall size of the source changes as the distance between the two paths changes; however, when you select the Preserve Height option, the height of the source remains unchanged as it is stretched or compressed between the two paths. The facetted and smooth options work the same as those for Two Source sweeps.

Boundary sweeps are made from one source and one path. The path can be either open or closed, but it must have at least two segments. The source must be open and its two ends must be positioned so that if a line were drawn between them, it would not intersect any portion of the source. The resulting 3D object is always closed. The Smooth surface option for Boundary sweeps does not have a sub-option for changing source objects into NURBS curves.

Editing 3D Objects
The Tool Options palette of both the Revolved Object and the Sweep Object tools have an Edit option. That option displays a dialog box that duplicates most of the Tool Options choices and also gives you a preview of the results of the current settings. In addition, for sweep objects, it allows you to make changes to source and path objects. This very useful dialog box is also displayed when you select Edit from the Query tool's dialog box.

About the Author: John E. Wilson