A 3D Form Synthesizer

auto-des-sys, Inc. frequently refers to form•Z as a "3D form synthesizer" to emphasize the program's ability to manipulate digital data in creating 3D shapes, just as a music synthesizer manipulates digital data in creating music. Often, your approach in creating 3D models with form•Z will be to create simple geometric shapes and then transform them into complex shapes. This month we will explore the form•Z tools that make these transformations possible.

Modeling a Telephone Headset
To give you an idea of how form•Z can create a fairly complex model from simple objects, we will go through the steps you might take in creating the 3D model of a telephone headset. First, the Vector Line tool is used, with object type set to 3D Extrusion, to create the two 3D objects shown in Figure 1(A). Then the Difference tool is used to subtract the top object from the bottom one, leaving the 3D object shown in Figure 1(B). The Difference tool removes the volume that one set of objects has in common with a second set and deletes the non-shared volume of the first set.

Figure 1. One of form•Z's strengths is its ability to manipulate relatively simple geometric shapes. This figure shows the steps you might take in constructing the 3D model of a telephone headset.

Next, the Cylinder tool is used to create the earpiece of the headset. The cylinder is tapered with the Draft Angle tool, and it is joined to the other 3D object with the Union tool. The model at this stage is shown in Figure 1(C).

The sharp edges and corners of the model are rounded with the Plain Round tool, as shown in Figure 1(D). You will commonly set form•Z's topological level (from the Topological Levels palette) to segment, and use the Pick tool to preselect the edges you want to round using of the Plain Round tool to create rounds on a single object that have different radius values.

Arc-shaped bulges in the sides of the headset are created with the Deform tool, as shown in Figure 1(E), and the model is finished by using the Deform tool again to curve it, as shown in Figure 1(F). I'll have more to say about the Deform tool later in this column.

Meshes
A form•Z mesh is a surface made of flat, three- or four-sided facets. You can create them directly with the C-Mesh tool that we discussed last month (December 2002, "Meshes and Nurbs"), or transform existing objects into meshes with tools in the Meshes and Deform palette. The Mesh tool transforms an object into a mesh that has facets with four sides. You establish the size of the facets as a tool option. The Q-Subz (Quadratic Subdivisions) tool also creates a mesh of four-sided facets, but it rounds the sharp edges and corners of 3D objects. The T-Subz (Triangular Subdivisions tool), which works very much like the Q-Subz tool, divides an object into three sided facets, as shown in Figure 2.

Figure 2. The tools in form•Z's Meshes and Deform palette allow you to transform sharp-edged solid objects into smooth-meshed objects, and to change the shape of meshed objects.

Mesh Displacements
A useful property of meshes lets you modify their shapes by moving their facets. You can use the Move tool to move individual facet corners by setting the topological level to Point, and you can move individual faces by setting the topological level to Face. By using the pick tool to preselect them, you can move multiple corners and faces simultaneously.

form•Z also has specialized tools on the Meshes and Deform palette that modify the shape of a mesh surface by moving its facets. One of them, the Move Mesh tool, moves a group of facets in the z-axis direction according to a predefined cross-section shape. With this tool, you can use an arc-shaped profile to change a planar meshed surface into a dome-shaped mesh. form•Z has six profiles, which are in the Profiles palette, and you can create your own profiles with the Define Profile tool. The area of the mesh you move can be circular, linear, or along a pre-drawn wire path.

The Disturb tool can create wave-like ridges in either linear or circular patterns in a mesh. The tool's options allow you to control the height of the waves and their distance apart. This tool can also create random bumps in a mesh. The Displace tool moves the points of a mesh relative to the gray color intensity of a bitmapped image. The lighter an area of the image is, the further the mesh points over the image are moved.

Deformations
As demonstrated in the description of the steps for creating a form•Z 3D model, the Deform tool, which is also in the Meshes and Deform palette, makes a variety of changes to the shape of a mesh. The portion of the model that is to be changed and the extent of the change are both controlled by a deformation box. Initially, the deformation box completely encloses the selected 3D objects, but you can move the upper and lower bounds of the box by clicking a horizontal edge and dragging it up or down to the position you want as you hold down the Option key on Macintosh computers or the Ctrl+Shift keys on Windows computers. Once you have the deformation box positioned, you click one of its horizontal edges, or one of its corners, and drag it to make the deformation. In Figure 2, for example, a corner of the deformation box is dragged to bulge the tubular mesh equally in the x and y directions. By selecting and dragging a horizontal edge of the deformation box, the bulge would have been only in the x- or y-axes directions.

The Deform tool offers the following seven types of deformations in its Tool Options palette:

• Bulge symmetrically stretches the center of the mesh inwardly or outwardly to create an arc-shaped profile. When the Through Center option is also selected, though, the upper and lower bounds of the deformation box are moved, while the mesh in the center remains fixed.
  
  
• Radial Bend creates an arc-shaped bend about an axis that is in the plane of the opposite end of the deformation box. If, however, the Through Center option is also selected, the axis is in a plane midway between the ends of the deformation box.
  
  
• Bezier Bend uses a bezier curve having three segments to create a variety of curved deformations, depending on which computer keys are held down as you drag an edge of the deformation box. The curve shape shown in Figure 2, for instance, is created by holding down the Option key of Macintosh computers and the Ctrl+Shift keys of Windows computers.
  
  
• Radial Shear creates deformations that are similar to the Bulge option, except the vertical sides of the deformation box remain parallel to each other.
  
  
• Shear deforms the mesh linearly as the selected end of the deformation box is slid to a new position in its plane. The opposite end of the deformation box is fixed, unless the Through Center option is also selected. Then, the center of the mesh is fixed as the ends of the deformation box move simultaneously in opposite directions.
  
  
• Taper creates a linear deformation in the mesh as the area of the selected end of the deformation box is increased or decreased in size. When the Through Center option is in effect, the center of the mesh remains fixed in size; as you change the size of one end of the deformation box, the other end changes symmetrically.
  
  
• Twist creates a helix-shaped deformation. The non-selected end of the deformation box remains fixed, unless the Through Center option is selected. Then, the ends are simultaneously twisted in opposite directions.