Using the Pipe Primitive

Although a pipe is a single primitive (regardless of how long it is and how many bends it has), geometrically, it is effectively a series of cylinders connected by torus sections. As illustrated in Figure A-1, the pipe must have a minimum of two end points (shown in blue). Between the end points can be any number of other points (shown in red) to designate bends in the pipe or changes in pipe diameter. All points (including end points) contain information to define the bend radius, outer diameter, and inner diameter.

To build a pipe, points can be appended after a given point, prepended before a given point, moved, or deleted; and the parameters at each point can be independently edited at any time.

One potentially confusing aspect of the pipe is that bend points do not always lie along the pipe’s path. This is because the bend radius dictates the path of the pipe between points. As shown in Figure A-2, which depicts the same pipe with three different bend radii, a small bend radius means the bend point will be closer to the path of the pipe, and a large bend radius means the point will be farther away. Also, because a bend is computationally equivalent to a section of torus, each point is constrained to accept only those bends that are consistent with the parameters of a torus (e.g., the user cannot specify a bend radius that is so small that it violates the defined characteristics of a torus).

In addition, because they are defining turns, points in a pipe are often nonlinear. However, as shown in Figure A-3, collinear points can also be used when a modeler simply wants to achieve a tapered or "stepped" inside or outer diameter on a straight-running tube. Examples of other potential uses include a notched axle on a vehicle, a pressed gear fitting, and a tapered end on a garden hose.

Nonetheless, it is good modeling practice to build your pipe with only those points needed to define its shape. It is not necessary to add extra collinear points along a long straight section of pipe. Note too that pipes are not required to have hollow volume in them at all. The modeler can set the inner diameter to 0 and achieve a solid shape.

Modelers should remember that when a pipe is made with the make or create command, the default values for the previously listed parameters are based upon the size of the view in the graphics window when the pipe is first created. This is important because modelers can sometimes find themselves unable to move or delete certain points due to relatively large bend radii (e.g., that might have been established when the pipe was first created in a relatively large graphics window). These large radii constrain the shape and prevent it from accepting mathematically invalid commands (e.g., a larger inner diameter than outer diameter or an unacceptably tight bend radius).

In addition to using the pipe primitive to make tubular objects such as electrical and hydraulic lines, it can be used to make other types of objects.

Consider, for example, the building of a wire coil. The pipe primitive can reduce the complexity of the process by avoiding some of the difficulties associated with combining geometry.

The main challenge of using the pipe to build a coil is to locate where the points should be in order to achieve the properly dimensioned geometry. We can start with the following measured dimensions:

In the example shown in Figure A-4, the coil diameter is 1/4 (0.25) in, the wire diameter is 1/32 (0.03125) in, and the height of each of the 10 coil sections is 7/32 (0.21875) in.

The key to properly and precisely positioning points to build a coil section is to use half of the coil diameter as an offset. The first and the last points in the coil must lie on the pipe’s path. These points are easily determined at 90° intervals from the center of the pipe (or, with a bit of trigonometry, at any interval). The rest of the points for the pipe are located at ± offsets in whichever plane is perpendicular to the pipe height vector from the center of the pipe with the proper height delta (which will generally be 1/4 of the height per coil section).

Obviously, the construction of this type of object is a little more advanced than the construction of many of the other types of objects discussed. Thus, the following text provides the user with step-by-step instructions that can also serve as a kind of template when using the pipe primitive to build a coil or similar object.

To build two turns of a coil at the origin with a coil diameter of 1000 mm, a wire diameter of 200 mm, and a coil height of400 mm (running along the +Z axis), the user would perform the following steps (or ones similar to them):

The raytraced image of the coil segment is shown in Figure A-5.