Sweep Representations:-

Sweep representations are used to construct three dimensional objects from two dimensional shape .There are two ways to achieve sweep: Translational sweep and Rotational sweep. In translational sweeps, the 2D shape is swept along a linear path normal to the plane of the area to construct three dimensional object. To obtain the wireframe representation we have to replicate the 2D shape and draw a set of connecting lines in the direction of shape, as shown in the figure (8)

In rotational sweeps, the 2D shape is rotated about an a axis of rotation specified in the plane of 2D shape to produce three dimensional object. This is illustrated in figure (9).

In general we can specify sweep constructions using any path. For translation we can vary the shape or size of the original 2D shape along the sweep path. For rotational sweeps, we can move along a circular path through any angular distance from 0° to 360°. These sweeps whose generating area or volume changes in size, shape or orientation as they are swept and that follow an arbitrary curved trajectory are called general sweeps .General sweeps are difficult to model efficiently for example, the trajectory and object shape may make the swept object intersect itself, making volume calculations complicated. Further more, general sweeps do not always generate solids. For example, sweeping a 2D shape in its own plane generates another 2D shape.

1. Solid-modeling packages often provide a number of construction techniques.

2. Sweep representations are useful for constructing three-dimensional objects that possess translational, rotational, or other symmetries.

3. We can represent such objects by specifying a two dimensional shape and a sweep that moves the shape through a region of space.

4. A set of two-dimensional primitives, such as circles and rectangles, can be provided for sweep representations as menu options.

5. Other methods for obtaining two-dimensional figures include closed spline curve constructions and cross-sectional slices of solid objects.

6. Figure below illustrates a translational sweep. The periodic spline curve in Figure (a) defines the object cross section.

1. We then perform a translational sweep by moving the control point’s p, through p3 a set distance along a straight line path perpendicular to the plane of the cross section.

2. At intervals along this path, we replicate the cross-sectional shape and draw a set of connecting lines in the direction of the sweep to obtain the wireframe representation shown in Fig (b).

3. An example of object design using a rotational sweep is given in Figure below this time, the periodic spline cross section is rotated about an axis of rotation specified in the plane of the cross section to produce the wireframe representation shown in Fig (b).

1. Any axis can be chosen for a rotational sweep. If we use a rotation axis perpendicular to the plane of the spline cross section in Fig. (a), we generate a two-dimensional shape.

2. But if the cross section shown in this figure has depth, then we are using one three-dimensional object to generate another.