Solid Modelling

SOLID MODELLING An important use of structures is in the design and representation of different types of systems. Architectural and engineering systems, such as building layouts and electronic circuit schematics, are commonly put together using computer- aided design methods. Graphical methods are used also for representing economic, financial, organizational, scientific, social, and environmental systems. Representations for these systems are often constructed to simulate the behaviour of a system under various conditions. The outcome of the simulation can serve as an instructional tool or as a basis for making decisions about the system. To be effective in these various applications, a graphics package must possess efficient methods for constructing and manipulating the graphical system representations. The creation and manipulation of a system representation is termed modelling. Any single representation is called a model of the system. Models for a system can be defined graphically, or they can be purely descriptive, such as a set of equations that defines the relationships between system parameters. Graphical models are often referred to as geometric models, because the component parts of a system are represented with geometric entities such as lines, polygons, or circles. We are concerned here only with graphics applications, so we will use the term model to mean a computer-generated geometric representation of a system. graphics scenes can contain many different kinds of objects: trees, flowers, clouds, rocks, water, bricks, wood panelling, rubber, paper, marble, steel, glass, plastic, and cloth, just to mention a few. So it is probably not too surprising that there is no one method that we can use to describe objects that will include all characteristics of these different materials. And to produce realistic displays of scenes, we need to use representations that accurately model object characteristics. Representation schemes for solid objects are often divided into two broad categories, although not all representations fall neatly into one or the other of these two categories. Boundary representations (Breps) describe a three-dimensional object as a set of surfaces that separate the object interior from the environment. Typical examples of boundary representations are polygon facets and spline patches. Space-partitioning representations are used to describe interior properties, by partitioning the spatial region containing an object into a set of small, non overlapping, contiguous solids (usually cubes). A common space-partitioning description for a three-dimensional object is an octree representation. SWEEP REPRESENTATIONS Sweep representations are useful for constructing three-dimensional objects that possess translational, rotational, or other symmetries. We can represent such objects by specifying a two dimensional shape and a sweep that moves the shape through a region of space. A set of two-dimensional primitives, such as circles and rectangles, can be provided for sweep representations as menu options. Other methods for obtaining two-dimensional figures include closed spline curve Constructions and crosssectional slices of solid objects. Figure here illustrates a translational sweep. The periodic spline curve in Fig. 1(a) defines the object cross section. We then perform a translational

Constructing a solid with a translational sweep. Translating the control points of the periodic spline curve in (a) generates the solid shown in (b), whose surface can be described with point function

P(u,v)

Sweep by moving the control points p0, through p3 a set distance along a straight line path perpendicular to the plane of the cross section. At intervals along this path we replicate the crosssectional shape and draw a set of connecting lines in the direction of the sweep to obtain the wireframe representation shown in Fig. 1(b). An example of object design using a rotational sweep is given in Fig. 2. 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. 2(b). 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. 2(a), we generate a two-dimensional shape. But if the cross section shown in this figure has depth, then we are using one three-dimensional object to generate another. In general, we can specify sweep constructions using any path. For rotational sweeps, we can move along a circular path through any angular distance from 0 to 360⁰. For noncircular paths, we can specify the curve function describing the path and the distance of travel along the path. In addition, we can vary the shape or size of the cross section along the sweep path. Or we could vary the orientation of the cross section relative to the sweep path as we move the shape through a region of space. Constructing a solid with a rotational sweep Rotating the control points of the periodic spline curve in (a) about the given rotation axis generates the solid shown in (b), whose surface can be described With point function

p(u,v).