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The
dimension of an object is the number of parameters needed to specify the position of a particular point of the object. A point that requires one parameter has one dimension; a point that requires two parameters has two dimensions, and so on.
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Points that lie on a curve are one-dimensional (1D).
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Points that lie on a surface are two-dimensional (2D).
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Points that lie within a volume are three-dimensional (3D).
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In
ACIS, one dimension refers to
wires (such as a line), two dimensions refers to
sheets (such as a plane), and three dimensions refers to
solids (such as a block or sphere). The dimension of an object in
ACIS is independent of the dimension of the space in which it resides. For example, if a curve, which is one-dimensional, exists in 3D object space, the curve itself is still a 1D entity.
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In
ACIS, the dimensionality of a region is a local property that describes the nature of the region surrounding a given point. For instance, if the region surrounding a point is like the region surrounding the center of a solid ball, then the region is 3D. If the region is like a disk (i.e., the region is constrained to lie on a surface), then the region is 2D. If the region is like a curve, then the region is 1D.
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Mixed dimensionality occurs when objects of different dimensionality are represented in the same model.
ACIS unambiguously represents bodies exhibiting mixed dimensionality and allows mixed dimensionality operations. A single body can contain 3D regions, 2D regions, and 1D regions. Figure 3-1 shows a valid
ACIS model consisting of two solid spheres with attached wires that are connected by a sheet. The entire model exists in 3D object space, but the sheet is a 2D entity and the wires are 1D entities.
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Figure 3-1. Mixture of Solid, Sheet, and Wire Regions in ACIS Model
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ACIS also permits the embedding of wires and sheets
within 3D regions. An embedded wire or sheet need not be connected to the outer boundary of the solid region, and it can be open or closed.
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Embedded sheets represent
slits or thin voids in the solid region; i.e., 2D regions that are
not in the point set of the solid. Wires embedded in a solid represent infinitely thin
worm holes in the solid region; i.e., 1D regions that are
not in the point set of the solid.
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Figure 3-2 shows a block that contains a single face floating within it, which is a valid construct in
ACIS.
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Figure 3-2. Embedded Face in Solid Region
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A wire when embedded in a sheet is no longer a distinct wire but rather a part of the loop structure of the faces of the sheet; however, it still represents an infinitely thin "crack" in the sheet; i.e., it is a 1D region that is
not in the point set of the sheet. This is an important concept in the understanding of the Boolean operations on bodies containing embedded wires and sheets.
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