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# Surfaces

The described tools are able to detect plain and cylindrical surface patches, so these are the two existing kinds of surfaces.

Figure 8: An object with Plane Surfaces and Cylindrical Surfaces. The entire surface of this object is modeled. The object coordinate system (OCS) is in the front corner.

The addition of more surface models, if corresponding detection tools are developed, is intended.

Both surface types are bounded by edges, so they are described by a closed loop of edges. This means that the end of one edge is the start of the next one. The end of the last edge is the start of the first.

Figure 9: Example for the surface type Plane Surface

Plane Surfaces are finite parts of a plane. An infinite large geometric plane is cut in two parts by a closed loop of edges (Figure 9). The parts with the finite area is the inner side. All bounding edges and their vertices are in this plane. The orientation of Circular Edges is identical to the surface normal.

Figure 10: Examples for the surface type Cylindrical Surface. Cone segment, frustum segment, frustum, cylinder, and cylinder segment.

cylindercirclesequalvirtual
cylinder segmentarcsequalstraight or rounded
conecirclesone equals zerovirtual
Cone segmentarcsone equals zerostraight or rounded
frustumcirclesunequalvirtual
frustum segmentarcsunequalstraight or rounded

Table 2: Special cylindricals and their structure

Cylindrical Surfaces (Figure 10) are defined as follows:

• They consist of two Circular Edges. If the Circular Edges are arcs, we say it is a segment. In this case the arcs are connected by Straight or Round Edges, otherwise the connections are Virtual Edges.
• The centers of the Circular Edges are forming the axis and both Circular Edges are perpendicular to this axis.
• One of the Circular Edges may have radius zero. In this case we say it is a cone.

The number of surface types is not restricted. If a new tool for detecting a certain structure in the range data is developed, a new surface model may be added.

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Last updated 1997/07/11, © Jochen Duckeck