By Dr. Hiroshi Toriya, Prof. Dr. Hiroaki Chiyokura (auth.), Dr. Hiroshi Toriya, Prof. Dr. Hiroaki Chiyokura (eds.)

3D CAD is without doubt one of the most vital applied sciences of the 90s for the engineering and production international. 3D CAD platforms gives you a aggressive aspect within the improvement of latest items. This booklet offers the improvement of a 3-dimensional CAD method and its wide variety of functions. It describes the recommendations of reliable versions, and the speculation of curves and surfaces and it illustrates those suggestions via "reals international" applications.

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The topological elements never change even when a model is translated, rotated, or scaled up and down. On the other hand, there are geometric elements which describe the shape of a model. These are explained below: • Surface Indicates the shape of a face in 3-dimensions. It is associated with the face in the topological elements. • Curve Indicates the shape of a line in 3-dimensions. It is associated with the edge in the topological elements. 28 3. __-- vertex loop edge---~ face Fig. 2. Topological elements of a solid model in a B-reps based system • Point Indicates coordinates in 3-dimensions.

6 An Example of Primitive Operations 45 • MOVE(BL vL) This is the operation to translate a body B by a vector v. The reverse operation is also MOVE. ) This is the operation to rotate a body B by the angle a about an axis that passes through a point p and has the direction of a vector v. The reverse operation is also ROTATE. ) This is the operation to scale a body B, f times with a reference point p in the direction indicated by a vector v. The reverse operation is also SCALE. ) This is the operation to convert a body B into a mirror image about a plane that passes through a point p and has a normal vector v.

There is a fault, however, in the winged-edge structure. Whereas the structure is based on the EE adjacency relationship of a solid, it cannot always represent the relationships. , a self-loop exists, the nine adjacency relationships of the topological elements cannot be completely obtained. Neither can the winged-edge structure represent the state where a vertex but no edges exists in space. This is because the winged-edge structure is based on edges and thus cannot be applied to a state where there is no edge.

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