By Mamoru Hosaka (auth.)
1 goals and contours of This ebook The contents of t. his booklet have been initially deliberate t. o be integrated in a publication en titled Geometric lIIodeling and CAD/CAM to be written by means of M. Hosaka and F. Kimura, yet because the draft. of my a part of the booklet was once comprehensive a lot in advance of Kimura's, we made up our minds to submit this half individually initially. In it, geometrically orientated uncomplicated tools and instruments used for research and synthesis of curves and surfaces utilized in CAD/CAM, a variety of expressions and manipulations of free-form floor patches and their connection, interference in addition to their qualit. y eval uation are taken care of. they're very important components and systems of geometric versions. And building and usage of geometric versions which come with free-form surfaces are defined within the software examples, within which the meth ods and the recommendations defined during this ebook have been used. within the succeeding publication which Kimura is to write down, complex issues corresponding to information constructions of geometric types, non-manifold versions, geometric inference in addition to tolerance difficulties and product versions, procedure making plans etc are to be integrated. Conse quently, the name of this e-book is modified to Modeling of Curves and Surfaces in CAD/CAM. positive factors of this e-book are the next. although there are first-class textual content books within the comparable box equivalent to G. Farin's Curves and Surfaces for CAD /CAM[l] and C. M.
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Extra info for Modeling of Curves and Surfaces in CAD/CAM
Sample text
52) We can determine the value of 82 from eq. 52), and Z2 from eq. 50). The intersection curve of the two cylinders is thus calculated. According to given values PI, P2, ¢ and d, the shape of intersection curve has two, one and no loop(s) and shows special shapes between their transitions, which has singular points where dzI/d8 l becomes indeterminate. A more general treatment of the intersection is explained in Chap. 4 and in Chap. 16. 7 Expressions of Movement of a Body by Reflection When a body moves in space, it is difficult for a person to grasp its positions and attitudes without visualizing it, for one cannot imagine correctly a motion of simultaneous translation and rotation.
Iii) Sweep the new small square on the face A in the direction x by length b. This creates two faces, three vertices and five edges. 13 Example of Euler operations Make a b x a rectangle at the corner on the side face B of the body. This creates one face, two vertices and three edges. (v) Sweep the new face in the y direction by length (a - b). This creates one face, two vertices and three edges. (vi) Make an a x a square on the upper face C . This creates one face, one vertex and two edges. (vii) Sweep the a x a square on the face C in the direction z by length (a - b).
7( a). Let a line L1 be the intersection line of M1 and M 2, and a line L2 be that of M3 and M 4, and the common perpendicular of L1 and L2 be L3. If M1 and M2 are parallel, then there is no intersection line L 1, and rotating the pair (M3' M 4) around L2 until M3 becomes orthogonal to M2, then interchanging the order of application of ll'h and M3, we get two pairs (M1' M 3) and (M2' M 4), which we consider the initial states of M1, M 2, M3 and M4 by renaming. Then by the following procedures the rotation axis and the rotation angle are determined.