By Pierre Bézier
The Mathematical foundation of the UNISURF CAD method bargains with the maths fascinated with using the UNISURF CAD procedure.
The publication is split into 5 chapters. Chapters 1 and a pair of take care of the fundamental ideas, expression of some extent, and hodographs of curves and patches. Chapters three and four take care of the quantity and parametric adjustments of curves and patches, and bankruptcy five covers the final and specified situations of mixing.
The textual content is suggested for mathematicians and architects who wish to understand extra concerning the mathematical element of the UNISURF CAD method.
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Remarks: 1. The vector b t tl appears with the same coefficient in both parts of (186). It is thus not constrained in any way. 2. In expression (186), we find the vectors b 0 2 , b 2 ) 0 , b'0 2 and b 2 0. Hence, they cannot all be defined by arbitrary decision. 3. If /c'(0) and /c"(0) are nil, the vectors b 0 2 , b 2 0 , b'0 2 and b'2Q are no longer present in (186) and are not submitted to any condition. In this case, the curves P(u,0), P'(0,w), P"(0,y), P'"(f,0) are tangent by pairs at P(0,0).
N). 3 Successive hodographs Repeating the operations described earlier, we obtain the general hodograph: (m-k + l)\ ( n - / + l ) ! d k + lP iu,v) ' duk. 4 Silhouette lines The silhouette line of a surface S, seen along a projecting direction D, is the contact line with a Determination of a characteristic net cylinder, the generatrices of which are parallel to D, and which is tangent to S. Its projection is the envelope of the projections of the generatrices of the surface onto a plane that does not contain D.
The surfaces are sectioned by the 50 Blending Figure 87 Four complementary patches Figure 85 Defining a fillet connection of C t , . . , C 4 with£ 1 > 2 ,. • • ,£4,1 belongs to the type: /z(w) = constant k(u) = 0 If then the connection of F with E{ 2 is controlled by the rule: h\,2=h\A k 'l,2=Q If this is the case along the four boundary lines of F, the degree of that patch is (3 x 3). 4^^2,3 til2 will be given the form: h'ia(