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This book is motivated by surfacesurface intersection problems (SSI) in R, selfintersection surfaces problem in R and three hypersurfaces intersection problems (SSSI) in R4. It presents algorithms for computing all the differential geometry properties of Frenet apparatus (t,n,b,?,t) of intersection curves of surfaces in R for transversal and tangential intersection. The surfaces may be implicit parameterization or parametric parameterization. It is also presents algorithms for computing all the differential geometry properties of intersection curves of Frenet apparatus (t,n,b1,b2,?1,?2,?3) of three hypersurfaces in R4 for transversal intersection. Some techniques for 4D visualization of objects in R4 have been given. Also some applications have been given and plotted.
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