一种基于正则参数化的降维细分算法(英文)

In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.     

Equi-multiresolution and FourierEqui-integrable Space

Let{V,,jeZ}beamu1tiresolution,withV;gV,+,.Inpractice,weoftenneedtoconsidertheequi-appr0ximati0nofamultiresolution(seeLl'2'3J)toafunctionspaceVorafunctionsetF.ThiscanbewrittenaswhereVGL'(R"),F=L'(R"),VI=L'(R')(IeZ),andPv,isaprojectionoperatorofLz(R")-Vz.ThuswecanusePv,finsteadoff,approximately.Investigati0nofthisproblemhasveryimportantpraticalvalueandthe0reticalsignificance.Considerations0fthisquestionalsoleadtobetterunderstandingformultiresolution.FromTheorem2weknowthatforalljeZ,V…