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Theory and Modern Applications

Table 1 Comparison of research work

From: Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications

Sr. no

Existing method [11]

Proposed method

1

Hu et al. presented the SG-Bernstein basis functions of order n with multiple shape parameters.

The GBTB functions are constructed with only two shape parameters.

2

Only simple SG-Bézier general cylinder has been constructed.

Two GBT-Bézier general cylinders can be connected by higher \(C^{2}\) continuity smoothness.

3

Two SG-Bézier ruled surface patches have been connected by only \(C^{1}\) continuity.

Two GBT-Bézier ruled surfaces can be connected by higher \(C^{k}\) (k = 2,3) continuity constraints.

4

Two adjacent SG-Bézier swung surface patches have been connected by only \(C^{1}\) continuity.

Two adjacent GBT-Bézier swung surfaces can be connected by higher \(C^{2}\) continuity conditions.

5

Composition of two SG-Bézier swept surfaces by only \(C^{0}\) continuity conditions.

Two adjacent GBT-Bézier swept surfaces can be connected by higher \(C^{1}\) and \(C^{2}\) continuity smoothness.

6

No set of algorithms has been constructed.

A set of algorithms can be constructed for explaining how to enforce these engineering surfaces in practice.