Sentence examples for degree reduction from inspiring English sources

Chen and Yang proposed in [15] an algorithm to degree reduce disk Bézier curves; they consider two cases, constrained degree reduction and non-constrained degree reduction.

Unlikely, degree reduction of disk Bézier curves has not been tackled by many researchers.

The problem of degree reduction and degree raising of triangular Bézier surfaces is considered.

The methods use the matrix representations of the degree reduction and degree raising.

Hu and Wang presented in [16] a method of degree reduction without any boundary conditions based on quadratic programming.

The global reduction of average degree is driven by the average degree reduction in the large periphery of the network.

Examples 1-4 show that the proposed WB-, (G^{0} -, (G^{1} -degree reduction methods in this paper give errors that are less than existing methods with and without continuity conditions; moreover, our methods are the first methods of this kind that consider geometric continuity with degree reductions.

It worth noting that the proposed methods in this paper are the first to consider geometric continuity with degree reductions.

The methods in [17] without interpolation (WIDR) and with interpolation (IDR) degree reductions of Said-Ball curves give errors of 3, 4, respectively.

Figure 7 Error functions by WB- (long-dashed); (pmb{G^{0}}) - (short-dashed), and (pmb{G^{1}}) - (dotted) degree reductions in Example  4.

Figure 4 Error functions for WB- (long-dashed); (pmb{G^{0}}) - (short-dashed), and (pmb{G^{1}}) - (dotted) degree reductions in Example  1.