Theory and Modern Applications
Table 3 Control points and errors for Q-Bézier curve of degree eight to degree quintic (\(\lambda _{1}=1\), \(\lambda _{2}=0\), \(\lambda _{3}=0\), \(\lambda _{4}=1\), \(\lambda _{5}=0\))
From: Approximate multi-degree reduction of Q-Bézier curves via generalized Bernstein polynomial functions
Constraint condition | Control points | Error |
|---|---|---|
Under unrestricted condition | \(\mathrm{P}_{0} = ( - 5.0124,0.01278)\), \(\mathrm{P}_{1} = ( - 9.4306,4.405)\), \(\mathrm{P}_{2} = ( - 1.5228,12.21)\), \(\mathrm{P}_{3} = (13.877,11.79)\), \(\mathrm{P}_{4} = (22.01,4.775)\), \(\mathrm{P}_{5} = (16.975,0.003712)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.29699 \times 10^{ - 4}\) |
Under \(C^{0}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 9.4415,4.4265)\), \(\mathrm{P}_{2} = ( - 1.5404,12.185)\), \(\mathrm{P}_{3} = (13.92,11.801)\), \(\mathrm{P}_{4} = (21.957,4.7767)\), \(\mathrm{P}_{5} = (17,0)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.59456 \times 10^{ - 4}\) |
Under \(C^{1}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 9.5,4.5)\), \(\mathrm{P}_{2} = ( - 1.5514,1.076)\), \(\mathrm{P}_{3} = (14.081,11.83)\), \(\mathrm{P}_{4} = (21.8,4.8)\), \(\mathrm{P}_{5} = (17,0)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.54881 \times 10^{ - 3}\) |