Theory and Modern Applications
Table 4 Control points and errors for Q-Bézier curve of degree eight to degree quintic (\(\lambda _{1}=1\), \(\lambda _{2}=0\), \(\lambda _{3}=0\), \(\lambda _{4}=0\), \(\lambda _{5}=0\))
From: Approximate multi-degree reduction of Q-Bézier curves via generalized Bernstein polynomial functions
Constraint condition | Control points | Error |
|---|---|---|
Under unrestricted condition | \(\mathrm{P}_{0} = ( - 5.0035,0.005137)\), \(\mathrm{P}_{1} = ( - 9.4843,4.451)\), \(\mathrm{P}_{2} = ( - 1.301,12.02)\), \(\mathrm{P}_{3} = (13.294,12.29)\), \(\mathrm{P}_{4} = (21.945,4.831)\), \(\mathrm{P}_{5} = (16.984, - 0.003849)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.93321 \times 10^{ - 5}\) |
Under \(C^{0}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 9.4828,4.4623)\), \(\mathrm{P}_{2} = ( - 1.3226,11.995)\), \(\mathrm{P}_{3} = (13.335,12.312)\), \(\mathrm{P}_{4} = (21.909,4.8191)\), \(\mathrm{P}_{5} = (17,0)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.18475 \times 10^{ - 4}\) |
Under \(C^{1}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 9.5,4.5)\), \(\mathrm{P}_{2} = ( - 1.3747,11.916)\), \(\mathrm{P}_{3} = (13.483,12.374)\), \(\mathrm{P}_{4} = (21.8,4.8)\), \(\mathrm{P}_{5} = (17,0)\) | \(d^{2}(\mathrm{r}_{8}^{*}(\theta ),\mathrm{r}_{5}(\theta )) = 0.17728 \times 10^{ - 3}\) |