Theory and Modern Applications
From: Approximate multi-degree reduction of Q-Bézier curves via generalized Bernstein polynomial functions
Constraint condition | Control points | Error |
---|---|---|
Under unrestricted condition | \(\mathrm{P}_{0} = ( - 5.0207,0.007382)\), \(\mathrm{P}_{1} = ( - 7.6988,4.167)\), \(\mathrm{P}_{2} = (3.0487,8.14)\), \(\mathrm{P}_{3} = (9.8918,3.853)\), \(\mathrm{P}_{4} = (7.0179, - 0.01358)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.50153 \times 10^{ - 4}\) |
Under \(C^{0}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 7.7184,4.1712)\), \(\mathrm{P}_{2} = (3.0507,8.1466)\), \(\mathrm{P}_{3} = (9.9157,3.8302)\), \(\mathrm{P}_{4} = (7,0)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.97175 \times 10^{ - 4}\) |
Under \(C^{1}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 7.8,4.2)\), \(\mathrm{P}_{2} = (3.0613,8.1701)\), \(\mathrm{P}_{3} = (10.0,3.75)\), \(\mathrm{P}_{4} = (7,0)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.8934 \times 10^{ - 3}\) |