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 | \(\mathrm{P}_{0} = ( - 4.9736,0.02432)\), \(\mathrm{P}_{1} = ( - 7.9384,4.08)\), \(\mathrm{P}_{2} = (2.3687,7.887)\), \(\mathrm{P}_{3} = (10.202,3.969)\), \(\mathrm{P}_{4} = (6.971, - 0.03129)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.13928 \times 10^{ - 3}\) |
Under \(C^{0}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 7.9148,4.1)\), \(\mathrm{P}_{2} = (2.3725,7.8947)\), \(\mathrm{P}_{3} = (10.16,3.9215)\), \(\mathrm{P}_{4} = (7,0)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.28678 \times 10^{ - 3}\) |
Under \(C^{1}\) constraint condition | \(\mathrm{P}_{0} = ( - 5,0)\), \(\mathrm{P}_{1} = ( - 7.8,4.2)\), \(\mathrm{P}_{2} = (2.3841,7.921)\), \(\mathrm{P}_{3} = (10.0,3.75)\), \(\mathrm{P}_{4} = (7,0)\) | \(d^{2}(\mathrm{r}_{6}^{*}(\theta ),\mathrm{r}_{4}(\theta )) = 0.31312 \times 10^{ - 2}\) |