The Bernstein Approximation

As explained in Chap. 3, curves and surfaces based on Hermite interpolation position vectors of 2 points Q₀and Q₁ and the tangent vectors at those points $$ {\dot Q_0} $$ and $$ {\dot Q_1} $$ (Chap. 3): 5.1$$ P\left( t \right) = \left[ {\begin{array}{*{20}{c}} {{t^3}}&{{t^2}}&t&1 \end{array}} \right]\left[ {\begin{array}{*{20}{r}} 2&{ - 2}&1&1 \\ { - 3}&3&{ - 2}&{ - 1} \\ 0&0&1&0 \\ 1&0&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{Q_0}} \\ {{Q_1}} \\ {{{\dot Q}_0}} \\ {{{\dot Q}_1}} \end{array}} \right]. $$