Duncan Marsh's book Applied Geometry for Computer Graphics and CAD stated
I'm really confused about this formula. First of all, why do we replace $w_i\mathbf{b_i}$ with $\mathbf{b_i}$ when $w_i=0$? From my understanding, I thought a weight of zero, $w_i=0$ ,just means that particular control point $\mathbf{b}_i$ won't have any effect on the curve, so the $\mathbf{b}_i$ component should be excluded from the formula. However if we follow the formula as stated in the book, this will not be the case, as we still have $\mathbf{b}_i$ in the numerator of our final formula $$\mathbf{B}(t)=\frac{w_0\mathbf{b_0}B_{0,n}+\cdots+ \mathbf{b_i}B_{i,n}+\cdots+w_n\mathbf{b_n}B_{n,n}}{w_0 B_{0,n}+\cdots+0 B_{i,n}+\cdots+w_n B_{n,n} }$$