Was looking at this video https://youtu.be/60VoL-F-jIQ?t=213 and a linear interpolation between two equations is mentioned. I don't understand how one linearly interpolates two equations. The video shows the following 2 equations and a 3rd one which is said to be the linear interpolation of the first two.
- $$a(x) = x^2$$
- $$b(x) = -(x-1)^2 + 1$$
- $$ c(x) = a(x)\cdot(1-x) + b(x) \cdot x$$
I don't understand how equation 3 was reached from equations 1 and 2?
Let's assume a(x),b(x) corresponds to N1,N2 respectively. Also if in the interpolation we use ξ instead of x below you can see the interpolation between the 2 functions which is nothing else than interpolation between 2 numbers actually along ξ[0,1].