Translations:B-Splines/42/en

At every spline position $$t$$ the sum of polynomials is 1 (indicated by the orange line). At the start only the red polynomial has an influence since all other polynomials are there 0. At greater $$t$$ the spline is described by a linear combination of different basis polynomials. In the image above, every polynomial is greater than 1 for the whole range $$0 < t < 1$$. This is not necessarily the case. As shown in the video, the basis polynomials are basically only greater than 0 for a certain spline position range. The interval at which a basis polynomial is greater than 0 is described by the knot vector. If you are interested in learning about the knot vector, have a look at this video.