# Is there a way to find the range and domain of a cubic spline?

Wolfram alpha is telling me there isn't. I guess this reduces down to finding the inflection point in some way and testing against points A and D.

Here's the equation I'm using.
$$x=(1-t)^3*A_{x}+3*((1-t)^2)*t*B_{x}+3*(1-t)*(t^2)*C_{x}+(t^3)*D_{x}$$ $$y=(1-t)^3*A_{y}+3*((1-t)^2)*t*B_{y}+3*(1-t)*(t^2)*C_{y}+(t^3)*D_{y}$$

• I presume first terms in your formulas are $(1-t)^3$, right? – Intelligenti pauca Mar 11 at 18:12
• What do you mean by "domain" here? The above functions are defined for any value of $t$. – Intelligenti pauca Mar 11 at 18:15
• @Aretino DOH. Also Re Domains: Splines are defined for t=[0:1] – Audiomatt Mar 12 at 3:27
• If so, why are you asking for the domain? – Intelligenti pauca Mar 12 at 7:03
• The [0,1] portion of the cubic polynomial will exist inside the rectangle defined by the xmin/xmax and ymin/ymax of the control points. In fact, it will lie inside the convex hull of the control points. – fang Mar 12 at 18:11