After researching about curves in computer graphics (splines in my case), I have come across something I did not know: Explicit functions like: y=x^2+2 are not the best way to interpolate between points because you could get 2 or more values for y for the same x. So, paremetric functions seem much better for this if we make the commonly used t parameter, the distance from origin, time, etc...
After studing a bit how to convert from explicit to parametric form I have been shocked when I have found in some texts they use these parametric cubic functions to interpolate through points:
x(t)=a*t^3 + b*t^2 + c*t +d y(t)=a2*t^3 + b2*t^2 + c2*t +d2
but wait... this is the exact same form the explicit function was:
y(x)= a*x^3 + b*x^2 + c*x + d
From what I have seen for other example functions in some math books the parametric funcions where not the same form that its explicit form counterpart.
Am I missing something?
Examples of the texts I'm refering to could be: