To use the functions you do not need a detailed explanation of what is going on internal to the function.
first get a vector of cubic polynomial coefficients using cspline() using two vectors being the passing points x and y.
(In the case of bspline() the two vectors are the knots)
Use this vector of cubic polynomial coefficients, the two vectors being the passing points x and y, and the point of interest in the interp() function.
https://community.ptc.com/t5/Mathcad/cspline/m-p/541847#M179328
Shows how to get the coefficients?
Try this for full explanation of creating spline coefficients.
A cubic spline solution where you specify the starting and ending slope plus the points enclosed. This will only confuse you. But it shows how the coefficients are calculated.
Calculate the equations within a cubic spline for the coaster of n points with known x,y values.
Result is vector of Coefficients A, B, C, D for each segment with equation of
y(x) = A.x3 + B.x2 + C.x + D
d.y(x)/dx = 3.A.x2 + 2.B.x + C
d2.y(x)/dx2 = 6.A.x + 2.B
dy/dx and d2y/dx2 continuous at each internal point,
dy/dx specified at each end point.
# segments is s=n-1
4.s unknowns are coefficients A,B,C,D for each of these segments
2.s equations for y(x) at end of each segment
2 equations for dy/dx at ends
s-1 equations for dy/dx across internal points
s-1 equations for d2y/d2x across internal points
Using these equations a large matrix A and right hand side vector b is formed.
Solve the equations for the coefficients.
Interpolation is just using the correct coefficient A,B,C,D along the spline.
Cheers
Terry
