I don't get why we introduce the big H terms? What's the difference between using the left hand equation and the right hand?
zy5476
I am also confused as the notation change. I think it might be to make all of the terms into cubic functions instead of 1 cubic 1 square etc. for better properties?
ttalati
I will try my best to explain what is going on. Basically we want to find an equation of a 3rd degree polynomial that interpolates the curve. This is represented by a matrix multiplication of 3 matrices. The previous slide went over how one of those interpretations was formed when we multiplied the right 2 matrix. This is the interpretation we get when we multiply the left 2 matrix. Essentially, when we do that we get a row vector, whose each element represents a different 3rd degree polynomial. When this row vector is multiplied by the column vector we get the final 3rd degree polynomial. In this manner the H_n(t) row vector consists of basis 3rd degree polynomials that we can adjust weights to using our column vector to represent any cubic polynomial.
I don't get why we introduce the big H terms? What's the difference between using the left hand equation and the right hand?
I am also confused as the notation change. I think it might be to make all of the terms into cubic functions instead of 1 cubic 1 square etc. for better properties?
I will try my best to explain what is going on. Basically we want to find an equation of a 3rd degree polynomial that interpolates the curve. This is represented by a matrix multiplication of 3 matrices. The previous slide went over how one of those interpretations was formed when we multiplied the right 2 matrix. This is the interpretation we get when we multiply the left 2 matrix. Essentially, when we do that we get a row vector, whose each element represents a different 3rd degree polynomial. When this row vector is multiplied by the column vector we get the final 3rd degree polynomial. In this manner the H_n(t) row vector consists of basis 3rd degree polynomials that we can adjust weights to using our column vector to represent any cubic polynomial.