| 摘要 |
A one-dimensional p-th order spline waveform (Cw) extending along the width or height of a picture device display screen is generated as a chain of sections of p-th order sub-functions (Sfi) of a position address (P). If n predetermined values (ai) are available, n-p p-th order sub-functions (Sfi) can be generated each in one of n-p sections (Si). q>/=(p+1) values (asi) are selected from an array containing the n predetermined values (ai) and then the q selected values (asi) are converted into sub-function coefficients (bi) determining each of the p-th order sub-functions (Sfi). Each of the p-th order sub-functions (Sfi) can be written as a linear combination of polynomials of the position address (P) multiplied with associated sub-function coefficients (bi). Further, each of the p-th order sub-functions (Sfi) can be imagined to be obtained by an addition, in a section (Si), of portions (pi) of basic functions (Fbi) each multiplied by an associated one of the predetermined values (ai). The basic functions (Fbi) are p-th order spline functions. Each of the portions (pi) of the basic functions (Fbi) is written as a linear combination of portion coefficients (cij) corresponding to polynomials of the position address (P). The polynomials range from zero order up to the p-th order. The portion coefficients (cij) determine the shape of the basic p-th order spline functions (Fbi). Each of the sub-function coefficients (bi) can be calculated from the selected values (asi) by multiplying a matrix including the portion coefficients (cij) with the selected values (asi). The matrix must be a spline matrix to obtain sub-functions (Sfi) together composing the spline waveform (Cw). The process of converting the selected values into one of the sub-function coefficients is the same in every section (Si) since a fixed matrix of portion coefficients (cij) or multiplication factors is used. |
