One Dimensional Spline Interpolation Algorithms
Together with its compagnion volume this book presents a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided design (CAD) and computer graphics.
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Polygonal Paths as Linear Spline Interpolants
Quadratic Spline Interpolants
Cubic Spline Interpolants
Polynomial Spline Interpolants of Degree Five
Rational Spline Interpolants
Exponential Spline Interpolants
Spline Interpolation and Smoothing in the Plane
B List of Subroutines
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20 CONTINUE RETURN ARRAY(N B-splines calculated calling must contain coefficient matrix contain the abscissa contains the values CONTINUE RETURN END continuously differentiable convex cubic Hermite spline cubic spline interpolants CUBSM1 curve Description desired spline coefficients Determination DIMENSION end conditions END IF CALL Error in solving evaluated example Figs function value Gaussian elimination given points GOTO 20 GRAD1 GRAD2B Hence Hermite interpolation Hermite spline interpolant IFLAG IFLAG=0 contain IFLAG=1 RETURN END interval INTONE knots linear system monotonically Newton's method Normal execution Number of given obtain polygonal path polynomial Program listing quadratic spline interpolant quintic rational spline interpolant RATSAK RATSCH RATSP1 Required subroutine RETURN END Figure second derivatives segments shape preservation sk(x spline function strictly diagonally dominant symmetric system of equations system TRIDIS tridiagonal tridiagonal matrix TRIDIS TRIPES values y'k X-AXIS Figure xfc,xfc+i xfc+i xk+i
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