ABSTRACT
Splines are irregular curve segments with known mathematical properties. Splines are frequently encountered in vector graphics when graphic objects are required to have a defined shape in 2D planes or 3D space or needs to be moved along a specified path. The shape of a spline curve is determined by control points along its path. Interpolating splines are those that actually interpolates through the control points. Based on the coordinates of control points, or slopes of lines along the curves, the graphics system calculates a mathematical representation of the curve before storing them onto disk. This chapter provides an introduction regarding the various types of interpolating splines and their representations using polynomials. The theoretical concepts about how spline equations are derived and the matrix algebra involved is discussed in detail followed by numerical examples and MATLAB codes to illustrate the processes. Each example is followed by a graphical plot to enable the reader visualize how the equations get translated into corresponding curves given their start points, end points, and other related parameters. The chapter also highlights the differences in these procedures both for standard or spatial form and parametric form of the spline equations using linear, quadratic, and cubic variants.
