ABSTRACT
This chapter discusses some of the common properties of splines and how these can be calculated from spline equations. First, it discusses the critical points namely minimum and maximum of spline curves. Additionally for splines of degree 3 or more, the point of inflection (POI) is of interest, which is where the curvature changes from concave to convex or vice versa. Next, it discusses how the tangent and normal to a spline curve can be calculated. The tangent to a curve is the derivative of the curve equation, while the normal is the line perpendicular to the tangent. The third property is calculation of length of a spline curve between any two given points, both for spatial as well as parametric equations. The fourth property is to calculate the area under a curve, which is bounded by a primary axis and two horizontal or vertical lines. An extension to this is calculation of area bounded by two curves. The fifth property is calculation of centroid of an area, the point of the center of gravity for plates of uniform density. The chapter ends with a discussion on interpolation and curve fitting for data points and a list of some commonly used built-in MATLAB functions for plotting 2D graphs and plots.
