ABSTRACT
This chapter presents two fundamental techniques: interpolation and computation of geometric intersections. Consider a function sampled at certain parametric values. Interpolation is a process by which this function is estimated at parametric values at which it has not been measured or sampled. Interpolation is based on the assumption that the function changes smoothly between the different sampled values. However, interpolation techniques differ based on the degree of smoothness of change assumed between the samples. Bilinear interpolation entails interpolating in one direction followed by interpolating in the second direction. The linear interpolation on the simplices yields unique interpolation coefficients which are also called barycentric coordinates of a point inside the simplex with respect to the vertices forming the simplex. Put a Face to the Name Linear regression, one of the most used optimization techniques, was conceptualized in 1894 by Sir Francis Galton, who was a cousin of Charles Darwin.
