Based on the function generator on [0,1], a class of complete
orthogonal function system called as the V-system is studied in this
paper. The V-system is composed by piecewise polynomials, and is
capable of exactly describing the geometric information expressed by
the popularly and widely used polynomial spline curves and surfaces.
The V-system has all of the beautiful properties of the U-system:
continuity, discontinuity, orthogonal completeness and
reproducibility. In addition, the V-system also has the concise
structure, compactly local support and multi-resolution capability.
The V-system is the generalization of the well-known Haar function
system, and is also a new class of practical and flexible wavelet
bases. By utilizing the concepts of the energy and the descriptor of
the V-system, we study the degree of similarity of geometric models
which can be used in image analysis and processing.