Five-point difference format-based interpolation curved surface generation method

Abstract

The invention discloses an interpolation curved surface generation method based on a five-point difference format, and relates to the technical field of three-dimensional modeling and curved surface generation, four NURBS curves are input, a parameter domain Omega is equally divided along a u direction and a v direction, and (n + 1) * (m + 1) grid points are obtained through discretization on the parameter domain Omega, and each grid point is a control point {Pi, ji = 0, 1, 2,..., n, j = 0, 1, 2,..., m} of an interpolation curved surface; wherein P0, j, Pn, j, Pi, 0, Pi, m are control points on the four NURBS curves, namely known control points; (Pi, ji = 1, 2,..., n-1, j = 1, 2,..., m-1) is an internal control point of the interpolation curved surface, namely an unknown control point; a five-point difference format is used for representing an internal control point and recording the internal control point as a vector P, solving of the internal control point is converted into solving AP = b, QR decomposition is carried out on a matrix A to make A = QR, solving of the internal control point is converted into solving RP = QTb, then solving is carried out to obtain the vector P, and an interpolation curved surface S (u, v) can be generated according to the control point. The invention provides a curved surface modeling method for interpolating a given boundary NURBS (Non-Uniform Rational B-Spline) curve based on a partial differential equation five-point difference format. The curved surface modeling method can be adaptive to the condition that the given boundary curve is complex to generate a regular curved surface interpolated to the boundary curve.