DefinePK

Abstract

Given a polyhedron mesh, the methods and theories to problems
related to normal controlled surface fitting are still not enough and suffer
from similar defects. We propose a new technique for fitting surfaces from 3D
data points and their associated normal vectors. Given vertices of surface and
their normal vectors constraints, this study presents some schemes to construct
G2 continuous Hermite interpolation surfaces. Firstly, combined three
tangent vector equation, methods to calculate tangent vector are presented.
Secondly, due to the length of two endpoint tangent vectors in Hermite interpolation
directly affects the shape of curve, even may produce sharp points and focal
points, this study adjusted the curve surface shape by controlling the input
coefficient and obtained the scope of coefficient by experiment. This study
also presents a method to reconstruct some common surfaces accurately, such
as spheres, columns and cones. In the end the error grid was analyzed between
the experimental results and the original surfaces.