I. M. Klucewicz

Aug 1, 1978

Citations

0

Influential Citations

31

Citations

Journal

Computer Graphics and Image Processing

Abstract

We develop a scheme which constructs a piecewise, interpolating C 1 surface through a set of arbitrarily spaced three-dimensional points {( x i , y i , z i ), i = 1, ..., N }. First the points { ( x i , y i ), i = 1, ..., N} are automatically triangulated. The z component of a data point can then be considered as an evaluation of some function F ( x, y ), i.e., z i = F ( x i , y i ). The Barnhill-Gregory Boolean sum interpolant, which is defined over a “standard” triangle in p-q space, is used to construct the surface. It interpolates to positional and normal derivative functions on the boundary of this triangle and thus can produce a C 1 scheme. Appropriate positional and normal derivative functions are defined for an arbitrary triangle in x-y space, and that triangle is mapped onto the standard triangle in p-q space. The transformed functions are used to define the functions required for the interpolant, taking into account how directions relative to the sides of the x-y triangle are affected by the transformation. In order to define normal derivative functions, x and y partial derivative values are needed. A method for approximating these partials based on the given data is described.

copied to clipboard