Surface drawing made simple J BuUand
A new approach to p/otting z = f(x,>,) from a tab/e ofz over a regu/ar x-y grid is exp/ained in comparison with other hidden-/ine methods. Its app/ication to drawing crosshatched and simp/e out/ine pictures of surfaces is described.
A single-valued continuous function of two variables can be represented in three-dimensional space by a surface over a fixed plane. The function may be represented graphically by a drawing of the surface with hidden lines eliminated. Several authors have published methods for drawing such pictures. They all use a similar method for eliminating hidden lines: the drawing is built up systematically from a front edge of the surface backwards, keeping a running record of the part of the page which is hidden by parts of the surface already drawn 1-3 . This strategy can be simplified if the function is represented by a rectangular table of function values at equally spaced values of the two independent variables. A method is proposed here which requires less computation and storage Postgraduate School of Electrical and Electronic Engineering, University of Bradford, West Yorkshire BD7 1 DP, UK than the previous methods. The method has been applied to produce crosshatched surface pictures and surface sketches which represent the surfaces by a very few lines.
PROBLEM
A single-valued continuous function F of two independent variables is specified by an MXN array Z where Z(I,J) = F(X(I), Y(J)) for X(1 ), X(2)... X(M) equally spaced and Y(1),Y(2) ... Y(N) equally spaced; a picture of the surface that represents the function is required.