@article{Hertlein:1977:CAC,
number = {3},
month = jul,
author = {Grace C. Hertlein},
optkey = {},
series = CGPACS,
localfile = {papers/Hertlein.1977.CAC.pdf},
address = {New York},
publisher = {ACM Press},
doi = {http://doi.acm.org/10.1145/563858.563902},
organization = {ACM SIGGRAPH},
journal = SIGGRAPH77,
volume = {11},
optstatus = {URL},
title = {{C}omputer {A}rt for {C}omputer {P}eople  {A} {S}yllabus},
abstract = {Surface display techniques, including contour mapping, usually use
an interpolant when data values are on a rectangular grid; but
when values are irregularly located some form of assumed or
estimated distanceweighting function is often used to estimate
the "influence" of data points at other locations. If moving
average (or some other) techniques are then applied, slopes may be
zero at data points; extrema may fall at data points exclusively;
or surfaces may not pass through data points.An alternative method
is proposed whereby a map area is automatically divided into
suitable triangular domains with a data point at each vertex.
Surface estimation and contour plotting are then performed
independently for each triangle using a measured or bestfit plane
associated with each data point. The approach requires the
utilization of three nonoriginal aspects: 1) the derivation of a
local homogeneous "area" coordinate system for any arbitrary
triangle; 2) the construction of a datastructure linking each
triangular domain with its three neighbouring triangles and three
associated data points, and 3) the use of a "conforming"
triangular finiteelement interpolating function.Use of the first
two of these concepts permits the economic generation and
optimization of a triangular mesh from a set of data points.
Optimization criteria used to define the "best" triangular
partition are described in some detail, along with computer timing
for this step. Use of the first and third concepts permits the
interpolation of a smooth surface over the whole map area even
though each triangular element is estimated and plotted
independently. The requirements for a suitable interpolating
function are discussed, and an interpolant is suggested that
preserves elevation and slope at each data point as well as
elevation and slope continuity between domains. Extrema need not
be located at data points but are constrained by their associated
planes. Contour line segments are produced by division of each
triangle into N2 subtriangles, elevation estimation at each
resulting node, and linear interpolation and plotting withing each
subtriangle. Resolution is then a function of N and local data
point density. Extension of the method to higher dimensions is
briefly discussed.},
year = {1977},
pages = {249254},
}
