TITLE: Variations in Solids: A Declarative Treatment
AUTHOR: Woodbury, R. F.
PUBLICATION: Computers and Graphics, Special Issue on Features and 
Geometric Reasoning, Vol. 14, No. 2, 173-188
DATE: 1990
ABSTRACT: Underlying the notions of variational geometry, design
prototypes, features, and representation of assemblies seems to be a
common concept of variations. This paper develops the core of a
monotonically declarative system for variation on solids. It
introduces a set of language constructs that are the basis for ASCEND,
an object-oriented equational-solving language. It presents equations
for representing certain spatial relationships between primitive
geometric elements. Using plex grammar notation, it develops a set of
Euler operators that are monotonic in the strict sense required by the
ASCEND language. These operators are collectively shown to generate
representations for all plane models of 2- manifold objects and to
generate only such representations. Finally, it presents the core of a
system for variations using the ASCEND language to implement both
equation models and the new Euler operators.