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SHREC'21: Quantifying shape complexity
Structure from appearance: topology with shapes, without points
ABSTRACT A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the
The topology of shapes made with points
TLDR
This paper examines the kind of topology that is applicable to shapes made with points and the topology of “point-free” pictorial shapes and the main differences between the two are summarized.
Some Open Problems Regarding the Number of Lines and Slopes in Arrangements that Determine Shapes.
A set $L$ of straight lines and a set $P$ of points in the Euclidean plane define an arrangement $\mathcal{A}$ = ($L$, $P$) of construction lines and registration marks, if and only if: (1) any point
Geometry of Arrangements that Determine Shapes
A shape in the universe $U^*$ has an underlying arrangement that consists of construction lines and registration marks. Relations between construction lines and registration marks in an arrangement
Analysis of shape grammars: Continuity of rules
TLDR
A characterization is provided that distinguishes the suitable mapping forms from those that are inherently discontinuous or practically inconsequential for continuity analysis, and it is shown that certain intrinsic properties of shape topologies and continuous mappings provide an effective method of computing topologies algorithmically.