  We introduce the {\em polygon cloud}, also known as a polygon set or {\em
soup}, as a compressible representation of 3D geometry (including its
attributes, such as color texture) intermediate between polygonal meshes and
point clouds. Dynamic or time-varying polygon clouds, like dynamic polygonal
meshes and dynamic point clouds, can take advantage of temporal redundancy for
compression, if certain challenges are addressed. In this paper, we propose
methods for compressing both static and dynamic polygon clouds, specifically
triangle clouds. We compare triangle clouds to both triangle meshes and point
clouds in terms of compression, for live captured dynamic colored geometry. We
find that triangle clouds can be compressed nearly as well as triangle meshes,
while being far more robust to noise and other structures typically found in
live captures, which violate the assumption of a smooth surface manifold, such
as lines, points, and ragged boundaries. We also find that triangle clouds can
be used to compress point clouds with significantly better performance than
previously demonstrated point cloud compression methods. In particular, for
intra-frame coding of geometry, our method improves upon octree-based
intra-frame coding by a factor of 5-10 in bit rate. Inter-frame coding improves
this by another factor of 2-5. Overall, our dynamic triangle cloud compression
improves over the previous state-of-the-art in dynamic point cloud compression
by 33\% or more.
