ACM Transactions on Graphics (Proc. ACM Siggraph 2019)

Authors:

Zhiyang Huang*, Nathan Carr^, Tao Ju*

Affiliations:

*Washington University in St. Louis, ^Adobe

Gallery: Our vectors (b) and surface (c) for samples from an
unstructured sketch (a). The inserts take a closer look between the
index and ring fingers (the line segments in the insert of (b) indicate
-g).

Gallery: Top row: sampling a torus surface with decreasing density
(a,b,c,d with 500, 200, 50, 25 points respectively), varying sampling
density (e), missing samples (f,g), and along 1-dimensional curves
(h,i). Middle row: optimized vectors $\bg$ visualized as oriented disks
(green/blue: front/back side). Bottom row: the VIPSS (lambda=0) colored
by distance from the original torus surface(see color bar; the
percentages are of the largest dimension of the shape).

Abtract

We
propose a new method for reconstructing an implicit surface from an
un-oriented point set. While existing methods often involve non-trivial
heuristics and require additional constraints, such as normals or
labelled points, we introduce a direct definition of the function from
the points as the solution to a constrained quadratic optimization
problem. The definition has a number of appealing features: it uses a
single parameter (parameter-free for exact interpolation), applies to
any dimensions, commutes with similarity transformations, and can
be easily implemented without discretizing the space. More
importantly, the use of a global smoothness energy allows our
definition to be much more resilient to sampling imperfections than
existing methods, making it particularly suited for sparse and
non-uniform inputs.