What is the problem addressed by the paper?
- How to represent smooth shapes?
- How to smooth surfaces?
- How to process range-scanned meshes?
- How to improv normal and boundary continuity?
image credit Alexa, et al.
What is the approach used to resolve the problem?
In differential geometry, a smooth surface is characterized by the existence of smooth local maps at any point. The Point Set Surfaces use differential geometry as a framework to approximate a smooth surface defined by a set of points. In order to resample the surface to generate an adequate representation of the surface, the authors use a point set (without connectivity) as a representation of shape.
What are the key ideas/observations behind the approach?
A manifold is a topological space that is locally Euclidean -Mathworld
Around every point there is a local neighbourhood that is topologically the same as an open unit ball.
We can create local parameterised neighbourhoods that cover the entire surface.
What are the limitations of the method?
Unknown yet to me.
What are the contributions of the method?
The concept and framework
The concept of Point Set Surfaces (PSS) is proposed by Alexa et al., in 2001 visualization conference; the similar idea of Minimum Least Square Meshes was proposed by Sorkine and Cohen-Or in 2004. There is also a beautiful course note called Practical Least-Squares for Computer Graphics by Fred Pighin and J.P. Lewis on this topic.They also shared the slides here.
image credit Alexa, et al.
A set of papers to follow up:
- Computing and Rendering Point Set Surfaces Slides
- Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression.
- Algebraic Point Set Surfaces
- Triangulating Point Set Surfaces
Finally,
who needs a skybox?
