Implicit Surfaces

Nick Toothman

• 1 min read

The feedback from SIGGRAPH prompted me to start reading more about implicit surfaces. Here's what I'm looking at:

  • Wiki entry on implicit surfaces.
  • Surface triangulation - turning implicit surfaces into polygons for rendering (as opposed to ray-tracing)
  • Hessian matrix - a square matrix of second-order partial derivatives of a scalar-valued function (scalar field)
  • See also: Jacobian matrix, a matrix of all first-order partial derivatives of a vector-valued function. If square, it's referred to as the Jacobian. We used these in animation for inverse kinematic solving
  • Implicit surfaces aka Metaballs, blobbies, or soft objects from Paul Bourke (June 1997). I believe this was referenced in the main paper I should refer to, which is:
  • Implicit Skinning: Real-Time Skin Deformation with Contact Modeling. They handle self-penetration and collision checking with snazzy implicit functions, but they do so in a neat way. They skin with LBS/DQS first, then use the bone transforms to transform each bone's implicit sub-mesh surface, then union/gradient blend them, THEN re-adjust vertex positions as needed to set them up. It's really quite an interesting and helpful approach. At the moment I'm only about halfway through the paper. I'll probably end up making a separate entry detailing my notes on it. It'd be super nice to have PDF upload on here so I can keep my Adobe Reader comments/highlights/etc.
  • Isosurface: all points on an isosurface has the same value. Think contour lines in cartography
  • Javascript/WebGL visualization tool:
  • Source: https://github.com/mikolalysenko/implicit-studio
  • Demo: http://mikolalysenko.github.io/implicit-studio/

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