Summary: The HybridTree: Mixing Skeletal Implicit
Surfaces, Triangle Meshes and Point Sets
in a Free-form Modeling System
R´emi All`egre , Eric Galin, Rapha¨elle Chaine, Samir Akkouche
LIRIS CNRS, Universit´e Claude Bernard Lyon 1, France
In this paper, we present a hybrid modeling framework for creating complex 3D
objects incrementally. Our system relies on an extended CSG tree that assembles
skeletal implicit primitives, triangle meshes and point set models in a coherent
fashion: we call this structure the HybridTree. Editing operations are performed
by exploiting the complementary abilities of implicit and polygonal mesh surface
representations in a complete transparent way for the user. Implicit surfaces are po-
werful for combining shapes with Boolean and blending operations, while triangle
meshes are well-suited for local deformations such as FFD and fast visualization.
Our system can handle point sampled geometry through a mesh surface reconstruc-
tion algorithm. The HybridTree may be evaluated through four kinds of queries,
depending on the implicit or explicit formulation is required: field function and gra-
dient at a given point in space, point membership classification, and polygonization.
Every kind of query is achieved automatically in a specific and optimized fashion
for every node of the HybridTree.