Recently, Runions et al. proposed a method for modeling trees, known as the space colonization algorithm (SCA). The SCA works by distributing points in the space enclosed by a surface (crown envelope). A tree grows towards these points and consumes them in the process. In this thesis, implicit methods are used for extending the range of trees that can be created by the SCA. Point distributions are central to the SCA, and implicit surfaces are naturally suited for generating these distributions, since it is easy to determine if a point belongs inside or outside an implicit surface. Furthermore, the field values of implicit surfaces can also be used to control the density of point distributions.
An implicit modeling system was developed for the interactive specification of crowns, and for extending the range of crown shapes that can be defined, thus ex- tending the flexibility of the SCA. This flexibility was further increased by generating different point distributions. A particularly interesting case was to limit point sets outside and in proximity to surfaces, thus causing trees to grow around surfaces, and allowing shapes to be suggested by the surrounding branching structures.
Vishal Kochhar. Application of implicit methods to the interactive modeling of trees. M.Sc. thesis, University of Calgary, January 2010.
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