L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Natural Visualizations

This paper demonstrates the prevalence of a shared characteristic between visualizations and images of nature. We have analyzed visualization competitions and user studies of visualizations and found that the more preferred, better performing visualizations exhibit more natural characteristics. Due to our brain being wired to perceive natural images [SO01], testing a visualization for properties similar to those of natural images can help show how well our brain is capable of absorbing the data. In turn, a metric that finds a visualization’s similarity to a natural image may help determine the effectiveness of that visualization. We have found that the results of comparing the sizes and distribution of the objects in a visualization with those of natural standards strongly correlate to one’s preference of that visualization

Recognition of plants using a stochastic L-system model

Recognition of natural shapes like leaves, plants, and trees, has proven to be a challenging problem in computer vision. The members of a class of natural objects are not identical to each other. They are similar, have similar features, but are not exactly the same. Most existing techniques have not succeeded in effectively recognizing these objects. One of the main reasons is that the models used to represent them are inadequate themselves. In this research we use a fractal model, which has been very effective in modeling natural shapes, to represent and then guide the recognition of a class of natural objects, namely plants. Variation in plants is accommodated by using the stochastic L-systems. A learning system is then used to generate a decision tree that can be used for classification. Results show that the approach is successful for a large class of synthetic plants and provides the basis for further research into recognition of natural plants