A new polynomial-time algorithm for linear programming
Combinatorica
Fractals everywhere
The algorithmic beauty of plants
The algorithmic beauty of plants
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
The object instancing paradigm for linear fractal modeling
Proceedings of the conference on Graphics interface '92
Spatial bounding of self-affine iterated function system attractor sets
GI '96 Proceedings of the conference on Graphics interface '96
Bounding ellipsoids for ray-fractal intersection
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Computer rendering of stochastic models
Communications of the ACM
Development models of herbaceous plants for computer imagery purposes
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Texturing and Modeling: A Procedural Approach
Texturing and Modeling: A Procedural Approach
New techniques for ray tracing procedurally defined objects
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Plants, fractals, and formal languages
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Minimal Simplex for IFS Fractal Sets
Numerical Analysis and Its Applications
On computability and some decision problems of parametric weighted finite automata
Journal of Automata, Languages and Combinatorics
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We present an algorithm to construct a tight bounding polyhedron for a recursive procedural model. We first use an iterated function system (IFS) to represent the extent of the procedural model. Then we present a novel algorithm that expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the recursively optimal bounding polyhedron, if it exists. Finally, we demonstrate examples of this algorithm on two and three dimensional recursive procedural models.