Billboard Clouds for Extreme Model SimplificationDécoret, Durand, Sillion & Dorsey

In Proceedings of SIGGRAPH 2003

Input model Optimal set of rectanglesTexture + transparency maps for the rectangles Billboard cloud rendering

Billboard clouds bridge the gap between polygon-based and image-based representations. They afford a high fidelity at extreme levels of simplification and provide significant rendering acceleration.

Billboard clouds are novel general primitives that consist in a set of rectangles with texture and alpha (transparency) masks.

The relighting of a Billboard cloud is enabled by the storage of normal maps. The set of planes through a point is a sheet in the dual space. Note that the dual f’ of f is at the intersection of the sheets of its vertices

FF dual of F dual of F

Primal space Dual plane space

The planes going through a sphere corresponds to the envelope between two sheets (in yellow for the red sphere)

Discretization of the set of planes that are valid for triangle F

Simplifying a model into a billboard cloud reduces to the choice of a set of planes that best approximate the input.

A plane is valid for a face if it goes through spheres centered on its vertices

Valid plane

Input simplified to 4 planes

Face

We use a dual space where planes are transformed into points.

For each point in the dual plane space, we compute how many triangles it can approximate. This provides a density in plane space, which we use to pick the best planes in a greedy fashion.

Density in plane space. Note the maxima corresponding to the faces of the

house.

Traditional simplification cannot handle an object as complex as the Eiffel tower.

Castle simplified to 167 billboards Madcat simplified to 171 billboards

Dinosaur simplified to 110 billboards

Billboard Cloud Construction

Curve of the number of rectangles needed for a given maximum error (in log-log).