Visualisation of implicit surfaces

Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

“…Although implicit surfaces are not naturally convertible to polygons, nonmanifold implicit surfaces polygonization methods exist [6]. A recent method proposed in [2] also allows converting manifold and nonmanifold implicit surfaces to polygons. It is a variation of the marching cubes algorithm [15] but using an octree to accelerate the conversion.…”

Adaptive Polygonisation of Non-Manifold Implicit Surfaces

“…This algorithm is an adaptation of a similar algorithm in [8] where we specify a search cube that defines the space in which we search for the surface, and then render it. This cube is the root node for the octree based adaptive subdivision algorithm.…”

“…If a valid polygonisation occurs, CreatePolygons returns true and the polygons are returned in a Polygons array. The relative flatness of the polygons are checked in PolygonFlat using criteria as given in [2] and [8]. If the polygons pass the flatness test they are tested for "cracks" and "repaired" if necessary (see [2] and [8]) using function FixHoles.…”

“…A number of authors have developed algorithms for rendering regular implicit surfaces using octree based adaptive subdivision techniques, starting with Bloomenthal's classic paper [2]. This was followed by algorithms by Suffern [3], [4] [5], Suffern and Fackerell [6], Schmidt [7] and Balsys and Suffern [8]. These algorithms start with a user specified search cube that is recursively subdivided in an octree fashion while the surface is present in an octant.…”

“…Since the plotting nodes can be at different depths in the octree, cracks can appear in the surface between adjacent nodes at different depths. Bloomenthal [2] and Balsys and Suffern [8] developed algorithms to fix these cracks.…”