Revision as of 06:56, 13 June 2024 edit Cleancutkid (talk \| contribs) Extended confirmed users 4,945 edits →Overview: dab fix, linking auxiliary function. also, in the given example, the plane is being translated upwards (and/or the plane is remaining constant at z=0 and the shape is translating down?) ← Previous edit		Revision as of 15:28, 27 June 2024 edit undo Cal3000000 (talk \| contribs) Extended confirmed users 694 edits No edit summary Tags: Visual edit Newcomer task Newcomer task: copyedit Next edit →
Line 8: == Overview == The figure on the right illustrates several ideas about LSM. In the upper- left corner is a [[bounded region]] with a well-behaved boundary. Below it, the red surface is the graph of a level set function <math>\varphi</math> determining this shape, and the flat blue region represents the ''X-Y'' plane. The boundary of the shape is then the zero-level set of <math>\varphi</math>, while the shape itself is the set of points in the plane for which <math>\varphi</math> is positive (interior of the shape) or zero (at the boundary). In the top row, the shape's topology changes as it is split in two. It is challenging to describe this transformation numerically by [[Parametrization (geometry)\|parameterizing]] the boundary of the shape and following its evolution. An algorithm can be used to detect the moment the shape splits in two and then construct parameterizations for the two newly obtained curves. On the bottom row, however, the plane at which the level set function is sampled is translated upwards, on which the shape's change in topology is described. It is less challenging to work with a shape through its level-set function rather than with itself directly, in which a method would need to consider all the possible deformations the shape might undergo.

Level-set method: Difference between revisions