Meshes from Shapes

Intro

Leggo is universal and consists of adding piece by piece to build something.

This is about connecting shapes to a linked mesh in a similar way. Algthough here a shape can be connected to a point or surface.

Algorithm

Have a data structure that given a point can say which linked shapes the point belongs to. This lookup must be fast.
As each new shape is added the linkages are updated.

If the new shape does not border a surface in the mesh then no linkes need to be made.

Linked Simplex Meshes

Here is an example of a H constructed in 2D.

Points Inverse in 2D

This is an edge lookup. Let there be a vector where the index refers to the first point. The vector is a pointer to a linked list where each node the second point and a list of simplexes associated with this edge.

Let the edges be uniquely identified by having the points ordered before entering the edge table so the lowest valued point index is the index in the vector of linked lists.

So how long it takes to determine if two edges intersect is linearly dependent with how many edges are about the points. For a balanced mesh this is finite so the lookup time is bounded.