Soft-Edge: efficient bithackery for making 3D collision meshes out of grids and stacked tile maps

indecipherable wailing guitar noises and tape echo sounds - Wata (Boris - Soft Edge)

soft-edge is a crate which provides utilities for dealing with 3D grids where the cells are colliders defined as convex hulls of subsets of the unit cube.

Things it gives you:

• Vertex, representing a vertex of the unit cube as an index in 0..8
• VertexSet, representing a subset of the vertices of the unit cube as a 1-byte bitset
• Atom, representing a valid convex non-coplanar subset of the vertices of the unit cube
• CompoundHull, representing a clippable convex hull of an Atom
• HullFacet, representing a polygon of a potentially clipped compound hull of an atom. Hull facets calculated from compound hulls of atoms will always be wound CCW.

Why?

If you've ever tried building a game physics system with a tile-based map before, you've probably run into the "crack problem". This is where if you have two adjacent tiles, things which should smoothly move over the "crack" between them (which mathematically does not exist because the vertices of these two tiles are shared) instead get caught on the crack, because during collision detection the object is moved into a tile by some force and ends up spuriously colliding with an unexposed edge of one tile.

soft-edge's CompoundHull type represents a sort of encoded tile collider with a join_exteriors method that erases any of these unexposed edges between two tiles, leaving you with the surface polygons that can't cause the crack problem. In addition, these clipping operations are extremely fast, requiring only three bitwise operations (maybe some more because they're done on only a subset of the bits of a thing, but still, it's fast.)

Does it work?

Uh, I think so. All the tests pass, at least?

Many things in this crate are specialized/brute forced/handwritten as lookup tables. I've fixed all the bugs I could find, but I'm sure there are more hiding somewhere, probably in mistakes in bit-significance or something. Though most bitwise ops are done through the bitvec crate exactly to avoid this as much as possible.

Vertex numbering

Vertices are numbered as follows:

  v3      v7
    *----*
v2 /| v6/|
  *----* |   +Y
  | *--|-*   ^ ^ +Z
  |/v1 |/v5  |/
  *----*     +--> +X
 v0    v4

For more convenience, a conversion between vertex index and unit cube coordinates:

// v0 is the origin.
v0 <=> {0, 0, 0} <=> 0b000
v1 <=> {0, 0, 1} <=> 0b001
v2 <=> {0, 1, 0} <=> 0b010
v3 <=> {0, 1, 1} <=> 0b011
v4 <=> {1, 0, 0} <=> 0b100
v5 <=> {1, 0, 1} <=> 0b101
v6 <=> {1, 1, 0} <=> 0b110
v7 <=> {1, 1, 1} <=> 0b111

This is derived as a bitwise representation 0bXYZ where the X bit represents whether or not the X axis is 1, Y bit is whether or not the Y axis is 1, etc.

"Exact" coordinates for vertex index deduplication

In order to facilitate vertex deduplication (for an indexed triangle mesh, for example) most of the output coordinates for things like the CompoundHull's facets (HullFacet) are presented using the Exact type. This wraps nalgebra's Point3<i32>, and is essentially just the same coordinates you would expect but scaled by a factor of 2 on every axis. This allows us to represent centroids of faces with no possibility of error, and also provides a hashable type which can be used to build a set mapping vertices to indices.

Generally speaking, how do you expect me to use this?

1. Encode your collision map as a grid of bytes, which correspond to valid Atoms. Deserialize these bytes into VertexSets using VertexSet::from_u8, and try to construct atoms from them with Atom::try_new.
2. Construct a three-dimensional grid consisting of the CompoundHulls of the atom grid elements, and then for every hull in the grid, join it with its neighbors on the proper axes.
3. Extract facets of these joined compound hulls as HullFacets, and then construct your collision geometry with them. This will end up as a very much non-convex mesh, which you may want to decompose into convex sub-meshes (but don't have to, if you do collisions directly on polygons and only allow contact normals which penetrate through their "surface" side.)

soft-edge attempts to produce hull facets with the correct winding order (CCW), which should allow you to easily calculate their normals. If it does not, this is a bug, and must be fixed.

License

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.