Topology

Topology is a fancy word for considering how the cells of a grid connect together, with no regard for their actual size or position in space.

In other words, it is treating a grid like it is a graph, where nodes of the graphs are cells of the grid, and there are edges for each pair of adjacent cells. The edges of the graph are labelled with cell dirs and rotation data, and the cells are labelled with their celltype.

Treating a grid as a graph is handy for many common algorithms, such as path finding and distance fields.

TryMove

There's only one key method relating to the topology of a graph.

bool IGrid.TryMove(Cell cell, CellDir dir, out Cell dest, out CellDir inverseDir, out Connection connection);

TryMove attempts to move from cell, along the edge labelled with dir. If it is sucessful, it returns the cell along the edge as dest, and gives some information on the edge traversed, inverseDir and connection. See rotations for how to interpret these.

With TryMove defined, an algorithm can explore the entire grid, one cell at a time.

If you don't care about rotation information, you can use the following simpler methods:

Cell? IGrid.Move(Cell cell, CellDir dir);
IEnumerable<Cell> IGrid.GetNeighbours(Cell cell)

There is also the Walker class, which represents a object standing on a given cell facing a given direction, and is a mutable interface to the same logic.

ParallelTransport

In Sylves, all movement is one-cell-at-a-time using the TryMove method above. But in some cases, that's not really useful.

For example, you might be working with a square grid, and want to move 100 units right. Calling TryMove one hundred times is not really great.

If you are always working with a square grid, then you can simply add 100 to the x co-ordinate of the Cell, and you don't need this section.

But if you need something that works generally across grids, you need ParallelTransport.

bool ParallelTransport(IGrid aGrid, Cell aSrcCell, Cell aDestCell, Cell srcCell, CellRotation startRotation, out Cell destCell, out CellRotation destRotation);

ParallelTransport imagines you have a path from aSrcCell to aDestCell on aGrid, and then repeats that same path on the current grid, with a fresh starting point and rotation. It then tells you where the path finishes. Sylves will detect if the grids are sufficiently similar, and employ co-ordinate arithmetic if it can, otherwise it falls back to walking the two paths cell-by-cell.

For example:

myGrid.ParallelTransport(new SquareGrid(1), new Cell(0, 0, 0), new Cell(100, 0, 0), new Cell(1, 2, 3), CubeRotation.Identity, out var destCell, out var destRotation)

Describes a path which moves 100 units to the right, and asks that path to rebased to start at (1,2,3). If myGrid is also a square grid, then this will result in destCell = (101, 2, 3), just as if we'd done the straightforward arithmetic.

Note

Grid symmetries offers a similar feature to ParallelTransport, but only uses a single grid.