Concepts

Least-cost path & global optimality

Why the route is the globally optimal corridor, not a greedy guess.

Given the cost surface, the optimal route is the path that minimises the accumulated cell cost from origin to destination:

P^{*} = \operatorname*{arg\,min}_{P} \sum_{k \in P} C_{\text{cell}}(k)

CO2GIS computes this with a chain of GRASS GIS algorithms, run through QGIS Processing.

The GRASS chain

Step	Algorithm	What it does
1	`r.cost`	Propagates the accumulated minimum cost from the origin across the whole cost surface (a raster Dijkstra). Also emits a movement-direction surface. Diagonal moves are allowed for better geometric fidelity.
2	`r.drain`	Back-traces from the destination, following the descending gradient of the accumulated-cost surface back to the origin → a path raster.
3	`r.thin`	Reduces the path to unit width, so it has clean line topology.
4	`r.to.vect`	Converts the thinned path raster into a line vector for display and for CAPEX.

Why it’s globally optimal

r.cost computes the true accumulated-cost value for every cell, considering all ways of reaching it — not just local neighbours. Because the full surface is solved first, r.drain recovers the globally optimal corridor, not a greedy local path that can get trapped by nearby cheap cells.

The route minimises cost, not distance. It will happily take a longer geometric path if that avoids expensive terrain — which is exactly the point.

Next: see how the route is priced in The COMET cost model (the “same factors, twice” idea) and the per-tab LCP and Price Estimation pages.