The decarbonization of economies around the world is crucial for reducing the impact of human-induced climate change. Many proposed means to achieve this decarbonization like the electrification of various sectors or the introduction of ‘new’ forms of energy such as hydrogen and carbon capture and storage require existing energy infrastructures to be expended or entirely new energy infrastructures to be created. Since energy networks are capital intensive, minimizing their construction costs is essential for their realization. Previous works studying the cost minimization of energy networks often neglect that their construction costs can be influenced by geographical areas such as mountain ranges, existing infrastructures or zoning rules. Using methods borrowed from graph theory and geometrical computing, a method has been developed that is able to find costoptimal energy infrastructures in a spatial context of geographic regions with different costs for constructing power cables or pipelines through them. The method models these geographical areas as triangles on which borders a user-defined number of points are uniformly placed representing potential entry and exit points for pipelines or power cables. Experimenting with 144 randomly generated routing problems has shown that, on average, increasing the number of these placed border points results in a reduction of the total network costs. Although, this effect flattens when more than 7 of these points are placed. The method is applied to two offshore electricity networks in the Dutch North sea. These cases demonstrate the method’s strength in identifying trade-offs between energy networks’ investment costs and their (negative) influence on their spatial surroundings. Additionally, the method’s outcomes are well-suited to be used as a springboard for dialogue in energy infrastructure decision-making processes. Further research could focus on the extension of the model, by including existing connections, or the improvement of the model, by implementing a different method for modelling geographical areas that has a higher accuracy and is computationally faster.