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The design of highly complex particle detectors used in High Energy Physics involves both CAD systems and physics simulation packages like GEANT4. GEANT4 is able to exchange detector geometries with CAD systems, conforming to the Standard for the Exchange of Product Model Data (STEP); Boundary Representation (B-Rep) models are transferred. Particle tracking is performed in these models, requiring efficient and accurate intersection computations from the geometrical modeller. The results of extending and optimising the modeller of GEANT4 form the contents of this thesis. Swept surfaces: surfaces of linear extrusion and surfaces of revolution have been implemented. The problem of classifying points on surfaces bounded by curves as being inside or outside has been solved. These tasks necessitated the extension and optimisation of code related to curves and lead to a re-design of this code. Emphasis was put on efficiency and on dealing with numerical errors. The results will be integrated into the upcoming beta test release of GEANT4.