Throughout this thesis, there is an underlying assumption that the quality of a computer graphics image is important. This thesis reports research into computer image synthesis for obtaining this quality. The introduction of discontinuity meshing into existing radiosity techniques has enabled images to be produced at levels of previously unobtainable quality. However, discontinuity meshing is a computationally intensive task and can generate extremely complex meshes. We started our investigation to obtain scalable discontinuity meshing methods by considering visual perception. The research approached the problem of mesh complexity reduction from the perspective of only discarding discontinuities which have a negligible \emphperceptible effect on a mesh. A comparison between a perception-based approach and a purely radiometrically-based approach demonstrates conclusively that techniques which take into account aspects of human perception can be much better at reducing mesh complexity without incurring visual artifacts. We analyse aspects of the discontinuity meshing process with a view to reducing both its computational complexity, and the complexity of the resulting surface meshes. We show how discontinuity meshing can be combined with clustered hierarchical radiosity. The computation of enhanced visibility information allows areas of the scene to be excluded which cannot either cause or contain perceptible shadows. With traditional discontinuity meshing systems, each light source is treated independently and thus the complexity of the meshes will typically rise linearly with the number of light sources. The research addresses this problem by computing an \empha priori approximation to the radiosity leaving each surface. Using this as a guide, a perception metric can determine if a particular light source can cause noticeable shadows. The combination of techniques investigated in this thesis has turned an unscalable algorithm which generates overly complex meshes into an algorithm which has manageable time and storage requirements whilst retaining the integrity of the full solution.