Viral recombination is a key evolutionary mechanism, aiding escape from host immunity, contributing to changes in tropism and possibly assisting transmission across species barriers. The ability to determine whether recombination has occurred and to locate associated specific recombination junctions is thus of major importance in understanding emerging diseases and pathogenesis. This paper describes a method for determining recombinant mosaics (and their proportions) originating from two parent genomes, using high-throughput sequence data. The method involves setting the problem geometrically and the use of appropriately constrained quadratic programming. Recombinants of the honeybee deformed wing virus and the Varroa destructor virus-1 are inferred to illustrate themethod from both siRNAs and reads sampling the viral genome population (cDNA library); our results are confirmed experimentally. Matlab software (MosaicSolver) is available.