Explicit interface tracking algorithms are used to track the evolving geometry and topology of deforming material interfaces, most often using triangle meshes. In work spanning more than forty years, this powerful approach has been applied extensively across computational physics, materials science, engineering, computer graphics, computer vision, and more. As a result, many different techniques have been proposed to carry out topological changes (merging, splitting, etc.) of explicit interfaces. However, the interdisciplinary nature of this topic has also led to a relatively fragmented body of literature. The present work therefore provides a thorough survey of topology change mechanisms used in explicit interface tracking, describing and categorizing the existing methods and tracing their evolution across domains. We consider both the two-phase case and generalizations to three or more phases, and conclude with a discussion of potential directions for future investigation.
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