Copy number amplifications (CNAs) are a hallmark of the cancer genome. Copy number increase of oncogenes on focally amplified regions imparts positive selective pressure to cells. Focal amplifications have been associated with genome instability and increased pathogenicity. Though important, the mechanisms causing focal CNAs are incompletely understood. Proposed mechanisms include chromosomal translocation with duplication, chromothripsis and more recently, circular extrachromosomal DNA (ecDNA). Thus, methods which reconstruct focal CNAs will enable a greater understanding of the various mechanisms by which CNAs arise in cancer, highlighting potential weaknesses or therapeutic targets. A previous method to analyze focal CNAs (Deshpande 2019), used next-generation sequencing (NGS) data to create a graph encoding the rearrangement breakpoints, as a prelude to identifying the full structure. Paths and cycles extracted from breakpoint graphs provide the signatures of rearrangement events, but rarely admit an unambiguous structure due to the complexity of focal CNAs. Here, we present a method, Amplicon Reconstructor (AR), integrating NGS data with optical mapping (OM) data or long-read data. OM provides physical maps of DNA which can be assembled into ultra-long OM contigs (N50 ~50 Mbp), providing larger scaffolds than other long-read strategies. AR scaffolds the combined data and employs a graph-based method to identify long paths and cycles in the breakpoint graph. Extensive simulations validate AR’s methodology, demonstrating the high fidelity of our approach. We applied AR to NGS & OM data from seven cell lines, using cytogenetic approaches to validate our findings. AR reconstructed complete ecDNA structures in three cell lines. In HCC827, AR enabled reconstruction of a 9 Mbp breakage fusion bridge structure and in K562, AR identified a complex rearrangement including the chr9-chr22 BCR-ABL fusion with regions from chr13. Our results provide genomic reconstructions giving new insight into focal CNA structure and origin, unavailable from measurements of breakpoints and copy numbers alone.