At the OTI symposium I was cutting some guilloche patterns and I talked with a few people about the trade-off of spacing versus amplitude for offset sine wave patterns. I decided to write out my way of calculating the offset (for a given amplitude) or calculating the amplitude (for a desired cut spacing). See the attached pdf file with the math. Also attached are xls spreadsheets so that you don't have to worry about the math. For Mac users, there is a .dmg disk image that can be used with Apple's "Numbers" spreadsheet.