Acquisitions (Details Textual) - USD ($) $ in Thousands	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019	Apr. 14, 2021	Feb. 23, 2021
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 226,201	$ 197,562	$ 338
Goodwill	928,358	782,087	$ 661,856
Goodwill, Acquired During Period	154,362	120,564
NUMECA
Business Acquisition [Line Items]
Cash acquired					$ 9,600
Cash consideration to acquire businesses, net of cash acquired	188,600
Goodwill					133,077
Acquired intangibles					$ 72,200
Pointwise
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired	$ 31,400
Goodwill				$ 16,700
Acquired intangibles				$ 16,700
AWR and Integrand
Business Acquisition [Line Items]
Cash consideration to acquire businesses, net of cash acquired		195,600
Cash acquired		$ 1,500
Acquired definite-lived intangible assets, weighted average useful life		9 years
Goodwill, Acquired During Period		$ 119,400
Net other identifiable assets and liabilities resulting from acquisitions		(25,100)
AWR and Integrand | Fair Value, Inputs, Level 3 [Member]
Business Acquisition [Line Items]
Acquired definite-lived intangible assets, fair value		$ 101,300