Reporting Segment And Geographic Information (Segment Revenue by Geography) (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2021	Jan. 01, 2021	Jan. 03, 2020
Revenue from External Customer [Line Items]
Segment revenue	$ 3,659.4	$ 3,152.0	$ 3,271.3
Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	1,422.7	1,231.0	1,258.2
Geospatial
Revenue from External Customer [Line Items]
Segment revenue	828.9	650.5	649.4
Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	771.3	630.0	571.4
Transportation
Revenue from External Customer [Line Items]
Segment revenue	636.5	640.5	792.3
North America
Revenue from External Customer [Line Items]
Segment revenue	1,866.1	1,647.2	1,795.3
North America | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	823.5	703.4	722.7
North America | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	337.3	249.9	263.0
North America | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	212.2	191.4	173.3
North America | Transportation
Revenue from External Customer [Line Items]
Segment revenue	493.1	502.5	636.3
Europe
Revenue from External Customer [Line Items]
Segment revenue	1,124.6	922.1	920.2
Europe | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	386.6	337.1	338.7
Europe | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	282.3	222.3	217.5
Europe | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	368.4	284.3	273.6
Europe | Transportation
Revenue from External Customer [Line Items]
Segment revenue	87.3	78.4	90.4
Asia Pacific
Revenue from External Customer [Line Items]
Segment revenue	447.3	403.3	375.1
Asia Pacific | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	188.4	165.7	165.3
Asia Pacific | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	161.4	138.2	122.7
Asia Pacific | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	67.3	64.5	47.4
Asia Pacific | Transportation
Revenue from External Customer [Line Items]
Segment revenue	30.2	34.9	39.7
Rest of World
Revenue from External Customer [Line Items]
Segment revenue	221.4	179.4	180.7
Rest of World | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	24.2	24.8	31.5
Rest of World | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	47.9	40.1	46.2
Rest of World | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	123.4	89.8	77.1
Rest of World | Transportation
Revenue from External Customer [Line Items]
Segment revenue	25.9	24.7	25.9
United States
Revenue from External Customer [Line Items]
Segment revenue	$ 1,687.4	$ 1,502.3	$ 1,641.0