Reporting Segment And Geographic Information (Segment Revenue by Geography) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2021	Jan. 03, 2020	Dec. 28, 2018
Revenue from External Customer [Line Items]
Segment revenue	$ 3,152.0	$ 3,271.3	$ 3,132.0
Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	1,231.0	1,258.2	1,087.7
Geospatial
Revenue from External Customer [Line Items]
Segment revenue	650.5	649.4	723.1
Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	630.0	571.4	568.1
Transportation
Revenue from External Customer [Line Items]
Segment revenue	640.5	792.3	753.1
North America
Revenue from External Customer [Line Items]
Segment revenue	1,647.2	1,795.3	1,670.0
North America | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	703.4	722.7	595.0
North America | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	249.9	263.0	290.6
North America | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	191.4	173.3	175.0
North America | Transportation
Revenue from External Customer [Line Items]
Segment revenue	502.5	636.3	609.4
Europe
Revenue from External Customer [Line Items]
Segment revenue	922.1	920.2	873.5
Europe | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	337.1	338.7	312.1
Europe | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	222.3	217.5	211.2
Europe | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	284.3	273.6	260.0
Europe | Transportation
Revenue from External Customer [Line Items]
Segment revenue	78.4	90.4	90.2
Asia Pacific
Revenue from External Customer [Line Items]
Segment revenue	403.3	375.1	418.3
Asia Pacific | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	165.7	165.3	152.7
Asia Pacific | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	138.2	122.7	171.7
Asia Pacific | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	64.5	47.4	46.4
Asia Pacific | Transportation
Revenue from External Customer [Line Items]
Segment revenue	34.9	39.7	47.5
Rest of World
Revenue from External Customer [Line Items]
Segment revenue	179.4	180.7	170.2
Rest of World | Buildings and Infrastructure
Revenue from External Customer [Line Items]
Segment revenue	24.8	31.5	27.9
Rest of World | Geospatial
Revenue from External Customer [Line Items]
Segment revenue	40.1	46.2	49.6
Rest of World | Resources and Utilities
Revenue from External Customer [Line Items]
Segment revenue	89.8	77.1	86.7
Rest of World | Transportation
Revenue from External Customer [Line Items]
Segment revenue	24.7	25.9	6.0
United States
Revenue from External Customer [Line Items]
Segment revenue	$ 1,502.3	$ 1,641.0	$ 1,518.1