Reporting Segment And Geographic Information (Segment Revenue by Geography) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 03, 2020	Sep. 27, 2019	Jun. 28, 2019	Mar. 29, 2019	Dec. 28, 2018	Sep. 28, 2018	Jun. 29, 2018	Mar. 30, 2018	Jan. 03, 2020	Dec. 28, 2018	Dec. 29, 2017
Revenue from External Customer [Line Items]
Revenue	$ 824.0	$ 783.9	$ 854.8	$ 801.6	$ 785.5	$ 795.2	$ 785.5	$ 742.2	$ 3,264.3	$ 3,108.4	$ 2,646.5
Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									1,254.2	1,065.5	829.4
Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									649.4	723.1	658.5
Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									568.4	567.1	481.0
Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									792.3	752.7	677.6
Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenue									3,271.3	3,132.0	2,649.3
Operating Segments [Member] | Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									1,258.2	1,087.7	830.5
Operating Segments [Member] | Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									649.4	723.1	658.5
Operating Segments [Member] | Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									571.4	568.1	482.0
Operating Segments [Member] | Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									792.3	753.1	678.3
North America [Member] | Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenue									1,795.3	1,670.0	1,412.6
North America [Member] | Operating Segments [Member] | Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									722.7	595.0	428.5
North America [Member] | Operating Segments [Member] | Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									263.0	290.6	257.5
North America [Member] | Operating Segments [Member] | Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									173.3	175.0	163.7
North America [Member] | Operating Segments [Member] | Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									636.3	609.4	562.9
Europe [Member] | Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenue									920.2	873.5	687.2
Europe [Member] | Operating Segments [Member] | Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									338.7	312.1	237.9
Europe [Member] | Operating Segments [Member] | Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									217.5	211.2	187.1
Europe [Member] | Operating Segments [Member] | Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									273.6	260.0	189.5
Europe [Member] | Operating Segments [Member] | Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									90.4	90.2	72.7
Asia Pacific [Member] | Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenue									375.1	418.3	380.0
Asia Pacific [Member] | Operating Segments [Member] | Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									165.3	152.7	127.2
Asia Pacific [Member] | Operating Segments [Member] | Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									122.7	171.7	162.5
Asia Pacific [Member] | Operating Segments [Member] | Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									47.4	46.4	52.6
Asia Pacific [Member] | Operating Segments [Member] | Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									39.7	47.5	37.7
Rest of World [Member] | Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenue									180.7	170.2	169.5
Rest of World [Member] | Operating Segments [Member] | Building and Infrastructure [Member]
Revenue from External Customer [Line Items]
Revenue									31.5	27.9	36.9
Rest of World [Member] | Operating Segments [Member] | Geospatial [Member]
Revenue from External Customer [Line Items]
Revenue									46.2	49.6	51.4
Rest of World [Member] | Operating Segments [Member] | Resources and Utilities [Member]
Revenue from External Customer [Line Items]
Revenue									77.1	86.7	76.2
Rest of World [Member] | Operating Segments [Member] | Transportation [Member]
Revenue from External Customer [Line Items]
Revenue									$ 25.9	$ 6.0	$ 5.0