▁ ▁As ▁the ▁sun ▁moves ▁across ▁the ▁sky ▁the ▁q ▁input ▁remains ▁high ▁along ▁the ▁sun - zen ith - anti - sun ▁line . ▁It ▁remains ▁zero ▁around ▁a ▁circle ▁based ▁on ▁the ▁sun ▁and ▁the ▁z en ith . ▁As ▁it ▁passes ▁the ▁z en ith ▁it ▁rot ates ▁toward ▁the ▁south ▁and ▁repe ats ▁the ▁same ▁pattern ▁until ▁sun set . ▁ ▁The ▁second ▁image ▁to ▁the ▁right ▁represents ▁the ▁u ▁input ▁mapped ▁onto ▁the ▁cel est ial ▁sphere . ▁The ▁u ▁st okes ▁parameter ▁changes ▁signs ▁depending ▁on ▁which ▁quadr ant ▁it ▁is ▁in . ▁The ▁four ▁quadr ants ▁are ▁defined ▁by ▁the ▁line ▁of ▁symmetry , ▁the ▁effective ▁East - Z en ith - West ▁plane ▁and ▁the ▁North - Z en ith - S outh ▁plane . ▁It ▁is ▁not ▁symmetric ▁because ▁it ▁is ▁defined ▁by ▁the ▁angles ▁ ± 4 5 ° . ▁ ▁In ▁a ▁sense ▁it ▁makes ▁two ▁circles ▁around ▁the ▁line ▁of ▁symmetry ▁as ▁opposed ▁to ▁only ▁one . ▁ ▁It ▁is ▁easily ▁understood ▁when ▁compared ▁with ▁the ▁q ▁input . ▁ ▁Where ▁the ▁q ▁input ▁is ▁half way ▁between ▁ 0 ° ▁and ▁ 9 0 ° , ▁the ▁u ▁input ▁is ▁either ▁positive ▁at ▁+ 4 5 ° ▁or ▁negative ▁at ▁− 4 5 ° . ▁Similarly ▁if ▁the ▁q ▁input ▁is ▁positive ▁at ▁ 9 0 ° ▁or ▁negative ▁at ▁ 0 ° ▁the ▁u ▁input ▁is ▁half way ▁between ▁+ 4 5 ° ▁and ▁− 4 5 ° .