Practical Linear Algebra: A Geometry Toolbox, Third edition
Gerald Farin & Dianne Hansford
CRC Press, Taylor & Francis Group, An A K Peters Book, 2013

Local to global coordinate system transformation
Move 2D slider in the local coordinate system and the corresponding point appears in the global system

(* global system *)
min1 = 0;
max1 = 10;
min2 = 0;
max2 = 10;
min = Min[min1,min2, max1, max2];
max = Max[min1,min2, max1, max2];

g1[l1_] := (1-l1)*min1 + l1*max1;
g2[l2_] := (1-l2)*min2 + l2*max2;

Manipulate[Graphics[{PointSize[Large],Red,Point[{g1[d[[1]]],g2[d[[2]]]}]},PlotRange->{{min,max},{min,max}}, Axes->True, GridLines->Automatic],{d,{0,0},{1,1}}, FrameLabel->{"Global goordinates"," ","Local to global coordinates"," "}]