Affine TransformationFunction mapping a bounding box to the unit cube or a target box
RescalingTransform[{{xmin, xmax}, {ymin, ymax}, …}, {{xpmin, xpmax}, …}]
RescalingTransform[{{xmin, xmax}, {ymin, ymax}, …}]
t = RescalingTransform[{{xmin, xmax}, {ymin, ymax}}]
→ TransformationFunction[{{(xmax - xmin)^(-1), 0, -(xmin/(xmax - xmin))}, {0, (ymax - ymin)^(-1), -(ymin/(ymax - ymin))}, {0, 0, 1}}]t = RescalingTransform[{{xmin, xmax}, {ymin, ymax}, {zmin, zmax}}]
→ TransformationFunction[{{(xmax - xmin)^(-1), 0, 0, -(xmin/(xmax - xmin))}, {0, (ymax - ymin)^(-1), 0, -(ymin/(ymax - ymin))}, {0, 0, (zmax - zmin)^(-1), -(zmin/(zmax - zmin))}, {0, 0, 0, 1}}]t = RescalingTransform[{{l1, u1}, {l2, u2}}, {{L1, U1}, {L2, U2}}]
→ TransformationFunction[{{(-L1 + U1)/(-l1 + u1), 0, L1 - (l1*(-L1 + U1))/(-l1 + u1)}, {0, (-L2 + U2)/(-l2 + u2), L2 - (l2*(-L2 + U2))/(-l2 + u2)}, {0, 0, 1}}]