A = (0.02, 4.6)
pts: {A}
T_4: {{0, 0}, {0, 0.2}}
T_3: {{-0.15, 0.26, 0}, {0.26, 0.15, 0.5}, {0, 0, 1}}
T_1: {{0.8, 0.07, 0}, {-0.07, 0.8, 1}, {0, 0, 1}}
T_2: {{0.19, -0.23, 0}, {0.23, 0.19, 1}, {0, 0, 1}}
list1: {ApplyMatrix[T_1, pts] + (0, 1), ApplyMatrix[T_2, pts] + (0, 1), ApplyMatrix[T_3, pts] + (0, 0.5), ApplyMatrix[T_4, pts]}
list2: {ApplyMatrix[T_1, list1] + (0, 1), ApplyMatrix[T_2, list1] + (0, 1), ApplyMatrix[T_3, list1] + (0, 0.5), ApplyMatrix[T_4, list1]}
list3: {ApplyMatrix[T_1, list2] + (0, 1), ApplyMatrix[T_2, list2] + (0, 1), ApplyMatrix[T_3, list2] + (0, 0.5), ApplyMatrix[T_4, list2]}
T1: {}
B = (-1.68, 3.8)
list4: {ApplyMatrix[T_1, list3] + (0, 1), ApplyMatrix[T_2, list3] + (0, 1), ApplyMatrix[T_3, list3] + (0, 0.5), ApplyMatrix[T_4, list3]}
list5: {ApplyMatrix[T_1, list4] + (0, 1), ApplyMatrix[T_2, list4] + (0, 1), ApplyMatrix[T_3, list4] + (0, 0.5), ApplyMatrix[T_4, list4]}
n = 1 (slider from 0 to 5, step 1)

Tool: Tool1
Tool1[ <List>, <List>, <List>, <List>, <List> ]
Input: T_2, T_1, T_3, T_4, pts
Output: list1

T_2: {{0.19, -0.23, 0}, {0.23, 0.19, 1}, {0, 0, 1}}
T_1: {{0.8, 0.07, 0}, {-0.07, 0.8, 1}, {0, 0, 1}}
T_3: {{-0.15, 0.26, 0}, {0.26, 0.15, 0.5}, {0, 0, 1}}
T_4: {{0, 0}, {0, 0.2}}
pts: {}
list1: {ApplyMatrix[T_1, pts] + (0, 1), ApplyMatrix[T_2, pts] + (0, 1), ApplyMatrix[T_3, pts] + (0, 0.5), ApplyMatrix[T_4, pts]}

Tool: Tool2
Input: T_2, T_1, T_3, T_4, pts
Output: list2

T_2: {{0.19, -0.23, 0}, {0.23, 0.19, 1}, {0, 0, 1}}
T_1: {{0.8, 0.07, 0}, {-0.07, 0.8, 1}, {0, 0, 1}}
T_3: {{-0.15, 0.26, 0}, {0.26, 0.15, 0.5}, {0, 0, 1}}
T_4: {{0, 0}, {0, 0.2}}
pts: {}
list1: {ApplyMatrix[T_1, pts] + (0, 1), ApplyMatrix[T_2, pts] + (0, 1), ApplyMatrix[T_3, pts] + (0, 0.5), ApplyMatrix[T_4, pts]}
list2 = Tool1(T_1, T_2, T_3, T_4, list1)