Space utilization algorithm or Mesh creation algorithm

Hey we are facing a space utilization problem or I am not clear what name I should give to problem.

Basically its a mesh problem.

I have tried to explain my problem using an image.

Problem statement is somewhat like below.

1. The box with the diagonal line is an item which has to be distributed in best proportion such as it should fit in all available container.


2. Containers are shown in different colors.


3. Now all containers will be in rectangle shape.


4. All containers has to be placed either in portrait mode or in landscape mode.

Both containers and item can be measured in width and height, for program they are pixels basically.

The program should give following output

1. Position of the container


2. Part of item the container has inside.


3. And Arrangement pattern.