This sounds to me like you’d need nesting software aimed at the clothing apparel market. When you make clothing, such as a suit, the weave/pattern of the fabric needs to match up, so that the sleeves will join up correctly with the body.

If the constraints are less, such as only needing to restrict the nesting angle of objects (e.g. 0/180 degrees) then 2D nesting software should suffice. Take a look at JETCAM, which has an extremely efficient nesting algorithm. It’s used in both the sheet metal and composite industry, with the latter having very expensive material – often upwards of $100 per square metre.