A tree-based support generation algorithm based on Fused Deposition Modeling is proposed to optimize support material consumption. The algorithm first identifies dangerous facets and partitions them. Support points are obtained using either a grid sampling method or a contour sampling method based on the ratio of the horizontal projection area of the dangerous area to the area of the bounding rectangle. Then, support segments are generated from top to bottom based on specified constraint angles. Slicing the support segments with height planes at specified intervals produces sliced support points. Finally, support contours and infill are generated around these points. To ensure model quality and facilitate support removal, a predetermined distance is maintained between the top of the support and the model, and the contour diameter decreases near the model. Experimental results comparing this algorithm with alternative support generation methods demonstrate its ability to effectively support overhanging regions while reducing printing time and material consumption.