Blending weight BSP Tree for mesh Boolean operations

Abstract

Boolean operations play an important role in geometry processing and CAD/ CAM. To accelerate it, spatial searching trees such as Binary Space Partitioning (BSP) Trees and KD-trees are utilized. In this paper, an approach is presented to construct the BSP Trees for the Boolean operation, where each model is efficiently located in a separate subspace. Unlike conventional methods to calculate the splitting plane, our method utilizes a size-distribution blending weighted squared distance in the BSP Tree construction, where the intrinsic weight is determined based on the size and distribution of the three-dimensional (3D) model and largely reflects the model shape. After determining the intrinsic size-distribution blending weighted squared distance, the effective splitting plane is calculated using the Weighted Squared Distance Minimization (WSDM) method. By utilizing the size-distribution blending weighted squared distance, the generated BSP Tree can divide the two models efficiently, even when dealing with 3D models that exhibit substantial geometric variations. In our experiments, the BSP Tree generated by our method reaches higher Intersecting Triangle Report Accuracy (ITRA) and Non-intersecting Triangles Removal Rate (NTRR), which means more efficient hierarchies than other techniques on two mesh models. The results of intersection tests time consumption and the Boolean operations demonstrate the effectiveness and efficiency of the BSP Tree generated by our method.