Splitting cubes: a fast and robust technique for virtual cutting

Abstract

This paper presents the Splitting Cubes, a fast and robust technique to perform interactive virtual cutting on deformable objects.The technique relies on two ideas. The first one is to embed the deformable object in a regular grid, to apply the deformation function to the grid nodes and to interpolate the deformation inside each cell from its 8 nodes. The second idea is to produce a tessellation for the boundary of the object on the base of the intersections of such boundary with the edges of the grid. Please note that the boundary can be expressed in any way, for example it can be a triangle mesh, an implicit or a parametric surface. The only requirement is that the intersection between the boundary and the grid edges can be computed. This paper shows how the interpolation of the deformation inside the cells can be used to produce discontinuities in the deformation function, and the intersections of the cut surface can be used to visually show the cuts on the oject.The Splitting Cubes is essentially a tessellation algorithm for growing, deformable surface and it can be applied to any method for animating deformable objects. In this paper the case of the mesh-free methods (MMs) is considered: in this context, we decribed a practical GPU friendly method, that we named the Extended Visibility criterion, to introduce discontinuities of the deformation.

CPU–GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL

“…The drawback is that the edge of the cut surface creates artificial discontinuity that negatively affects numerical stability of deformation. This can be solved by calculating diffraction distance [8] or using visibility disk [9]. Also as mentioned before, additional mechanism is needed to construct cut surface geometry.…”

“…Cutting of deformable object with meshfree deformation method [8,9] typically inserts new nodes around the cut surface and updates visibility between nodes occluded by the cut surface. The drawback is that the edge of the cut surface creates artificial discontinuity that negatively affects numerical stability of deformation.…”

“…Meshfree deformation method (MDM) [7][8][9] does not use mesh as FEM does. Instead object is discretized directly into nodes.…”

Key techniques of haptic related computation in virtual liver surgery

“…The most meaningful methods for soft body splitting are as following: Steinemann [3]proposed a real-time method, which reconstructed the incision surface when the cutter interacted with the body, but it could not handle the case multi-cut on the same region because the quality of reconstructed surface is relatively poor. Pietroni [5]proposed a Splitting Cube method which derived from the famous Matching Cube method, it could achieve high quality results when the number of the cube is enough. Seiler [6]presented an adaptive octree based approach for interactive cutting of deformable objects, their method performed a Boolean operation when the cutter pressed on the object.…”

Robust interactive cutting based on an adaptive octree simulation mesh

“…Pauly et al [25] present a complete point-based simulation framework that can handle cutting and fracturing. Subsequently, the approaches of Steinemann et al [32] and Pietroni et al [26] improved the performance of topology changing operations significantly. Summarizing, although these approaches perform very well for challenging scenarios, they are less appropriate in the user-interactive context.…”