In this study, we developed and implemented a cost-reducing, real-time virtual welding simulator to train welder candidates. In order to make a real-time welding simulation, a three-dimensional weld bead form was designed. We used a parabola as the basic bead slice shape, considering the similarity between the parabola and the bead slice. During the welding process, the parameters of the weld bead shape are calculated at each time step using an artificial neural network. This network determines the shape of the weld bead and the depth of penetration, based on inputs received from the sensor device that tracks the motions of the torch. After the parabola’s parameters have been determined, the voxel map and corresponding hash-based octree data structure are generated in real-time. By using the voxelized data, a weld bead isosurface consisting of triangles is reconstructed with a marching cubes algorithm allowing us to generate more realistic weld seam shapes. We used multi-threaded programming for voxelization and isosurface extraction to reduce the computation cost on high-resolution virtual scenes. The isosurface extraction times for different thread counts and also a feature comparison with other simulators in the literature are shown in this paper.