CPU-GPU Algorithms for Triangular Surface Mesh Simplification

6 Suzanne M. Shontz and Dragos M. Nistoroperation, the algorithm terminates. This also ensures that the edge-collapseoperation is performed uniformly and exhaustively across all elements assignedto the GPU, and that no one area is more or less simplified or deformed. Thepseudocode for the naïve GPU marking simplification algorithm is given inAlgorithm 2.Algorithm 2 The GPU Marking Simplification Algorithmfunction GPU-Mark(mark, elements, vertices)for all T ∈ N(mark) do GPU thread T : mark-as-affected(T )end forend functionfunction GPU-Mark-Simplify(elements, vertices)for all T = (v 1, v 2, v 3) ∈ elements doif not marked(T ) thencollapse((v 1, v 2))mark-as-collapsed((v 1, v 2))GPU-Mark(T )end ifend forend function2.3 GPU Inverse Reduction AlgorithmWe propose a GPU mesh simplification algorithm that leverages the fullstrength of the GPU. Unlike our previous algorithms in which one elementwas examined at each iteration of the main loop to determine which elementswere not affected, we now examine twice as many elements per iteration, witheach element examined by a different GPU thread. To take full advantageof the architecture of the GPU, a soft-grained blocking [21] method based ontest-and-set [1] is used to decide if any edge of an element should be collapsed.We attempt to lock each vertex in an element by calling test-and-set on theaffected bit of each vertex in the element. Pseudocode for the GPU inversereduction simplification algorithm is given in Algorithm 3.Correctness. The GPU-Simp-Try method attempts to lock each vertex ofan element by checking to make sure the vertex has not already been collapsed.If it finds that a vertex has already been locked, it releases all previously-lockedvertices. Therefore, if a thread successfully locks v 1 , v 2 , and v 3 for element t,this means that no other thread has locked any t n ∈ N(t), either currently orpreviously. Therefore, the algorithm simplifies the mesh both uniformly andexhaustively, ensuring that no one area is too simplified or deformed.