CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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4 Suzanne M. Shontz and Dragos M. NistorFig. 1. An edge-collapse on e = (v 1, v 2).of a mesh M = (vertices, elements), the CPU simplifies the first k% of theelements, and the GPU simplifies the remaining elements. The workload splittingis performed once as a preprocessing step. Locks are used to ensure thatconflicting updates are not made in the simplification process.Since edge-collapse operations should be performed uniformly on the mesh,we mark the elements which have been affected by previous edge collapses sothat they do not take part in subsequent edge-collapse operations.Define N(T ) for T = (v a , v b , v c ) to be elements which contain any of thevertices v a , v b , or v c . If edge e = (v 1 , v 2 ) between elements T 1 = (v 1 , v 2 , v 3 )and T 2 = (v 4 , v 2 , v 1 ), for example, has been collapsed, then the elements inN(T 1 )∪N(T 2 ) are considered affected. The elements shaded in gray in Figure 2would be considered affected if edge (v 1 , v 2 ) were collapsed.Fig. 2. Elements considered affected by edge-collapse of (v 1, v 2).Since each edge-collapse operation causes neighboring elements to becomeaffected, there is a hard limit on the number of edge-collapse operations,and on the amount of simplification performed per iteration of the algorithm.Additional simplification may be obtained by performing additional iterationsof the algorithms.
CPU-GPU Algorithms for Triangular Surface Mesh Simplification 52.1 CPU Edge-Collapse AlgorithmTo simplify portions of the mesh using the CPU, we propose a simple edgecollapsealgorithm. The CPU edge-collapse algorithm iterates over all CPUassignedelements. Each element is examined to see if it is affected, and ifan element T = (v 1 , v 2 , v 3 ) that is not affected is found, an edge-collapse isperformed on (v 1 , v 2 ). When all elements are affected or have taken part inan edge-collapse operation, the algorithm terminates. This ensures that theedge-collapse operation is performed uniformly and exhaustively across theelements assigned to the CPU, and that no one area is more or less simplifiedor deformed. Pseudocode for the CPU edge-collapse simplification algorithmis given in Algorithm 1.Algorithm 1 The CPU Edge-Collapse Simplification Algorithmfunction mark-as-affected(element)for all v ∈ element doaffected[v] ← trueend forend functionfunction mark-as-collapsed((v 1, v 2))for all T ∈ elements ⊃ {v 1, v 2} docollapsed[T ] ← trueend forend functionfunction CPU-Simplify(elements, vertices)for all T = (v 1, v 2, v 3) ∈ elements doif T ∈N(affected elements) thenmark-as-affected(T )elsecollapse((v 1, v 2))mark-as-collapsed((v 1, v 2))end ifend forend function2.2 GPU Marking AlgorithmWe propose a naïve GPU algorithm to simplify portions of the mesh based onthe edge-collapse operation. The naïve GPU marking simplification algorithmworks by searching through all elements assigned to the GPU one at a time.If an element T = (v 1 , v 2 , v 3 ) that is not affected is found, an edge-collapseis performed on (v 1 , v 2 ), and all T n ∈ N(T ) are concurrently marked as affected.When all elements are affected or have taken part in an edge-collapse
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CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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