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2018

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“…Then, the computation of the boundary ∂ (A ⊕ B) is related to the computation of the convolution surface M N of the two boundary surfaces M and N. We always assume in the following that M and N are smooth surfaces with normal vector fields − → n M and − → n N , respectively. The convolution surface is defined to be M N := {x + y : x ∈ M, y ∈ N, and − → n M − → n N } , (1.2) where − → n M (x) and − → n N (y) are mutually parallel normal vectors at points x and y ([4], [2] ). In particular, if A and B are convex objects, the boundary ∂ (A ⊕ B) of the Minkowski sum A ⊕ B is exactly given by the convolution surface M N. Unfortunately, for non-convex objects this property is no longer true.…”

confidence: 99%

“…Then, the computation of the boundary ∂ (A ⊕ B) is related to the computation of the convolution surface M N of the two boundary surfaces M and N. We always assume in the following that M and N are smooth surfaces with normal vector fields − → n M and − → n N , respectively. The convolution surface is defined to be M N := {x + y : x ∈ M, y ∈ N, and − → n M − → n N } , (1.2) where − → n M (x) and − → n N (y) are mutually parallel normal vectors at points x and y ([4], [2] ). In particular, if A and B are convex objects, the boundary ∂ (A ⊕ B) of the Minkowski sum A ⊕ B is exactly given by the convolution surface M N. Unfortunately, for non-convex objects this property is no longer true.…”

confidence: 99%