doubly linked list - An exercise of Computational Geometry: half-edge, next and twin -


i trying solve exercise of book "computational geometry - algorithms , applications, de berg". exercise [2.7] says: "given doubly-connected edge list representation of subdivision twin(e) = next(e) holds every half-edge e, how many faces can subdivision have @ most?"

i think solution edge links 2 vertexs, , twin may next. so, face infinity face. more pairs of vertex linked edge, if disjoint on each. there other possibilities???

i you're correct.

given next(e) equals twin(e) half-edges e, incidentface(next(e)) equals incidentface(twin(e)). , since know incidentface(e) equals incidentface(next(e)) can conclude incidentface(e) equals incidentface(twin(e)) half-edges. no edge lies on boundary of 2 different faces. , if no edge bounds 2 different faces, there cannot more 1 face.


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