The supercover of an \(m\)-flat is a discrete analytical object. (English) Zbl 1157.68067
Summary: The aim of this paper is to show that the supercover of an \(m\)-flat (i.e. a Euclidean affine subspace of dimension \(m\)) in Euclidean \(n\)-space is a discrete analytical object. The supercover of a Euclidean object \(F\) is a discrete object consisting of all the voxels that intersect \(F\). A discrete analytical object is a set of discrete points that is defined by a finite set of inequalities. A method to determine the inequalities defining the supercover of an \(m\)-flat is provided.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
Keywords:
discrete geometry; computer graphics; supercover; \(m\)-flat; discrete analytical object; arbitrary dimensionReferences:
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