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The simplest type of "balanced" design (t=1) is known as a tactical configuration or 1-design. The corresponding incidence structure in geometry is known simply as a configuration, see Configuration (geometry). Such a design is uniform and regular: each block contains k elements and each element is contained in r blocks.
The points of the design are the points of the plane, and the blocks of the design are the lines of the plane. [14] As such it is a valuable example in (block) design theory. With the points labelled 0, 1, 2, ..., 6 the lines (as point sets) are the translates of the (7, 3, 1) planar difference set given by {0, 1, 3} in the group Z / 7Z. [14]
Geometrical design (GD) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes [1] and is closely related to geometric modeling. Core problems are curve and surface modelling and representation.
The resulting 0–1 matrix M is the incidence matrix of a symmetric 2 − (4a − 1, 2a − 1, a − 1) design called an Hadamard 2-design. [8] This construction is reversible, and the incidence matrix of a symmetric 2-design with these parameters can be used to form an Hadamard matrix of order 4a.
Given an integer α ≥ 1, a tactical configuration satisfying: For every anti-flag (B, m) there are α flags (A, l) such that B I l and A I m, is called a partial geometry. If there are s + 1 points on a line and t + 1 lines through a point, the notation for a partial geometry is pg(s, t, α). If α = 1 these partial geometries are generalized ...
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.The shapes studied in geometric modeling are mostly two- or three-dimensional (solid figures), although many of its tools and principles can be applied to sets of any finite dimension.
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
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