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A monotone rectilinear polygon is a monotone polygon which is also rectilinear. A T-square is a fractal generated from a sequence of rectilinear polygons with interesting properties. Algorithmic problems involving rectilinear polygons
The T-puzzle, a T shape can be assembled with the four pieces on the left. The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle , two right trapezoids and an irregular shaped pentagon .
A rectilinear polygon can always be covered with a finite number of vertices of the polygon. [1] The algorithm uses a local optimization approach: it builds the covering by iteratively selecting maximal squares that are essential to the cover (i.e., contain uncovered points not covered by other maximal squares) and then deleting from the polygon the points that become unnecessary (i.e ...
In the visual arts, shape is a flat, enclosed area of an artwork created through lines, textures, or colours, or an area enclosed by other shapes, such as triangles, circles, and squares. [1] Likewise, a form can refer to a three-dimensional composition or object within a three-dimensional composition. [2]
The area of a self-intersecting polygon can be defined in two different ways, giving different answers: Using the formulas for simple polygons, we allow that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region. For example, the central convex pentagon in the center of a ...
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles.It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle.
The taxicab distance is also sometimes known as rectilinear distance or L 1 distance (see L p space). [1] This geometry has been used in regression analysis since the 18th century, and is often referred to as LASSO. Its geometric interpretation dates to non-Euclidean geometry of the 19th century and is due to Hermann Minkowski.
Geometrically K 3 forms the edge set of a triangle, K 4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K 7 as its skeleton. [15] Every neighborly polytope in four or more dimensions also has a complete skeleton. K 1 through K 4 are all planar graphs.