A polycube is a solid figure formed by joining one or more equal cubes face to face. It is a polyform whose base form is a cube. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube and the Bedlam cube are examples of packing problems based on polycubes.
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Solid modeling
Solid modeling (or modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional solids. Solid modeling is distinguished from related areas of geometric modeling and computer graphics by its emphasis on physical fidelity.
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Affine geometry
In mathematics affine geometry is the study of geometric properties which remain unchanged by affine transformations, i.e. non-singular linear transformations and translations. The name affine geometry, like projective geometry and Euclidean geometry, follows naturally from the Erlangen program of Felix Klein.
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Spline (mathematics)
In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots). In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher degrees.
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3D modeling
In 3D computer graphics, 3D modeling is the process of developing a mathematical representation of any three-dimensional surface of object (either inanimate or living) via specialized software. The product is called a 3D model. It can be displayed as a two-dimensional image through a process called 3D rendering or used in a computer simulation of physical phenomena. The model can also be physically created using 3D printing devices. Models may be created automatically or manually.
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Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. Another name is equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. The term oblong is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as 10px¿.
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Manifold
In mathematics, a manifold is a mathematical object that on a small enough scale resembles Euclidean space. For example, seen from far away, the surface of the planet Earth is not flat and Euclidean, but on a smaller scale, one may describe each region via a geographic map, a projection of the surface onto the Euclidean plane. A precise mathematical definition of a manifold is given below. Lines and circles (but not figure eights) are one-dimensional manifolds (1-manifolds).
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Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
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