affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space...

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent...

parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation...

applied. The world-to-image plane projection is a 3D homogeneous coordinate system transformation (aka: 3D projection, affine transformation, or projective...

In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...

A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These...

plane curve. If the curve is contained in an affine space or a projective space, one can take a projection for such a birational equivalence. These birational...

simplest case, when the sets are affine spaces, was analyzed by John von Neumann. The case when the sets are affine spaces is special, since the iterates...

the orthogonal projection onto a line that does not pass through the origin is an affine, not linear, transformation. Parallel projections are also linear...

algebraic variety can be neither affine nor projective. To give an example, let X = P1 × A1 and p: X → A1 the projection. Here X is an algebraic variety...

through P. See Affine space § Projection for an accurate definition, generalized to any dimension.[citation needed] The concept of projection in mathematics...

algebra Clifford algebra Geometric algebra Affine space Affine transformation Affine group Affine geometry Affine coordinate system Flat (geometry) Cartesian...

having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain...

numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has...

Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine...

be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at...

Graffk(V) is the topological space of all affine k-dimensional subspaces of V. It has a natural projection p:Graffk(V) → Grk(V), the Grassmannian of all...

Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve...

translation, rotation and scaling of the image which needs to be transformed, Affine or projective transform. Projective transformation is the farthest an image...

an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each...

the k + 1 points u 0 , … , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 − u 0 , … , u k − u 0 {\displaystyle...

acquired with a large focal length, an affine homography is a more appropriate model of image displacements. An affine homography is a special type of a general...

for a linear projection P. If A represents a linear involution, then x→A(x−b)+b is an affine involution. One can check that any affine involution in...

of dimensional analogy in visualizing higher dimensions is in projection. A projection is a way of representing an n-dimensional object in n − 1 dimensions...

an affine variety to A1, we can define regular maps from one affine variety to another. First we will define a regular map from a variety into affine space:...

are graphics employed in video games and pixel art that use a parallel projection, but which angle the viewpoint to reveal facets of the environment that...

the spherical and cylindrical coordinates for three-dimensional space. An affine line with a chosen Cartesian coordinate system is called a number line....

still further by integrating instead over k {\displaystyle k} -dimensional affine subspaces of R n {\displaystyle \mathbb {R} ^{n}} . The X-ray transform...

Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional...

Kanade. They used an affine factorization approach to extract 3D from images sequences. However, the assumption of orthographic projection is a significant...