Maps that depict the surface of the Earth also use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture.

* Roman surface, self-intersecting immersion of the real projective plane into three-dimensional geometrical space

** 3D scanner, which digitizes the three-dimensional shape of a real object

The Roman surface or Steiner surface ( so called because Jakob Steiner was in Rome when he thought of it ) is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry.

In the Web definitions can be found which define the DEM as a digital regularly spaced GRID and a DTM as a real three-dimensional model ( TIN ).

Often, what he paints comes to life or becomes a real, three-dimensional object.

For instance, in the three-dimensional real vector space we have the following example.

The camera obscura's optical reduction of a real scene in three-dimensional space to a flat rendition in two dimensions influenced western art, so that at one point, it was thought that images based on optical geometry ( perspective ) belonged to a more advanced civilization.

* Mechanical motion tracking systems like Gametrak use cables attached to gloves for tracking position of physical elements in three-dimensional space in real time.

Blue Gene / L was the first supercomputer ever to run over 100 TFLOPS sustained on a real world application, namely a three-dimensional molecular dynamics code ( ddcMD ), simulating solidification ( nucleation and growth processes ) of molten metal under high pressure and temperature conditions.

It is natural to ask whether one can similarly define a multiplication on a three-dimensional real vector space such that every non-zero element has an inverse.

He said they used " more-conventional methods of motion control, animation, models, and rotoscoping to create a real, three-dimensional world, because ... computer graphics alone can sometimes lend a more flat, sterile image.

Lent ’ s dozen stories get as close to three-dimensional writing as is possible .” Paul Denham, notes the struggle a critic faces with the book and labels but also sees that struggle as an impediment “ from its real emotional power of a story ( or series of stories, if you prefer ) about the joy and pain of being a family .” Two reviews in The Globe and Mail concentrate on structure and theme.

( This list is closely related to, but not identical with, the Bianchi classification of the three-dimensional real Lie algebras into nine classes.

* Campus real three-dimensional map

Naturally the analogues of contour integrals will be harder to handle: when n = 2 an integral surrounding a point should be over a three-dimensional manifold ( since we are in four real dimensions ), while iterating contour ( line ) integrals over two separate complex variables should come to a double integral over a two-dimensional surface.

All real objects occupy a three-dimensional space.

However, the modelling study also states that " Given the complex, three-dimensional nature of the real Pine Island glacier ... it should be clear that the [...] model is a very crude representation of reality.

* Campus real three-dimensional map

* Campus real three-dimensional map

As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras.

* Campus real three-dimensional map

Maps that depict the surface of the Earth use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture.

A long-standing philosophy of modeling is manifest in its editorial features of layout design and operation, in which the model is viewed as a three-dimensional and temporal compression of the real world, so that, for example, the motive power, freight, trackage and scenery of a real-world railroad are formed into a layout which captures the spirit of not only the equipment and region of the railroad but also its purpose and how it operates.

The first one views the electric and magnetic fields as three-dimensional vector fields.

The three-dimensional Euclidean space R < sup > 3 </ sup > is a vector space, and lines and planes passing through the origin ( mathematics ) | origin are vector subspaces in R < sup > 3 </ sup >.

In both of these models the electrons are seen as a gas traveling through the lattice of the solid with an energy that is essentially isotropic in that it depends on the square of the magnitude, not the direction of the momentum vector k. In three-dimensional k-space, the set of points of the highest filled levels ( the Fermi surface ) should therefore be a sphere.

The main goal of X-ray crystallography is to determine the density of electrons f ( r ) throughout the crystal, where r represents the three-dimensional position vector within the crystal.

For an irrotational vector field in three-dimensional space the inverse-square law corresponds to the property that the divergence is zero outside the source.

* is the position vector which defines a point in three-dimensional space.

The figure above makes use of a convenient representation of the last three Stokes parameters as components in a three-dimensional vector space.

In a three-dimensional space ( n = 3 ), this is an arrow from p to q, which can be also regarded as the position of q relative to p. It may be also called a displacement vector if p and q represent two positions of the same point at two successive instants of time.

In a three-dimensional space, another important way of defining a plane is by specifying a point and a normal vector to the plane.

For example, the three-dimensional object physics calls angular velocity is a differential rotation, thus a vector in the Lie algebra tangent to SO ( 3 ).

At any location, the Earth's magnetic field can be represented by a three-dimensional vector ( see figure ).

In mathematics, the cross product, vector product, or Gibbs ' vector product is a binary operation on two vectors in three-dimensional space.

Fluid flow is characterized by a velocity vector field in three-dimensional space, within the framework of continuum mechanics.

In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word " normal " is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc.

This may be contrasted with the vector cross product, which does: in a three-dimensional vector space, the three vectors in the equation will always form a right-handed set ( or a left-handed set, depending on how the cross product is defined ), thus fixing an orientation in the vector space.

A vector v (< font color ="# CC0000 "> red </ font >) represented by < p >• tangent basis vectors (< font color =" orange "> yellow </ font >, left: e < sub > 1 </ sub >, e < sub > 2 </ sub >, e < sub > 3 </ sub >) to the coordinate curves ( black ),</ p > < p >• dual basis, covector basis, or cobasis (< font color =" blue "> blue </ font >, right: e < sup > 1 </ sup >, e < sup > 2 </ sup >, e < sup > 3 </ sup >), normal vectors to coordinate surfaces (< font color ="# 3B444B "> grey </ font >),</ p > in three-dimensional | 3d general curvilinear coordinates ( q < sup > 1 </ sup >, q < sup > 2 </ sup >, q < sup > 3 </ sup >), a tuple of numbers to define point in a position space.

Introduction of more holes, e. g. five holes arranged in a " plus " formation, allow measurement of the three-dimensional velocity vector.