The projection of the spiral motion in a rotating horizontal plane is shown at the right of the figure.

The various specializations of the cylindric equal-area projection differ only in the ratio of the vertical to horizontal axis.

* projection aperture: at least 2 mm ( 0. 080 in ) less than camera aperture on the vertical axis and at least 0. 4 mm ( 0. 016 in ) less on the horizontal axis

The algorithm will be initially presented only for the octant in which the segment goes down and to the right ( x < sub > 0 </ sub >≤ x < sub > 1 </ sub > and y < sub > 0 </ sub >≤ y < sub > 1 </ sub >), and its horizontal projection is longer than the vertical projection ( the line has a negative slope whose absolute value is less than 1.

Isometric projection corresponds to rotation of the object by ± 45 ° about the vertical axis, followed by rotation of approximately ± 35. 264 ° arcsin ( tan ( 30 °)) about the horizontal axis starting from an orthographic projection view.

* projection aperture: at least less than camera aperture on the vertical axis and at least less on the horizontal axis

It involves the simultaneous projection of three reels of silent film arrayed in a horizontal row, making for a total aspect ratio of 4: 1 ( 1. 33 × 3: 1 ).

For all practical purposes a local Earth axis set is used, this has X and Y axis in the local horizontal plane, usually with the x-axis coinciding with the projection of the velocity vector at the start of the motion, on to this plane.

A grid bearing is measured in relation to the fixed horizontal reference plane of grid north, that is, using the direction northwards along the grid lines of the map projection as a reference point.

A cornice is horizontal molded projection that completes a building or wall ; or the upper slanting part of an entablature located above the frieze.

However, NACA studies indicated that the V-tail surfaces must be larger than simple projection into the vertical & horizontal planes would suggest, such that total wetted area is roughly constant ; reduction of intersection surfaces from three to two, does, however, produce a net reduction in drag through elimination of some interference drag.

Given the initial velocity of a particle launched from the ground, the downward ( i. e. gravitational ) acceleration, and the projectile's angle of projection θ ( measured relative to the horizontal ), then a simple rearrangement of the SUVAT equation

It follows that ω determines uniquely a bundle map v: TP → V which is the identity on V. Such a projection v is uniquely determined by its kernel, which is a smooth subbundle H of TP ( called the horizontal bundle ) such that TP = V ⊕ H.

Figure 8 shows that the perspective projection of the horizontal top line of the wall intersects at the retina — actually, in true life, at the focal point slightly in front of the retina and from where it is inverted.

Figure 9 shows the projection of the horizontal bottom line of the wall and its great circle of intersection ( H ).

In a Fischer projection, all horizontal bonds project toward the viewer, while vertical bonds project away from the viewer.

Plan view or " planform " is defined as a vertical orthographic projection of an object on a horizontal plane, like a map.

A plan view is an orthographic projection of a 3-dimensional object from the position of a horizontal plane through the object.

This technique is called anamorphic projection and various implementations have been marketed under several brand names, including CinemaScope, Panavision and Superscope, with Technirama implementing a slightly different anamorphic technique using vertical expansion to the film rather than horizontal compression.

where h denotes the projection to the horizontal subspace, H < sub > x </ sub > defined by the connection, with kernel V < sub > x </ sub > ( the vertical subspace ) of the tangent bundle of the total space of the fiber bundle.

A picture plane is the imaginary flat surface which is usually located between the station point and the object being viewed and is ordinarily a vertical plane perpendicular to the horizontal projection of the line of sight to the object's order of interest.

The Mollweide is a pseudocylindrical projection in which the equator is represented as a straight horizontal line perpendicular to a central meridian one-half its length.

Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is

* The projection of to the vertical subspace needs to agree with metric on the fiber over a point in the manifold M.

Denote by the projection to the subspace.

* The tensor-to-vector projection in multilinear subspace learning is a multilinear map as well.

These constructions also make the Grassmannian into a metric space: For a subspace W of V, let P < sub > W </ sub > be the projection of V onto W. Then

Observe that P is a projection involved in this supremum precisely if the range of P is an invariant subspace of.

* If V is an inner product space and W is a subspace, the kernel of the orthogonal projection V → W is the orthogonal complement to W in V.

The matrix H < sub > n </ sub > can be viewed as the representation in the basis formed by the Arnoldi vectors of the orthogonal projection of A onto the Krylov subspace.

The idea of the Arnoldi iteration as an eigenvalue algorithm is to compute the eigenvalues of the orthogonal projection of A onto the Krylov subspace.

is the orthogonal projection of the original signal f or at least of the first approximation onto the subspace, that is, with sampling rate of 2 < sup > k </ sup > per unit interval.

and equip it with the subspace topology and the projection map π ′: f < sup >*</ sup > E → B ′ given by the projection onto the first factor, i. e.,

The map X is linear and it is a projection on the subspace Π < sub > n </ sub > of polynomials of degree n or less.

Mathematically, the first vector is the orthogonal, or least-squares, projection of the data vector onto the subspace spanned by the vector of 1's.

The second residual vector is the least-squares projection onto the ( n − 1 )- dimensional orthogonal complement of this subspace, and has n − 1 degrees of freedom.

Let e < sub > N </ sub > be the projection onto the subspace NΩ.

where p denotes the projection from TM to M. In other words, a vector field is a section of the tangent bundle.

at each point v ∈ TM ; here π < sub >∗</ sub >: TTM → TM denotes the pushforward ( differential ) along the projection π: TM → M associated to the tangent bundle.

Some authors define stereographic projection from the north pole ( 0, 0, 1 ) onto the plane z = − 1, which is tangent to the unit sphere at the south pole ( 0, 0, − 1 ).

* The natural projection on the tangent bundle on a manifold.

This projection maps each tangent space T < sub > x </ sub > M to the single point x.

That is, for a vector v in the tangent bundle of the cotangent bundle, the application of the tautological one-form θ to v at ( x, ω ) is computed by projecting v into the tangent bundle at x using and applying ω to this projection.

In the special case of a manifold isometrically embedded into a higher dimensional Euclidean space, the covariant derivative can be viewed as the orthonormal projection of the Euclidean derivative along a tangent vector onto the manifold's tangent space.

The geodesic curvature is the norm of the projection of the derivative on the tangent plane to the submanifold.

Like the stereographic projection and gnomonic projection, orthographic projection is a perspective ( or azimuthal ) projection, in which the sphere is projected onto a tangent plane or secant plane.

The equations for the orthographic projection onto the ( x, y ) tangent plane reduce to the following:

As usual, TM denotes the tangent bundle of M with its natural projection π < sub > M </ sub >: TM → M given by

* The projection of C onto a plane from a point on a tangent line of C yields a cuspidal cubic.

More abstractly, given an immersion ( for instance an embedding ), one can define a normal bundle of N in M, by at each point of N, taking the quotient space of the tangent space on M by the tangent space on N. For a Riemannian manifold one can identify this quotient with the orthogonal complement, but in general one cannot ( such a choice is equivalent to a section of the projection ).

As with the Mercator projection, the region near the tangent ( or secant ) point on a Stereographic map remains very close to true scale for an angular distance of a few degrees.

In the ellipsoidal model, a stereographic projection tangent to the pole will have a scale factor of less than 1. 003 at 84 ° latitude and 1. 008 at 80 ° latitude.