Normal (geometry) in the context of Unit vector

In geography, latitude is a geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east-west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.

On its own, the term latitude normally refers to the geodetic latitude as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, and the plane of the equator.

In physics, angular velocity (symbol ω or ⁠${\displaystyle {\vec {\omega }}}$⁠, the lowercase Greek letter omega), also known as the angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.

The magnitude of the pseudovector, ${\displaystyle \omega =\|{\boldsymbol {\omega }}\|}$, represents the angular speed (or angular frequency), the angular rate at which the object rotates (spins or revolves). The pseudovector direction ${\displaystyle {\hat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}/\omega }$ is normal to the instantaneous plane of rotation or angular displacement.

An orbital pole is either point at the ends of the orbital normal, an imaginary line segment that runs through a focus of an orbit (of a revolving body like a planet, moon or satellite) and is perpendicular (or normal) to the orbital plane. Projected onto the celestial sphere, orbital poles are similar in concept to celestial poles, but are based on the body's orbit instead of its equator.

The north orbital pole of a revolving body is defined by the right-hand rule. If the fingers of the right hand are curved along the direction of orbital motion, with the thumb extended and oriented to be parallel to the orbital axis, then the direction the thumb points is defined to be the orbital north.

In mechanics, the normal force ${\displaystyle F_{N}}$ is the component of a contact force that is perpendicular to the surface that an object contacts. In this instance normal is used in the geometric sense and means perpendicular, as opposed to the meaning "ordinary" or "expected". A person standing still on a platform is acted upon by gravity, which would pull them down towards the Earth's core unless there were a countervailing force from the resistance of the platform's molecules, a force which is named the "normal force".

The normal force is one type of ground reaction force. If the person stands on a slope and does not sink into the ground or slide downhill, the total ground reaction force can be divided into two components: a normal force perpendicular to the ground and a frictional force parallel to the ground. In another common situation, if an object hits a surface with some speed, and the surface can withstand the impact, the normal force provides for a rapid deceleration, which will depend on the flexibility of the surface and the object.

An Amici prism, named for the astronomer Giovanni Battista Amici, is a type of compound dispersive prism used in spectrometers. The Amici prism consists of two triangular prisms in contact, with the first typically being made from a medium-dispersion crown glass, and the second from a higher-dispersion flint glass. Light entering the first prism is refracted at the first air–glass interface, refracted again at the interface between the two prisms, and then exits the second prism at near-normal incidence. The prism angles and materials are chosen such that one wavelength (colour) of light, the centre wavelength, exits the prism parallel to (but offset from) the entrance beam. The prism assembly is thus a direct-vision prism and is commonly used as such in hand-held spectroscopes. Other wavelengths are deflected at angles depending on the glass dispersion of the materials. Looking at a light source through the prism thus shows the optical spectrum of the source.

By 1860, Amici realized that one can join this type of prism back-to-back with a reflected copy of itself, producing a three-prism arrangement known as a double Amici prism. This doubling of the original prism increases the angular dispersion of the assembly and also has the useful property that the centre wavelength is refracted back into the direct line of the entrance beam. The exiting ray of the center wavelength is thus not only undeviated from the incident ray, but also experiences no translation (i.e. transverse displacement or offset) away from the incident ray's path.

Sound power or acoustic power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time. It is defined as "through a surface, the product of the sound pressure, and the component of the particle velocity, at a point on the surface in the direction normal to the surface, integrated over that surface." The SI unit of sound power is the watt (W). It relates to the power of the sound force on a surface enclosing a sound source, in air.

For a sound source, unlike sound pressure, sound power is neither room-dependent nor distance-dependent. Sound pressure is a property of the field at a point in space, while sound power is a property of a sound source, equal to the total power emitted by that source in all directions. Sound power passing through an area is sometimes called sound flux or acoustic flux through that area.

The bidirectional reflectance distribution function (BRDF), symbol ${\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}$, is a function of four real variables that defines how light from a source is reflected off an opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, ${\displaystyle \omega _{\text{i}}}$, and outgoing direction, ${\displaystyle \omega _{\text{r}}}$ (taken in a coordinate system where the surface normal ${\displaystyle \mathbf {n} }$ lies along the z-axis), and returns the ratio of reflected radiance exiting along ${\displaystyle \omega _{\text{r}}}$ to the irradiance incident on the surface from direction ${\displaystyle \omega _{\text{i}}}$. Each direction ${\displaystyle \omega }$ is itself parameterized by azimuth angle ${\displaystyle \phi }$ and zenith angle ${\displaystyle \theta }$, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr, with steradians (sr) being a unit of solid angle.

Surface roughness or simply roughness is the quality of a surface of not being smooth and it is hence linked to human (haptic) perception of the surface texture. From a mathematical perspective it is related to the spatial variability structure of surfaces, and inherently it is a multiscale property. It has different interpretations and definitions depending on the disciplines considered.

In surface metrology, surface roughness is a component of surface finish (surface texture). It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth. Roughness is typically assumed to be the high-frequency, short-wavelength component of a measured surface. However, in practice it is often necessary to know both the amplitude and frequency to ensure that a surface is fit for a purpose.

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ${\displaystyle E}$), and is denoted by the symbol ${\displaystyle \times }$. Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product).

The magnitude of the cross product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The units of the cross-product are the product of the units of each vector. If two vectors are parallel or are anti-parallel (that is, they are linearly dependent), or if either one has zero length, then their cross product is zero.

An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that point. The osculating circle provides a way to understand the local behavior of a curve and is commonly used in differential geometry and calculus.

More formally, in differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p. Its center lies on the inner normal line, and its curvature defines the curvature of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named circulus osculans (Latin for "kissing circle") by Leibniz.

A point cloud is a discrete set of data points in space. The points may represent a 3D shape or object. Each point position has its set of Cartesian coordinates (X, Y, Z). Points may contain data other than position such as RGB colors, normals, timestamps and others. Point clouds are generally produced by 3D scanners or by photogrammetry software, which measure many points on the external surfaces of objects around them. As the output of 3D scanning processes, point clouds are used for many purposes, including to create 3D computer-aided design (CAD) or geographic information systems (GIS) models for manufactured parts, for metrology and quality inspection, and for a multitude of visualizing, animating, rendering, and mass customization applications.

In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I₀ cos θ. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.

A surface which obeys Lambert's law is said to be Lambertian, and exhibits Lambertian reflectance. Such a surface has a constant radiance/luminance, regardless of the angle from which it is observed; a single human eye perceives such a surface as having a constant brightness, regardless of the angle from which the eye observes the surface. It has the same radiance because, although the emitted power from a given area element is reduced by the cosine of the emission angle, the solid angle, subtended by surface visible to the viewer, is reduced by the very same amount. Because the ratio between power and solid angle is constant, radiance (power per unit solid angle per unit projected source area) stays the same.