curvilinear
- (Mathematics) consisting of, bounded by, or characterized by a curved line
- (Mathematics) along a curved line: curvilinear motion.
- (Mathematics) maths (of a set of coordinates) determined by or determining a system of three orthogonal surfaces
What does the name curvilinear mean?
While the terms linear and nonlinear have standard definitions in statistics, the term curvilinear does not have a standard meaning. It generally is used to describe a curve that is smooth (no discontinuities) but the underlying mathematical model could be either linear or nonlinear.
How to pronounce curvilinear?
Below is the UK transcription for 'curvilinear' :
- Modern IPA: kə́ːvɪlɪ́nɪjə
- Traditional IPA: ˌkɜːvɪˈlɪniːə
- 5 syllables : "KUR" + "vi" + "LIN" + "ee" + "uh"
How to use curvilinear in a sentence?
Curvilinear in a sentence
- (1) One of the first examples of a curvilinear glasshouse, it stands as a reminder of bygone eras in Belfast's history.
- (2) Finish the detail drawing of any other curvilinear product.
- (3) Then, linear equation is turned back into curvilinear equation.
- (4) Orthogonal Curvilinear Coordinates. ...
What are some examples of curvilinear motion?
Examples of Motion
- Sliding. This is one of the most prominent examples of rectilinear motion. ...
- Boomerang. Boomerangs display one of the most captivating phenomena, it is way too exciting to see it return to the thrower after following a curved path.
- Bowling. ...
- Planets around the sun. ...
- Spinning Top. ...
- Pendulum. ...
- Guitar Strings. ...
- Ticking of Clock. ...
- Sewing Machine Needle. ...
What are curvilinear lines in art?
The style is characterized by a curving line used to form abstract patterns, such as spirals, circles, swirls, and S-shapes, as well as to define human facial features. The straight line and the right angle are practically nonexistent in both the abstract and the anthropomorphic types of ornamentation.
What is a curvilinear shape?
Curvilinear shapes are composed of curved lines and smooth edges. They give off a more natural feeling to the shape. In contrast, rectilinear shapes are composed of sharp edges and right angles, and give off a sense of order in the composition. They look more human-made, structured, and artificial.
What is the definition of curvilinear translation?
When the paths of motion for any two points on the body are parallel lines, he motion is called rectilinear translation. If the paths of motion are along curved lines which are equidistant, the motion is called curvilinear translation.
Who invented the curvilinear Art?
It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book La Perspective curviligne, which was translated into English in 1987 as Curvilinear Perspective: From Visual Space to the Constructed Image and published by the University of California Press.
What is a curvilinear graph?
While the terms linear and nonlinear have standard definitions in statistics, the term curvilinear does not have a standard meaning. It generally is used to describe a curve that is smooth (no discontinuities) but the underlying mathematical model could be either linear or nonlinear.
What is curvilinear triangle?
The deltoid curve is another type of curvilinear triangle, but one in which the curves replacing each side of an equilateral triangle are concave rather than convex. It is not composed of circular arcs, but may be formed by rolling one circle within another of three times the radius.
What is another word for curvilinear?
In this page you can discover 14 synonyms, antonyms, idiomatic expressions, and related words for curvilinear, like: curvilineal, arced, arched, arciform, bent, bowed, curved, rounded, straight, rectilinear and polygonal.
What is the difference between rectilinear translation and curvilinear translation?
In rectilinear motion all particles of the body travel the same distance along parallel straight lines. In curvilinear motion the trajectories of individual particles of the body are curved, although the orientation of the body in space does not change.
How do you pronounce curvilinear triangle?
0:010:22How to pronounce curvilinear - YouTubeYouTubeStart of suggested clipEnd of suggested clipCrudo línea juvenil rubén ya juvenil pudo venir.MoreCrudo línea juvenil rubén ya juvenil pudo venir.
Why is Biomorphism important?
Biomorphism became a major theme in Surrealist art, led by Arp, who was one of the group's founders, in 1924. Along with Joan Miró, and Yves Tanguy, he felt that biomorphic images reflected the connection between the human subconscious and reality more accurately.
What is Biomorphism in art?
Sculpture de Silence, CorneilleHans ArpAlou with TalonsHans ArpBiomorphism/Artworks
Do humans see in curvilinear perspective?
Curvilinear perspective is theoretically like the human eye, which has a 180-degree field of view (although we typically focus on the 45-degree field directly in front of us).
What is a curvilinear line?
Curvilinear lines are smooth lines or curves, like the curves we see in trigonometric functions or parabolic functions . “Curvilinear” refers to something more complicated though, than just a simple curve or set of curves—it’s a set of curves with a purpose.
What is a curvilinear regression?
For example, during curvilinear regression, the procedure considers an infinite number of curves—or at the least, a very large family of curves. That leads us to a slightly more formal (and general) definition: In general, we can say that something is curvilinear if it is formed (or characterized by) a set of curved lines.
What are cylindrical coordinates?
But so are cylindrical coordinates (an extension of two-dimensional polar coordinates to three-dimensional) and spherical polar coordinates. If there’s a one to one mapping between coordinate systems, we can convert between them.
What is the name of the coordinate system for intersections?
If the intersections are right angles, the system is called an orthogonal coordinate system.
Do you need a large number of lines to have a curvilinear coordinate system?
That doesn’t mean you need to have a large number of lines: a single curved line still counts as a set of one. A curvilinear coordinate system has cooordinate curves Θ and base vectors (a) which are tangent to those curves.
Is a curvilinear coordinate a generalized coordinate system?
You can think of curvilinear coordinates as a generalized coordinate system, free of the straight line restraints that you see with a Euclidean system. Curvilinear coordinates don’t have to be based on curved lines. Cartesian coordinates are one type of curvilinear coordinate systems.
What is curvilinear coordinates?
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible ...
What is the name of the coordinate system that is curved?
This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.
Why is the position of the indices of the vectors the opposite of that of the coordinates?
Note that, because of Einstein's summation convention, the position of the indices of the vectors is the opposite of that of the coordinates.
How to write coordinates of vector space?
The coordinates of this space can be denoted by: x = ( x1, x2 ,..., xn ). Since this is a vector (an element of the vector space), it can be written as:
Which coordinate system is used to describe the motion of a particle in a rectangular box?
While one might describe the motion of a particle in a rectangular box using Cartesian coordinates, the motion in a sphere is easier with spherical coordinates. Spherical coordinates are the most common curvilinear coordinate systems and are used in Earth sciences, cartography, quantum mechanics, relativity, and engineering .
How are coordinate axes determined?
The coordinate axes are determined by the tangents to the coordinate curves at the intersection of three surfaces. They are not in general fixed directions in space, which happens to be the case for simple Cartesian coordinates, and thus there is generally no natural global basis for curvilinear coordinates.
How to know when to use curvilinear regression?
The easiest way to know whether or not you should use curvilinear regression is to create a scatterplot of the predictor variable and response variable. If the scatterplot displays a linear relationship between the two variables, then simple linear regression is likely appropriate to use.
What is a curvilinear regression model?
Curvilinear regression is the name given to any regression model that attempts to fit a curve as opposed to a straight line. Common examples of curvilinear regression models include: Quadratic Regression: Used when a quadratic relationship exists between a predictor variable and a response variable.
When to use cubic regression?
Cubic Regression: Used when a cubic relationship exists between a predictor variable and a response variable. When graphed, this type of relationship has two distinct curves on a scatterplot:
Is a scatterplot a curvilinear regression?
However, if the scatterplot shows a quadratic, cubic, or some other curvilinear pattern between the predictor and response variable, then curvilinear regression is likely more appropriate to use.
What are the two forms of curvilinear systems?
Curvilinear systems generally take one of two forms: simple, constant-radii sections (such as a 90- or 180-degree turn) together with straight sections, or variable-radii sections (think of a free-form, squiggly line) combined with straight sections.
Why do curvilinear systems use wheels?
For this reason, many curvilinear systems use wheels or rollers to guide and support the load. The main benefit of wheels and rollers in combined linear and curved motion is that they don’t require the highly accurate running surfaces that recirculating bearings require.
What are the challenges of curvilinear motion?
One of the challenges of curvilinear motion is that the moving component — the carriage or slider — must be able to operate around the curves and through the transitions between straight and curved sections. For this reason, many curvilinear systems use wheels or rollers to guide and support the load. The main benefit of wheels and rollers in combined linear and curved motion is that they don’t require the highly accurate running surfaces that recirculating bearings require. Roller carriages can also be adjusted to add preload and stiffness, and both wheels and rollers are able to withstand environments with particulate contamination, such as dust and chips.
What is a plain bearing?
Plain bearings are also inherently self-aligning, so the risk of binding and excessive wear due to curved motion sections is reduced.
What is curved guide?
Guides and tracks that provide curved motion are often put in the same category as curvilinear guides, but curved guides only provide motion that occurs along a radius, and don’t include straight sections of motion.
When to use conveying type?
The former is typical of a conveying-type application, often used when a part needs to be moved around an assembly or inspection station. The latter is often found when parts or components need to be moved in a generally straight line, but with some deviations to avoid obstacles.
Is travel linear or rotary?
In single-axis motion systems, travel is typically either linear (in a straight line) or rotary (in a partial or complete circle). But some applications call for a system that combines straight sections of motion with curved sections — referred to as curvilinear motion.
What is a graphical representation of a curvilinear correlation?
The graphical representation of a curvilinear correlation is like an inverted U.
What is linear correlation?
Linear correlation is referred to as the measure of relationship between two random variables with values ranging from -1 and 1. It is proportional to covariance and can be interpreted in the same way as covariance.
Curvilinear Coordinates
- Curvilinear coordinates are a coordinate system used for Euclidean spacewhere the coordinate lines (think: the x and y-axis, and the grid lines on your graph paper) may be curved. You can think of curvilinear coordinates as a generalized coordinate system, free of the straight line restraints that you see with a Euclidean system. Curvilinear coordi...
Why Use Curviliear coordinates?
- If you wanted to map a roller coaster, a spherical cell, or the shape of a biological cell, the usual lines in a x-y plane won’t quite do. However, if you have an infinite number of curvesto play with, then you would be able to create a more accurate representation of just about every real-life system. These representations can help you to see aspects of the problem that might not be rea…
Curvilinear Regression
- Curvilinear regression involves finding the equation of a curved line that fits a particular set of data points. You might use this type of regression if you’ve begun analyzing a data set with linear regression, and then you realize that the correlation between your x and y variables doesn’t really look like a straight line— it looks more like a curve. Polynomial regression(which includes quadr…
References
- Antoni, M. (2018). Calculus with Curvilinear Coordinates: Problems and Solutions. Springer. 1.16 Curvilinear Coordinates. Retrieved September 12, 2019 from: http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/Part_III/Chapter_…
Overview
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and …
Orthogonal curvilinear coordinates in 3 dimensions
For now, consider 3-D space. A point P in 3d space (or its position vector r) can be defined using Cartesian coordinates (x, y, z) [equivalently written (x , x , x )], by , where ex, ey, ez are the standard basis vectors.
It can also be defined by its curvilinear coordinates (q , q , q ) if this triplet of numbers defines a single point in an unambiguous way. The relation between t…
Vector calculus
In orthogonal curvilinear coordinates, since the total differential change in r is
so scale factors are
In non-orthogonal coordinates the length of is the positive square root of (with Einstein summation convention). The six independent scalar products gij=hi.hj of the natural basis vectors generalize the three scale factors defined above for orthogonal coordinates. The nine gij are the componen…
Covariant and contravariant bases
Spatial gradients, distances, time derivatives and scale factors are interrelated within a coordinate system by two groups of basis vectors:
1. basis vectors that are locally tangent to their associated coordinate pathline: b i = ∂ r ∂ q i {\displaystyle \mathbf {b} _{i}={\dfrac {\partial \mathbf {r} }{\partial q^{i}}}} are contravariant vectors (denoted by lowered indices), and
Integration
Consider the one-dimensional curve shown in Fig. 3. At point P, taken as an origin, x is one of the Cartesian coordinates, and q is one of the curvilinear coordinates. The local (non-unit) basis vector is b1 (notated h1 above, with b reserved for unit vectors) and it is built on the q axis which is a tangent to that coordinate line at the point P. The axis q and thus the vector b1 form an angle with …
Generalization to n dimensions
The formalism extends to any finite dimension as follows.
Consider the real Euclidean n-dimensional space, that is R = R × R × ... × R (n times) where R is the set of real numbers and × denotes the Cartesian product, which is a vector space.
The coordinates of this space can be denoted by: x = (x1, x2,...,xn). Since this is a vector (an element of the vector space), it can be written as:
Transformation of coordinates
From a more general and abstract perspective, a curvilinear coordinate system is simply a coordinate patch on the differentiable manifold E (n-dimensional Euclidean space) that is diffeomorphic to the Cartesian coordinate patch on the manifold. Two diffeomorphic coordinate patches on a differential manifold need not overlap differentiably. With this simple definition of a curvilinear coordinate system, all the results that follow below are simply applications of standar…
Vector and tensor algebra in three-dimensional curvilinear coordinates
Note: the Einstein summation convention of summing on repeated indices is used below.
Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature in mechanics and physics and can be indispensable to understanding work from the early and mid-1900s, for example the text by Green and Zerna. Some useful relations in the algebra of vectors and second-order tensors in curvilinear coordinates are given in this section. …