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36 relations: Affine space, Angular velocity, Animation, Bézier curve, Computer graphics, Covering space, De Casteljau's algorithm, Derivative, Dot product, Euler's formula, Exponential function, Exponential map (Riemannian geometry), Exponentiation, Geodesic, Great circle, Interpolation, Jack Elton Bresenham, Lie group, Linear combination, Linear interpolation, Natural logarithm, One-parameter group, Parallel transport, Power series, Quaternion, Quaternions and spatial rotation, Real number, Rotation, Rotation around a fixed axis, Rotation group SO(3), SIGGRAPH, Subtended angle, Tangent space, Time complexity, Versor, 3-sphere.
Affine space
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
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Angular velocity
In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.
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Animation
Animation is a dynamic medium in which images or objects are manipulated to appear as moving images.
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Bézier curve
A Bézier curve (pronounced in French) is a parametric curve frequently used in computer graphics and related fields.
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Computer graphics
Computer graphics are pictures and films created using computers.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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De Casteljau's algorithm
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Exponential map (Riemannian geometry)
In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself.
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Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
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Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
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Great circle
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Jack Elton Bresenham
Jack Elton Bresenham (born 11 October 1937, Clovis, New Mexico, US) is a former professor of computer science.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linear interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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One-parameter group
In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism from the real line \mathbb (as an additive group) to some other topological group G. That means that it is not in fact a group, strictly speaking; if \varphi is injective then \varphi(\mathbb), the image, will be a subgroup of G that is isomorphic to \mathbb as additive group.
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Parallel transport
In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold.
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Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
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Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
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Quaternions and spatial rotation
Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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Rotation around a fixed axis
Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion.
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Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
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SIGGRAPH
SIGGRAPH (Special Interest Group on Computer GRAPHics and Interactive Techniques) is the annual conference on computer graphics (CG) convened by the ACM SIGGRAPH organization.
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Subtended angle
In geometry, an angle subtended by an arc, line segment, or other curve is one whose two rays pass through the endpoints of the arc.
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Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Versor
In mathematics, a versor is a quaternion of norm one (a unit quaternion).
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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SLERP, Spherical linear interpolation.
References
[1] https://en.wikipedia.org/wiki/Slerp
