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  2. Line integral convolution - Wikipedia

    en.wikipedia.org/wiki/Line_integral_convolution

    Texture-based methods, like LIC, avoid these problems since they depict the entire vector field at point-like (pixel) resolution. [ 1 ] Compared to other integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt ...

  3. Phase plane - Wikipedia

    en.wikipedia.org/wiki/Phase_plane

    The phase plane method refers to graphically determining the existence of limit cycles in the solutions of the differential equation. The solutions to the differential equation are a family of functions. Graphically, this can be plotted in the phase plane like a two-dimensional vector field.

  4. Scientific visualization - Wikipedia

    en.wikipedia.org/wiki/Scientific_visualization

    The primary methods for visualizing two-dimensional (2D) scalar fields are color mapping and drawing contour lines. 2D vector fields are visualized using glyphs and streamlines or line integral convolution methods. 2D tensor fields are often resolved to a vector field by using one of the two eigenvectors to represent the tensor each point in ...

  5. Cremona diagram - Wikipedia

    en.wikipedia.org/wiki/Cremona_diagram

    The Cremona diagram, also known as the Cremona-Maxwell method, is a graphical method used in statics of trusses to determine the forces in members (graphic statics). The method was developed by the Italian mathematician Luigi Cremona .

  6. Method of averaging - Wikipedia

    en.wikipedia.org/wiki/Method_of_averaging

    The advantage of this method is the extension to more general settings such as infinite-dimensional systems - partial differential equation or delay differential equations. J. Hale presents generalizations to almost periodic vector-fields. [4]

  7. Integral curve - Wikipedia

    en.wikipedia.org/wiki/Integral_curve

    This equation says that the vector tangent to the curve at any point x(t) along the curve is precisely the vector F(x(t)), and so the curve x(t) is tangent at each point to the vector field F. If a given vector field is Lipschitz continuous, then the Picard–Lindelöf theorem implies that there exists a unique flow for small time.

  8. Vector calculus - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus

    Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.

  9. Nine-point stencil - Wikipedia

    en.wikipedia.org/wiki/Nine-point_stencil

    Or, for different anisotropic effects using the same vector field [14] θ = arctan ⁡ ( V y / − V x ) {\displaystyle \theta =\arctan(V_{y}/-V_{x})} It is important to note that, regardless of the values of θ {\displaystyle \theta } , the anisotropic propagation will occur parallel to the secondary direction c2 and perpendicular to the ...