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  2. Level-set method - Wikipedia

    en.wikipedia.org/wiki/Level-set_method

    Left image shows zero-level solution. Right image shows the level-set scalar field. The Level-set method (LSM) is a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. LSM can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these ...

  3. Scalar projection - Wikipedia

    en.wikipedia.org/wiki/Scalar_projection

    Vector projection of a on b (a 1), and vector rejection of a from b (a 2). In mathematics, the scalar projection of a vector on (or onto) a vector , also known as the scalar resolute of in the direction of , is given by:

  4. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry , the dot product of the Cartesian coordinates of two vectors is widely used.

  5. Quaternion - Wikipedia

    en.wikipedia.org/wiki/Quaternion

    A quaternion of the form a + 0 i + 0 j + 0 k, where a is a real number, is called scalar, and a quaternion of the form 0 + b i + c j + d k, where b, c, and d are real numbers, and at least one of b, c, or d is nonzero, is called a vector quaternion. If a + b i + c j + d k is any quaternion, then a is called its scalar part and b i + c j + d k ...

  6. Lattice constant - Wikipedia

    en.wikipedia.org/wiki/Lattice_constant

    Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.

  7. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    Diagram for geometric proof. This proof is valid only if the line is not horizontal or vertical. [5] Drop a perpendicular from the point P with coordinates (x 0, y 0) to the line with equation Ax + By + C = 0. Label the foot of the perpendicular R. Draw the vertical line through P and label its intersection with the given line S.

  8. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    2.1.4 Scalar curvature. 2.1.5 ... is the absolute value of the determinant of the matrix of scalar ... and the traceless Ricci tensor are symmetric 2-tensors: ...

  9. Feynman diagram - Wikipedia

    en.wikipedia.org/wiki/Feynman_diagram

    The remaining two half-lines in the two X s can be linked to each other in two ways, so that the total number of ways to form the diagram is 4 × 3 × 4 × 3 × 2 × 2, while the denominator is 4! × 4! × 2!. The total symmetry factor is 2, and the contribution of this diagram is divided by 2.