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  2. Second moment of area - Wikipedia

    en.wikipedia.org/wiki/Second_moment_of_area

    An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where

  3. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...

  4. Quadric - Wikipedia

    en.wikipedia.org/wiki/Quadric

    In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.

  5. Bézier curve - Wikipedia

    en.wikipedia.org/wiki/Bézier_curve

    The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...

  6. Quartic surface - Wikipedia

    en.wikipedia.org/wiki/Quartic_surface

    If the base field is ⁠ ⁠ or ⁠ ⁠ the surface is said to be real or complex respectively. One must be careful to distinguish between algebraic Riemann surfaces , which are in fact quartic curves over ⁠ C {\displaystyle \mathbb {C} } ⁠ , and quartic surfaces over ⁠ R {\displaystyle \mathbb {R} } ⁠ .

  7. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables.

  8. First fundamental form - Wikipedia

    en.wikipedia.org/wiki/First_fundamental_form

    In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which is induced canonically from the dot product of R 3. It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consistent with the ambient space.

  9. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    A simple example of a regular surface is given by the 2-sphere {(x, y, z) | x 2 + y 2 + z 2 = 1}; this surface can be covered by six Monge patches (two of each of the three types given above), taking h(u, v) = ± (1 − u 2 − v 2) 1/2. It can also be covered by two local parametrizations, using stereographic projection.