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  2. Contour integration - Wikipedia

    en.wikipedia.org/wiki/Contour_integration

    A smooth curve that is not closed is often referred to as a smooth arc. [6] The parametrization of a curve provides a natural ordering of points on the curve: () comes before () if <. This leads to the notion of a directed smooth curve. It is most useful to consider curves independent of the specific parametrization.

  3. Wire-frame model - Wikipedia

    en.wikipedia.org/wiki/Wire-frame_model

    In 3D computer graphics, a wire-frame model (also spelled wireframe model) is a visual representation of a three-dimensional (3D) physical object. It is based on a polygon mesh or a volumetric mesh, created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using (straight) lines or curves.

  4. Reuleaux triangle - Wikipedia

    en.wikipedia.org/wiki/Reuleaux_triangle

    The other supporting line may touch the triangle at any point on the opposite arc, and their distance (the width of the Reuleaux triangle) equals the radius of this arc. [ 11 ] The first mathematician to discover the existence of curves of constant width, and to observe that the Reuleaux triangle has constant width, may have been Leonhard Euler ...

  5. Curve - Wikipedia

    en.wikipedia.org/wiki/Curve

    In Euclidean geometry, an arc (symbol: ⌒) is a connected subset of a differentiable curve. Arcs of lines are called segments, rays, or lines, depending on how they are bounded. A common curved example is an arc of a circle, called a circular arc. In a sphere (or a spheroid), an arc of a great circle (or a great ellipse) is called a great arc.

  6. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    Every bounded convex curve is a rectifiable curve, meaning that it has a well-defined finite arc length, and can be approximated in length by a sequence of inscribed polygonal chains. For closed convex curves, the length may be given by a form of the Crofton formula as times the average length of its projections onto lines. [8]

  7. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    A parametric C r-curve or a C r-parametrization is a vector-valued function: that is r-times continuously differentiable (that is, the component functions of γ are continuously differentiable), where , {}, and I is a non-empty interval of real numbers.

  8. Solid modeling - Wikipedia

    en.wikipedia.org/wiki/Solid_modeling

    A solid part model generally consists of a group of features, added one at a time, until the model is complete. Engineering solid models are built mostly with sketcher-based features; 2-D sketches that are swept along a path to become 3-D. These may be cuts, or extrusions for example.

  9. Smoothness - Wikipedia

    en.wikipedia.org/wiki/Smoothness

    Smooth functions with given closed support are used in the construction of smooth partitions of unity (see partition of unity and topology glossary); these are essential in the study of smooth manifolds, for example to show that Riemannian metrics can be defined globally starting from their local existence.

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