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A building's surface detailing, inside and outside, often includes decorative moulding, and these often contain ogee-shaped profiles—consisting (from low to high) of a concave arc flowing into a convex arc, with vertical ends; if the lower curve is convex and higher one concave, this is known as a Roman ogee, although frequently the terms are used interchangeably and for a variety of other ...
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.
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane, with edges being drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles. In some cases, line segments of the line itself are also allowed as ...
A plane curve is the image of any continuous function from an interval to the Euclidean plane.Intuitively, it is a set of points that could be traced out by a moving point. More specifically, smooth curves generally at least require that the function from the interval to the plane be continuously differentiable, and in some contexts are defined to require higher derivative
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.
The curve-shortening flow is an example of a geometric flow, and is the one-dimensional case of the mean curvature flow. Other names for the same process include the Euclidean shortening flow, geometric heat flow, [1] and arc length evolution. As the points of any smooth simple closed curve move in this way, the curve remains simple and smooth ...
Single color line drawing algorithms involve drawing lines in a single foreground color onto a background. They are well-suited for usage with monochromatic displays. The starting point and end point of the desired line are usually given in integer coordinates, so that they lie directly on the points considered by the algorithm.
The most familiar examples are the straight lines in Euclidean geometry. On a sphere, the images of geodesics are the great circles. The shortest path from point A to point B on a sphere is given by the shorter arc of the great circle passing through A and B. If A and B are antipodal points, then there are infinitely many shortest paths between ...
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