1, the definition of curve smoothness
Curve smoothness is a concept in mathematics, which can be defined as the characteristic that a curve can satisfy a certain functional relationship with infinitesimal accuracy. A smooth curve is characterized by constant change, and the curve will keep a continuous motion behavior without turning.
Smooth curve is an important concept in mathematical analysis, but its definition has some limitations. When every point on a curve has a tangent, and the tangent rotates continuously with the movement of the tangent point, the curve is called a smooth curve. The arc of a smooth curve is solvable.
2, the use of smooth curve
This definition emphasizes the continuity of the slope of the curve, and the slope changes very little, which makes the curve appear smooth. Curve smoothness is an abstract mathematical concept, which assumes many fine mathematical details and can be used to represent the curve behavior of a curve or multiple curves.
It can be used in the fields of mathematical analysis, geometric processing and computer graphics processing, and provides a simple and easy-to-use tool for these applications.
3, the method of curve smoothing
In computer drawing, the problem of curve smoothing is often encountered. There are many methods to smooth curves, generally there are two. One requires the fitting curve to pass through discrete points strictly, and the other requires fitting a curve according to the general trend of point sequence according to the principle of least square method, and the deviation between the curve and discrete points is small.
Smooth curves can be used in the following fields:
1, aesthetic field
Smoothness of curves is an important visual feature. We are used to seeing smooth curves in art, design and architecture, rather than sharp or angled straight lines and broken lines. Smooth curves are more natural, comfortable and beautiful, more in line with our body shape and the surrounding natural environment, and more in line with human aesthetic habits and preferences.
2. Physical field
The smoothness of curves is related to some basic principles in physics. In mechanics, some key concepts, such as momentum, angular momentum and energy, all involve the smoothness of curves. If the curve is not smooth, there will be strange behavior, which makes these physical quantities unable to be calculated correctly or inconsistent with the physical laws.
Therefore, in engineering design and scientific research, the curve must be smooth to ensure the accuracy and reliability of the results.
3. Engineering field
The smoothness of curves is particularly important in engineering applications, because it is related to the stability and strength of materials and structures. Smooth curves are more durable and firm for various machines and structures, while reducing friction and wear and prolonging service life.