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The principle of parametric design can be defined as mathematical design, where the relationship between the design elements is shown as parameters which could be reformulated to generate complex geometries, these geometries are based on the elements’ parameters, by changing these parameters; new shapes are created simultaneously.
In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
Since these parameters reduce all of the information in a profile to a single number, great care must be taken in applying and interpreting them. Small changes in how the raw profile data is filtered, how the mean line is calculated, and the physics of the measurement can greatly affect the calculated parameter.
For any point on the sphere, calculate ^, that being the unit vector from to the sphere's origin. Assuming that the sphere's poles are aligned with the Y axis, UV coordinates in the range [ 0 , 1 ] {\\displaystyle [0,1]} can then be calculated as follows:
The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, [1] [2] when the rectangle is oriented as a "landscape".
The Lode coordinates are most easily computed using the mechanics invariants.These invariants are a mixture of the invariants of the Cauchy stress tensor, , and the stress deviator, , and are given by [3]
For the case of a single parameter and data that can be summarised in a single sufficient statistic, it can be shown that the credible interval and the confidence interval coincide if the unknown parameter is a location parameter (i.e. the forward probability function has the form (|) = ()), with a prior that is a uniform flat distribution; [6 ...
In probability theory and statistics, a shape parameter (also known as form parameter) [1] is a kind of numerical parameter of a parametric family of probability distributions [2] that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).