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For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
In parametric adjustment, one can find an observation equation h(X) = Y relating observations Y explicitly in terms of parameters X (leading to the A-model below). In conditional adjustment , there exists a condition equation which is g ( Y ) = 0 involving only observations Y (leading to the B-model below) — with no parameters X at all.
In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
Instead of manually calculating the results of parametric equations, he could automatically derive the shape of the catenary curves through the force of gravity acting on the strings. [11] Frei Otto's tensegrity structures, designed for the 1972 Summer Olympics in Munich, are an example of a non-digital parametric process.
Parametric models are contrasted with the semi-parametric, semi-nonparametric, and non-parametric models, all of which consist of an infinite set of "parameters" for description. The distinction between these four classes is as follows: [citation needed] in a "parametric" model all the parameters are in finite-dimensional parameter spaces;
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .
Figure 1. An example structural equation model after estimation. Latent variables are sometimes indicated with ovals while observed variables are shown in rectangles. Residuals and variances are sometimes drawn as double-headed arrows (shown here) or single arrows and a circle (as in Figure 2).
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three- dimensional ( solid figures ), although many of its tools and principles can be applied to sets of any finite dimension.