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简介

The two most common methods of representing curves and surfaces in geometric modeling are implicit equations and parametric functions.// 两个最基础的方法在表示曲面和形状在几何建模是隐式表示和显示表示

隐式表示

The implicit equation of a curve lying in the xy plane has the form f(x, y) = 0.
This equation describes an implicit relationship between the x and y coordinates
of the points lying on the curve. For a given curve the equation is unique up to
a multiplicative constant. An example is the circle of unit radius centered at the
origin, specified by the equation f(x, y) = x2 + y 2 - 1 = 0 (Figure 1.1).
// 类似 f(x, y) = x2 + y 2 - 1 = 0

显示表示

In parametric form, each of the coordinates of a point on the curve is represented separately as an explicit function of an independent parameter
C(u) = (x(u),y(u))
// 类似 C(u) = (x(u), y(u))