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geometrical and topological representation of the object
may be not unique, since it depends on either the
procedures used to generate the model or the internal
geometric kernels used by CAD packages. Traditional
feature recognition methods have difficulties with variablegeometry and topology. To overcome this drawback, Sonthi
et al. [9] proposed the CR approach as a general approach
for feature recognition in solid models. The B-rep model of
a molded part is first converted to the CR-rep which
provides a unique correspondence to the real models.
Herein, a CR is defined as an edge-connected partition of
the face set in B-rep with identical curvature property.
According to the signs of Gauss ( ) and Mean curvature
( ) there are six curvature region types of the model. The
detail classification is summarized in Table 1.
From Table 1 it can be seen that some elementary
surfaces such as plane, cylinder, cone, and sphere fall
automatically into one of the types in Table 1. As for the
freeform surfaces represented by B-splines geometry the
situation is relative complex. A freeform surface may
contain several types of CR or only be a single type of
CR completely. In this paper symbolic computation is used
to derive the curvature scalar fields of the freeform surface
and to help decompose the surface into different curvature
regions. This is a global approach and it eliminates the
accuracy problems that arise from discrete methods. The
detail of the approach is described as follows:Let be a2regular parametric surface. The
Gaussian curvature is a scalar value and is defined
Assuming the surface is
curvature continuous, a locus of points satisfying =0 is
called a parabolic curve, since it separates “elliptic”
regions of positive Gaussian curvature from “hyperbolic”
regions of negative Gaussian curvature on the surface.
Because is regular the problem of computing =0 is
equivalent to solve the bivariate polynomial Δ ¼
is zero. Δ
is rational and representable as a scalar field B-spline
surface by symbolic computation [15]. Then numerical
scheme is used to approximate the intersection curve
between Δ and the plane =0.Finally,theparameter
values of the parabolic line of the Δ can serve as the
parameter values of trimming curves of the original
surface = ( ) and each of the trimmed region is 在塑料注塑模具设计过程中，产品的凹陷和突出部位（DP）容易影响成型零件从模具中顶出，这提出了一种优化DP特征的方法，这种方法是基于曲面的曲率，具体体现在实体的B-rep模型的特性上。在于凹陷和突出的特点之间的转换，突出的特点是容易破坏零件在模具中脱模方向上的顶出，要通过几何形状和可修改的形状尺寸来改善零件的顶出拔模，这种方法可以改善孤立和相交特征平面和自由表面。可以优化减少分模的方向的信息，并提供决策以支持模具设计，比如如选择分型信息方向，分型线和分型面等。案例研究已验证了这种方法的可行性。23489
关键词：注塑模具、自由曲面特征的注塑识别、底切、顶出方向。