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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 a2
regular parametricsurface. 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
: ðÞ ðÞ : ðÞ ðÞ : ðÞ ðÞ
2
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 摘要：在注塑模具，凹模和凸模（DP）防止从模具中除去模塑部件的设计被称为退刀槽。本文介绍了基于实体的B- Rep模型的曲率性质的曲率区域内的代表性认识的DP功能的方法。公认的凸模和凹模之间的转换。突出的特点是潜在的削弱影响脱模方向模制部件的选择。通过可能的撤离方向退刀的几何推理和可见性映射计算得出。这种方法可以识别孤立与平面相交特性,二次曲面和自由表面。确定潜在的干涉及其可能的撤离方向，可以为模具设计如选择脱模方向、分型线和面等提供设计信息，以分析验证设计方法的可行性。
关键词：注射成型 自由曲面特征的识别 退刀槽 退出方向