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为研究工业产品三维建模中的曲线及曲面拼接问题,通过分析贝塞尔曲线连续性的数学意义和成立条件,得出连续性与控制点位置之间的联系;计算并总结出贝塞尔曲线在G0,G1,G2连续时,相邻控制点几何关系的规律,该规律也适用于相邻NURBS曲线及曲面的连续性调节,并通过实例应用进行了验证。结论表明:曲线及曲面控制点的几何规律可用于预判、调节曲线及曲面的连续性,有助于设计师通过三维模型准确表达产品造型。
In order to study the curve and surface stitching problem in 3D modeling of industrial products, the relationship between continuity and control point position is obtained by analyzing the mathematical meaning and establishment conditions of Bezier curve continuity. The rule of the geometric relation between adjacent control points when G0, G1, G2 is continuous, which is also applicable to the continuity adjustment of the adjacent NURBS curves and surfaces, is validated through examples. The conclusion shows that the geometric rules of curve and surface control points can be used to predict, adjust the continuity of curves and surfaces, which helps designers to accurately represent the product shape through 3D models.