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一般化的贝齐尔样模型及其在曲线和表面建模中的应用
Moavia Ameer1, Muhammad Abbas1, Madiha Shafiq1
11 Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
PloS one
|June 3, 2024
概括
本研究介绍了具有可调整形状参数的一般化贝齐尔样表面 (gBS),用于计算机辅助设计中的复杂表面建模. 与传统的贝齐尔模型相比,拟议的连续性约束提供了对表面形状和位置的增强控制.
科学领域:
- 计算机图形 计算机图形
- 几何设计 几何设计
- 计算机辅助设计和制造 (CAD/CAM)
背景情况:
- 复杂表面的建模是汽车和航空航天等行业的一个关键挑战.
- 由于其几何性质,贝齐尔曲线和表面在CAGD/CAM中得到了广泛的研究.
- 连续性约束 (参数和几何) 对于连接表面来创建复杂的设计至关重要.
研究的目的:
- 为具有不同形状参数的一般化贝齐尔样表面 (gBS) 提出新的连续性约束.
- 解决传统贝齐尔模型中遇到的复杂表面的建模和设计方面的局限性.
- 开发Bézier-like曲线 (gBC) 的通用C3和G3连续性约束,以及gBS的G1/G2约束.
主要方法:
- 开发Bézier-like曲线 (gBC) 的通用C3和G3连续性约束.
- 对于一般化的贝齐尔样表面 (gBS) 制定必要和足够的G1和G2连续性约束.
- 分析数值示例与图形表示,以验证拟议的约束.
主要成果:
- 拟议的gBS模型有效地解决了标准贝齐尔表面固有的形状和位置调整问题.
- 与现有方法相比,一般化的连续性约束可以更好地控制表面设计.
- 通过调整形状参数来改变曲线形状的能力克服了传统贝齐尔模型的一个关键限制.
结论:
- 开发的广义贝齐尔样表面 (gBS) 和它们的连续性约束为复杂的表面建模提供了一种优越的方法.
- 拟议方案通过结合现有方法的特征,同时减轻其缺点,提高了几何设计能力.
- 可调整的形状参数提供了更大的设计灵活性,使该模型非常适合工程应用.
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