基于工程图的三维形体重建方法研究
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摘要
基于工程图的三维形体重建技术是计算机辅助设计与图形学、人工智能领域的重要研究方法,其主要任务是依据形体在二维视图的几何投影信息和拓扑信息构造对应的三维形体,是一个从低维到高维的变换过程。针对目前已有算法在重建效率和应用范围方面存在的问题,本文对基于工程图重建三维形体的关键技术进行了研究,主要工作包括：
1.提出了一个基于实际工程图的预处理算法。首先,针对现有算法只能处理标准三视图的不足,提出了一个多视图自动分离算法。接着,依据视图之间的位置关系判别视图的投影方向和所属投影平面,构造复合三视图。最后,将已经确定投影方向和投影平面的视图转换到空间坐标系,以方便后续的重建过程。该算法从实际工程图中提取几何信息构造复合三视图,将同一个投影方向的多个视图归属到一个复合视图,既满足现有三维重建算法的输入条件,又能处理更多更复杂的工程图样,为三维重建技术的实用化提供了一个新的思路。
2.提出了一个从三视图重建复杂组合体的重建算法。针对具有复杂遮挡关系的组合体三视图轮廓搜索不完备的问题,提出了基于动态子视图划分的投影轮廓搜索算法。在应用传统角度判别法找出三视图中所有基环后,以基环为线索动态划分单向子视图并搜索惯性环,对已找到的环进行二元组匹配。接着,依据二元匹配环组动态划分双向子视图并搜索惯性环；最后,从已找到的所有环中搜索基本形体的投影轮廓,通过拉伸或旋转构建基本形体,对基本形体应用正则布尔运算形成最终三维形体。算法既保证了构成组合体的每个基本形体的投影轮廓环不被遗漏、重建结果正确,又避免了穷举式的轮廓环搜索,提高了三维重建的效率。
3.提出了一个从三视图构建曲面相贯体的新算法。二次曲面体相交时产生的相贯线一般是高次空间曲线,无法用二维投影精确地表达,通常用拟合的光滑曲线表达,甚至简化为圆弧或直线段,导致相交曲面体的轮廓投影被破坏。而现有构建曲面体的算法都要求曲面体的投影轮廓是完整和精确的,均不适用于曲面相贯体的重建。针对这种情况,本文提出了一种基于四种投影轮廓线索的启发式搜索算法处理曲面相贯体的重建,利用曲面相交时留下的最小迹线在二维视图中恢复曲面体相交之前的正确和完整的投影轮廓,进而重建出完整的曲面体。与以往算法相比,本文提出的曲面相贯体重建算法可以处理视图中出现的简化画法或拟合曲线,解决了二次曲面相交形成的高次空间曲线的投影不精确的问题,扩大了基于CSG表示的重建算法的覆盖域。
Reconstruction of three dimensional solids from three-view engineering drawings is a problem of research interest in fields of computer aided design, computer graphics and artificial intelligence, which main task is to recover a three dimensional shape from its two dimensional geometric projections and topology information. This dissertation focuses on several key technologies of the solid reconstruction from engineering drawing to solve the existing problems in the domain of reconstructed objects and the process efficiency. The main contributions are summarized as follows.
1. A method is presented to preprocess the initial engineering paper before reconstructing the solid. At First, a method based on bounding boxes of elements is presented to automatically divide multi views in the drawing to solve the problem that only three-view drawings can be dealt with by existing methods. Then, a Composite-Three-View is constructed from the views by their projection orientation. Finally, the views are all translated from the drawing coordinate systems to the three dimensional coordinate systems for the conveninence of following processes. By constructing Composite-Three-View from practical multi-view drawings, the method can group all views in one projection plane into one Composite-View, which acts as an intermedium from practical engineering drawings to standard three-view drawings required by existing algorithms. The presented method can extend the types of engineering drawings dealt with by the reconstruction algorithm to multi-view drawings.
2. A new method is presented to reconstruct complicated complex solids. An algorithm, based on dynamic division of sub-views, is proposed to find out profile loops from complicated three views of complex with some elementary volumes concealed from others. First of all, fundamental loops are searched out using traditional turn-to-most-left method. Then, inertia loops are searched in unidirectional-sub-views, which are divided from orthographic views using the fundamental loops as hints. Finally, bidirectional-sub-views are divided using the Double-Matching-Loops generated from existing loops, and inertia loops are found out in the bidirectional-sub-views. Using extrusion or rotation, elementary volumes are generated from Triple-Matching-Loops constructed from loops found out previously, and Boolean operations are applied on the elementary volumes to generate the solution solid. Experiments show that the proposed algorithm can find out all profile loops of the elementary volumes of the complex, including the obscured ones, effectively and completely, which ensures the correctness of the solution solid.
3. Anew approach is presented to reconstruct curved solids composed of elementary volumes intersecting with one another from three-view engineering drawings. Intersection curves arising from two intersecting curved surfaces are mostly higher order spatial curves, which cannot be described exactly by orthographic projections and normally represented as smooth curves passing through several key points or even simplified as arcs or lines. Approximated sketches of higher order intersection curves in two dimensional views will result in the invalidation of existing methods that need the exact projection information as input. Based on some heuristic hints, our method is able to recover the complete and correct half-profiles of the intersecting elementary volumes using the least traces left by them, which ensure the correctness of solution solids constructed finally.
1.提出了一个基于实际工程图的预处理算法。首先,针对现有算法只能处理标准三视图的不足,提出了一个多视图自动分离算法。接着,依据视图之间的位置关系判别视图的投影方向和所属投影平面,构造复合三视图。最后,将已经确定投影方向和投影平面的视图转换到空间坐标系,以方便后续的重建过程。该算法从实际工程图中提取几何信息构造复合三视图,将同一个投影方向的多个视图归属到一个复合视图,既满足现有三维重建算法的输入条件,又能处理更多更复杂的工程图样,为三维重建技术的实用化提供了一个新的思路。
2.提出了一个从三视图重建复杂组合体的重建算法。针对具有复杂遮挡关系的组合体三视图轮廓搜索不完备的问题,提出了基于动态子视图划分的投影轮廓搜索算法。在应用传统角度判别法找出三视图中所有基环后,以基环为线索动态划分单向子视图并搜索惯性环,对已找到的环进行二元组匹配。接着,依据二元匹配环组动态划分双向子视图并搜索惯性环；最后,从已找到的所有环中搜索基本形体的投影轮廓,通过拉伸或旋转构建基本形体,对基本形体应用正则布尔运算形成最终三维形体。算法既保证了构成组合体的每个基本形体的投影轮廓环不被遗漏、重建结果正确,又避免了穷举式的轮廓环搜索,提高了三维重建的效率。
3.提出了一个从三视图构建曲面相贯体的新算法。二次曲面体相交时产生的相贯线一般是高次空间曲线,无法用二维投影精确地表达,通常用拟合的光滑曲线表达,甚至简化为圆弧或直线段,导致相交曲面体的轮廓投影被破坏。而现有构建曲面体的算法都要求曲面体的投影轮廓是完整和精确的,均不适用于曲面相贯体的重建。针对这种情况,本文提出了一种基于四种投影轮廓线索的启发式搜索算法处理曲面相贯体的重建,利用曲面相交时留下的最小迹线在二维视图中恢复曲面体相交之前的正确和完整的投影轮廓,进而重建出完整的曲面体。与以往算法相比,本文提出的曲面相贯体重建算法可以处理视图中出现的简化画法或拟合曲线,解决了二次曲面相交形成的高次空间曲线的投影不精确的问题,扩大了基于CSG表示的重建算法的覆盖域。
Reconstruction of three dimensional solids from three-view engineering drawings is a problem of research interest in fields of computer aided design, computer graphics and artificial intelligence, which main task is to recover a three dimensional shape from its two dimensional geometric projections and topology information. This dissertation focuses on several key technologies of the solid reconstruction from engineering drawing to solve the existing problems in the domain of reconstructed objects and the process efficiency. The main contributions are summarized as follows.
1. A method is presented to preprocess the initial engineering paper before reconstructing the solid. At First, a method based on bounding boxes of elements is presented to automatically divide multi views in the drawing to solve the problem that only three-view drawings can be dealt with by existing methods. Then, a Composite-Three-View is constructed from the views by their projection orientation. Finally, the views are all translated from the drawing coordinate systems to the three dimensional coordinate systems for the conveninence of following processes. By constructing Composite-Three-View from practical multi-view drawings, the method can group all views in one projection plane into one Composite-View, which acts as an intermedium from practical engineering drawings to standard three-view drawings required by existing algorithms. The presented method can extend the types of engineering drawings dealt with by the reconstruction algorithm to multi-view drawings.
2. A new method is presented to reconstruct complicated complex solids. An algorithm, based on dynamic division of sub-views, is proposed to find out profile loops from complicated three views of complex with some elementary volumes concealed from others. First of all, fundamental loops are searched out using traditional turn-to-most-left method. Then, inertia loops are searched in unidirectional-sub-views, which are divided from orthographic views using the fundamental loops as hints. Finally, bidirectional-sub-views are divided using the Double-Matching-Loops generated from existing loops, and inertia loops are found out in the bidirectional-sub-views. Using extrusion or rotation, elementary volumes are generated from Triple-Matching-Loops constructed from loops found out previously, and Boolean operations are applied on the elementary volumes to generate the solution solid. Experiments show that the proposed algorithm can find out all profile loops of the elementary volumes of the complex, including the obscured ones, effectively and completely, which ensures the correctness of the solution solid.
3. Anew approach is presented to reconstruct curved solids composed of elementary volumes intersecting with one another from three-view engineering drawings. Intersection curves arising from two intersecting curved surfaces are mostly higher order spatial curves, which cannot be described exactly by orthographic projections and normally represented as smooth curves passing through several key points or even simplified as arcs or lines. Approximated sketches of higher order intersection curves in two dimensional views will result in the invalidation of existing methods that need the exact projection information as input. Based on some heuristic hints, our method is able to recover the complete and correct half-profiles of the intersecting elementary volumes using the least traces left by them, which ensure the correctness of solution solids constructed finally.
引文
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