正投影法融合三维造型的研究

Integration of Orthographic Projection and 3D Modeling

由于正投影法的逻辑性不够严密,使得空间想象力的形成依赖于经验。从数学方法具有普适性的视角引出逻辑思维在形成空间想象力中的优点和不足。阐述几何拉伸和压缩原理,应用两几何形体求交集的方法实现逻辑严密的空间想象。通过交集运算设计三维模型,验证所述原理、方法的正确性,并以视图与三维造型的联系来说明形成空间想象的具体途径。研究结果表明,正投影与三维造型融合是更为合理的物体表达方法。

The formation of space imagination depends on experience because the projection method is not strict enough. The advantages and disadvantages of logical thinking in theformation of spatial imagination are derived from the perspective of the universality of mathematicalmethods. The principles of geometric stretching and compression were expounded,and the method of intersection of two geometric bodies was used to realize the space imagination with strict logic. Thethree-dimensional （3D） model wasdesigned by intersection operation to verifycorrectness of the method,and the concrete way to form spatial imagination was illustrated by therela t ion be t ween view and 3D modeling. The results show that the fusion of orthog3D modeling is a more reasonable way to express objects.