In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimizati...In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.展开更多
Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric...Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric functions, which is however very useful to human cognition as well as emotion. In this paper, we proposed a concept and theory of geometric basis （GB） as the solving cell for geometric computing. Each GB represents a basic geometric operation. GB works as both expressing and solving cell just like the concept of basis in linear algebra by which every element of the vector space can be expressed. For 3D problems, with a procedure of a projections reduction, the problem can be reduced to plane and the reduction function can be designed as a GB. A sequence of GB can construct a higher layer GB. Then, by the traversal of tree, a sequence of GB is got and this sequence is just the construction process and also the solution of this geometric problem.展开更多
基金Thanks for the reviewers’comments to improve the paper.This research was supported by the National Nature Science Foundation of China under Grant Nos.61772163,61761136010,61472111,Zhejiang Provincial Natural Science Foundation of China under Grant Nos.LR16F020003,LQ16F020005.
文摘In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.
文摘Geometric computing is an important tool in design and manufacturing and in arts. Conventionally, geometric computing is taken by algebraic computing. The vivid intuition of objects in visualization is lost in numeric functions, which is however very useful to human cognition as well as emotion. In this paper, we proposed a concept and theory of geometric basis （GB） as the solving cell for geometric computing. Each GB represents a basic geometric operation. GB works as both expressing and solving cell just like the concept of basis in linear algebra by which every element of the vector space can be expressed. For 3D problems, with a procedure of a projections reduction, the problem can be reduced to plane and the reduction function can be designed as a GB. A sequence of GB can construct a higher layer GB. Then, by the traversal of tree, a sequence of GB is got and this sequence is just the construction process and also the solution of this geometric problem.
