Three-dimensional Green Coordinate Theory And Its Application

In recent years,the three-dimensional deformation algorithm has developed rapidly,and various mature three-dimensional model deformation techniques have been widely used in various industries.It has gradually become a research hots pot in the field of computer graphics.Based on the theoretical research on various existing three-dimensional deformation algorithms,we introduce a deformation algorithm based on Green's coordinates for closed polyhedral cages.This coordinate is derived from the Green's third integral equation,which can represent both the vertex position of the cage and the direction of the cage surface.By deriving the display form of the Green's coordinates,we prove that the Green's coordinates can obtain spatial deformation with con-formal properties.In particular,they are con-formal maps in two dimensions,and they can be generalized into three-dimensional space to form a quasi-con formal map.From the three-dimensional Green coordinates,the explicit form of the three-dimensional Green coordinates is used only.The geometry of the cage and the position of the point is explicitly represented and subjected to rigorous numerical verification to prove that the result is correct.Through the display form of the three-dimensional Green coordinates,we prove the con-formality of the three-dimensional Green coordinates,and thus obtain the explicit representation of the three-dimensional Green coordinate gradient.Then,based on the theoretical knowledge of the extension extension,based on the display form we obtained,we derive and prove the explicit expression of the three-dimensional Green coordinate to the extension.