Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method n...Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.展开更多
The automated design of imaging systems involving no or minimal human effort has always been the expectation of scientists,researchers and optical engineers.In addition,it is challenging to choose an appropriate start...The automated design of imaging systems involving no or minimal human effort has always been the expectation of scientists,researchers and optical engineers.In addition,it is challenging to choose an appropriate starting point for an optical system design.In this paper,we present a novel design framework based on a point-by-point design process that can automatically obtain high-performance freeform systems.This framework only requires a combination of planes as the input based on the configuration requirements or the prior knowledge of designers.This point-by-point design framework is different from the decadeslong tradition of optimizing surface coefficients.Compared with the traditional design method,whereby the selection of the starting point and the optimization process are independent of each other and require extensive amount of human effort,there are no obvious differences between these two processes in our design framework,and the entire design process is mostly automated.This automated design process significantly reduces the amount of human effort required and does not rely on advanced design skills and experience.To demonstrate the feasibility of the proposed design framework,we successfully designed two highperformance systems as examples.This point-by-point design framework opens up new possibilities for automated optical design and can be used to develop automated optical design in the areas of remote sensing,telescopy,microscopy,spectroscopy,virtual reality and augmented reality.展开更多
基金Project (No. G1998030401) supported by the National Natural Sci-ence Foundation of China
文摘Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.
基金supported by the National Basic Research Program of China(973,No.2011CB706701).
文摘The automated design of imaging systems involving no or minimal human effort has always been the expectation of scientists,researchers and optical engineers.In addition,it is challenging to choose an appropriate starting point for an optical system design.In this paper,we present a novel design framework based on a point-by-point design process that can automatically obtain high-performance freeform systems.This framework only requires a combination of planes as the input based on the configuration requirements or the prior knowledge of designers.This point-by-point design framework is different from the decadeslong tradition of optimizing surface coefficients.Compared with the traditional design method,whereby the selection of the starting point and the optimization process are independent of each other and require extensive amount of human effort,there are no obvious differences between these two processes in our design framework,and the entire design process is mostly automated.This automated design process significantly reduces the amount of human effort required and does not rely on advanced design skills and experience.To demonstrate the feasibility of the proposed design framework,we successfully designed two highperformance systems as examples.This point-by-point design framework opens up new possibilities for automated optical design and can be used to develop automated optical design in the areas of remote sensing,telescopy,microscopy,spectroscopy,virtual reality and augmented reality.
