Nanjing Institute of Astronomical Optics & Technology, National Astronomical Observatories, Cas

Ying Li

Bin Liang

Yi Zheng

Changpeng Ding

Lifeng Tang

Kai Wei

Zhaoxiang Wu

The invention discloses a method for correcting the pointing errors of a biaxial rotation system based on the spherical cap function, comprising: error collection: selecting stars or radio sources distributed evenly in a star catalogue for tracking and observation to obtain the theoretical position and measurement position of the stars, and subtracting the measurement positions and the theoretical positions to obtain the error distribution; error model fitting: selecting a suitable orthogonal spherical cap function for the obtained error distribution and performing fitting to calculate an error fitting coefficient, the orthogonal spherical cap function model comprising a hemispheric harmonic function HSH, a Zernike spherical cap function ZSF, and a longitudinal spherical cap function LSF; and error control and compensation: putting the error model and the related fitting coefficient into a pointing control system for compensation. In the present method for correcting the pointing errors of a biaxial rotation system based on a spherical cap function, the model has strong stability and is not easily affected by measurement noise; there is no need to determine the form of the model on the bases of the frame form of the telescope, and the correction accuracy is high.

Method for correcting pointing errors of biaxial rotation system based on spherical cap function

The invention discloses a method for rendering on the basis of hemispherical orthogonal function, the method comprising the following steps: selecting rendering fragments and establishing a local coordinate system; acquiring a bidirectional reflectance distribution function of a material; if global illumination is an orthogonal function, determining a rotation matrix of an orthogonal function coefficient according to the rotation angles of the global coordinate system and the local coordinate system, and calculating a local orthogonal function illumination coefficient; converting the local orthogonal function illumination coefficient into a hemispherical orthogonal function illumination coefficient; sampling to obtain the spatial distribution of a bidirectional reflection distribution function of a rendered material; obtaining a hemispherical orthogonal function of the bidirectional reflection distribution function of the rendered material; and using the dot product of a hemispherical orthogonal function coefficient of illumination and a hemispherical orthogonal function coefficient of the bidirectional reflection distribution function of the rendered material and accumulating to obtain the light intensity in the reflection direction. A hemispherical harmonic function(HSH) is used to fit measurement data or theoretically derived data of a BRDF, which may avoid the difficulty of fitting that accurs for a hemispherical harmonics function due to data being missing in the lower hemisphere.

Method for rendering on basis of hemispherical orthogonal function

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Jiangsu, China

Ying Li