Real-time rendering method of algebra B-spline surface

Abstract

The invention discloses an ABS real-time rendering method based on NR iterative algorithm, comprising seven steps: 1) inputting the relevant information of ABS to be rendered and calculating the Lipschitz constant, and converting ABS into piecewise Bezier surface patches; 2) using MC algorithm to extract the iso-surface of ABS; 3) calculating the polar surface of ABS in real time; 4) rendering iso-surface to obtain the iso-surface and the initial values of the silhouette contour line of the iso-surface; 5) aggregating the initial values of the silhouette contour line of the iso-surface, according to ABS and the polar surface equation thereof, using NR iterative algorithm to calculate the initial silhouette contours, so as to be obtain the silhouette contour line with floating point precision, and correcting the silhouette contour line; 6) calculating the intersections of each pixel sight line of the silhouette contour line and Bezier surface; 7) by NR iterative algorithm, using adjacent Bezier surfaces information to iterate and get accuracy, so as to obtain right intersections of all light and algebra B-spline surface, and then using the intersections information, the relative location of light source and viewpoint, and the material of a curved surface itself to calculate illumination. The method of the invention can realize the rendering of an algebraic surface for arbitrary frequency.

Description

technical field [0001] The invention relates to computer graphics real-time rendering technology, in particular to a real-time rendering method of algebraic B-spline surface based on Newton-Raphson (abbreviated as NR) iterative algorithm. Background technique [0002] The core problem of the ray casting algorithm for algebraic surfaces is the calculation of the intersection of rays and surfaces. Since unary equations of less than five degrees can be analyzed for roots, Blinn has also done a lot of work on the theoretical basis and robustness of analytical roots in recent years. Based on this, Loop proposed the analysis of piecewise algebraic surfaces based on GPU. For a robust real-time rendering algorithm, see Loop C., Blinn J.: Real-timeGPU rendering of piecewise algebraic surfaces.In SIGGRAPH'06, pp.664-670, but this method cannot be done more than 4 times The drawing of the algebraic surface. [0003] For the intersection algorithm of general algebraic surfaces, the al...

AI Technical Summary

Problems solved by technology

Reimers et al. used the B-spline node insertion algorithm to obtain real-time rendering effects in 2008, Reimers M., Seland J.: Raycasting algebraic surfaces using the frustum form. Comput. Graph. Forum 27, 22008), 361-370, but the method It is limited to a single surface, and it will introduce a lot of complex function compound operations, and it does not perform well in terms of normal direction and anti-aliasing

[0004] As far as we know, there is no real-time rendering algorithm for high-order piecewise continuous algebraic B-spline surfaces

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