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Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上,深入研究了纹理映射的基本原理与过程,根据反向纹理映射对纹理随机采样的特殊要求,提出了一种可满足存储空间和寻址时间的纹理压缩存储算法;通过对纹理映射中几何变换理论的进一步深入探讨,提出了整体参数化和面片参数化的概念,并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式;针对现有的两步映射算法所存在的中间曲面—球面的参数化问题,提出一种等积映射方法,较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射;从信号采样的角度深入分析了纹理映射中走样产生的原因,提出了改进的区域求和表算法,使图形生成的效果有所提高;还分析了一般的扫描线算法在透视变换中所存在的问题,提出了一种正确的插值算法,从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

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