Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections

We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the parameterizations in projective space are polynomial, whenever it is possible. They are also near-optimal in the sense that the number of distinct square roots appearing in the coefficients of these functions is minimal except in a small number of cases (characterized by the real type of the intersection) where there may be an extra square root.     

NURBS在二次曲面中的应用

介绍了NURBS构造二次曲面(圆锥面为例)的方法,并且在VC环境下,基于OpenGL实现对曲面控制点的修改.与传统Bezier曲面的修改相比,NURBS修改控制点或权因子更方便.     

配极对应在画法几何中的应用

介绍了配极对应的基本概念,以及利用配极对应的基本原理解决画法几何中求直线与二次曲面贯穿点的作图和求二次曲面切平面的作图。     

Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm

We present an exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational coefficients. The output functions parameterizing the intersection in projective space are polynomial, whenever it is possible, which is the case when the intersection is not a smooth quartic (for example, a singular quartic, a cubic and a line, and two conics). Furthermore, the parameterization is near-optimal in the sense that the number of distinct square roots appearing in the coefficients of these functions is minimal, except in a small number of well-identified cases where there may be an extra square root. In addition, the algorithm is practical: a complete and efficient C++ implementation is described in Lazard et al. [Lazard, S., Peñaranda, L.M., Petitjean, S., 2006. Intersecting quadrics: An efficient and exact implementation. In: 20th ACM Symposium on Computational Geometry, 2004. Computational Geometry: Theory and Applications 35 (1–2), 74–99 (special issue)].     

Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils

We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently the type of the real intersection. This classification is at the core of the design of the algorithms, presented in Part III, for computing, in all cases of singular intersection, a near-optimal parameterization with polynomial functions, that is a parameterization in projective space whose coordinate functions are polynomial and such that the number of distinct square roots appearing in the coefficients is at most one away from the minimum.     

C interpolation on smooth manifolds with one-parameter transformations

This paper presents a method for Cⁿ interpolation on smooth manifolds by performing one-parameter transformations on them. Continuity of interpolating curves is achieved by smooth transitions between the transformations. Interpolating curves have local control. Constructing of curves on quadrics, SO(3, R) and GL(3, R) is considered.     

高斯曲面拟合在对空红外点目标检测中的应用

针对天空背景红外点目标检测时云层边缘产生的虚警,根据点目标的高斯分布特性,提出采用高斯曲面拟合算法,首先利用传统目标检测算法检测得到目标和云层边缘,然后获取其高斯曲面拟合参数,最后计算偏态系数和峰度系数,根据偏态和峰度系数的差异,区别目标和云层。实验结果证明,该方法能有效地区别目标和云层边缘干扰,从而降低目标检测算法的虚警率。     

基于CCD标定的微像素精度图像定位技术

基于光电成像器件CCD的点目标定位技术被广泛运用于天文定位、侦察等民用及军用方面。传统点目标定位精度一般为亚像素级,受CCD自身成像误差限制,目标定位精度难以大幅提高。提出通过干涉条纹对CCD进行标定,从而得到CCD频域像素响应函数的精确表达式,由此重构高质量的目标入射光场图像,进而提高光电成像系统对点目标定位的精度。首先建立了干涉条纹标定CCD及目标光场图像重构的理想模型,并通过仿真验证了点目标图像重构效果以及最终点目标的定位精度。仿真结果表明,经干涉条纹标定CCD后,重构的目标光场图像质量得到大幅度的提升,接近于CCD像面前入射光场图像,通过高斯曲面拟合得到点目标形心坐标及其微位移的提取精度均达微像素级别,相比于传统的亚像素定位,定位精度得到了大幅度的提高。     

Branching blend of natural quadrics based on surfaces with rational offsets

A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of degree (6,3). The general theory of PN surfaces is developed using Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. The construction is extended via inversion to a PN branching blend of degree (8,4) between Dupin cyclide and a natural quadric.