齐次坐标

齐次坐标在计算机图形学中是有用的，将3D场景投影到2D平面的过程中就用到它了。

Homogeneous coordinates are very useful and fundamental concept in computer graphics , such as projecting a3D scene onto a2D plane .

最后，利用齐次坐标讨论了NURBS曲线的延伸算法。

Finally , extension algorithms for NURBS curves are discussed by means of homogeneous coordinates .

NURBS曲线方程具有三种等价形式：有理分式表示、有理基函数表示和齐次坐标表示。

NURBS curve equation has three kinds of the equivalence form , i.e. rational fraction , rational base function and homogeneous coordinate .

基于齐次坐标空间，提出了一种NURBS曲线曲面和有理Bezier曲线曲面降阶的简便方法。

Based on homogeneous coordinates , this paper presents a convenient algorithm for approximate degree reduction of NURBS and rational Bezier curves and surfaces .

针对Zernike拟合时的藕合与混淆，采用先用齐次坐标变换去除刚体位移，再用奇异值分解进行Zernike拟合。

To solve-the coupling and mixture of Zernike polynomials fit method , rigid-body displacement is removed with coordinate transformation and then fitted with Zernike polynomials .

采用NURBS曲线的齐次坐标表示，给出了通过控制顶点和权因子同时改变来修改NURBS曲线形状的一种方法。

This paper provides an approach to shape modification of NURBS curves by altering the weights and the location of the control points simultaneously . A homogeneous coordinate representation is introduced to solve the problem .

论文研究了目前常用的控制方法，并采用标准的DH法建立机器人数学模型，运用齐次坐标变换建立了正运动学方程。

Topic analysis of the current control methods commonly used , and the DH standard mathematical model was established by the robot , the use of homogeneous transformation equations of motion are established .

按Denavit-Hartenberg方法建立了操作臂齐次坐标方程，进行了运动学分析，求出了运动学反解；

The homogeneous transformation equation of manipulator is created according to the Denavit-Hartenberg method , and the kinematics solution and inverse kinematics solution are analyzed .

为此，采用Denavit-Hartenberg坐标系，通过齐次坐标变换建立了7DOF番茄收获机械手的运动学模型，并对正运动学及逆运动学进行了求解。

This paper used Denavit-hartenberg coordinate to build kinematic modal of tomato harvesting manipulator with 7-DOF through homogeneous transformation . And solved the Direct Kinematic and Inverse Kinematic equations .

利用NURBS曲面的齐次坐标表示，首先解释了NURBS曲面权因子的几何意义，直观地证明了单个权因子变化时，曲面上的点被拉向或被推离控制顶点的方向。

With the representation of homogeneous coordinates , we explain the geometric sense for the weights of NURBS surface firstly , and then prove in the paper that when one weight changes , the points of NURBS surface move toward or away from the control points .

采用D-H方法建立了弧面分度凸轮机构的坐标系，利用齐次坐标变换推导了弧面分度凸轮的曲面方程。

The theory of D-H is used to build the coordinate system of the globoidal indexing cam mechanism in this paper , the surface equation of the globoidal indexing cam is attained through coordinate transformation and verified based on the MATLAB software .

采用齐次坐标变换法建立位置逆解方程。

The inverse ki-nematic models are built using the coordinate transformation method .

齐次坐标在结构几何组成分析中的应用

Application of homogeneous coordinates in geometrical compositive analysis of structures

基于齐次坐标变换的陀螺框架加工误差分析

Error Analysis of Precise Gyroscope Frame Machining Based on Homogeneous Coordinate Transformation

齐次坐标变换在空间机构分析中的应用曲线的极切线坐标及其应用

Transformation of homogeneous coordinates and its application in the analysis of spatial mechanism

成形车刀刃形曲线齐次坐标的解析与应用

The Analysis and Application of Figuration Cutting Tool ′ s Blade Curve in Homogeneous Coordinate

首先，介绍坐标平移和坐标旋转的齐次坐标变换概念；

First , the concept of homogeneous transformation is explained , including the coordinate translation and rotation .

齐次坐标及应用

Homogeneous Coordinates and its Applications

通过建立基于反转原理的通用模型、坐标系和齐次坐标变换技术，导出了平面凸轮的轮廓方程、压力角和曲率半径的一般表达式。

Their general expressions are derived based on an inverse model with special coordinate systems and homogeneous transformation techniques .

根据空间齐次坐标的变换模型，推导出多轴数控加工的后置处理算法；

According to homogeneous coordinate transition model , the postposition processing algorithm in multi-axis numerical control machining is deduced .

本文将齐次坐标变换理论结合刀具与工件联结链矢量概念建立了加工中心误差运动综合补偿模型。

An error synthesis model for the machining centers is set up by using homogeneous coordinate transformation and tool workpiece connection vector .

对应特征点的三维重建是根据三角测量的方法计算其投影矩阵，然后用奇异值分解求出特征点的三维齐次坐标。

Feature points ' 3D coordinates are computed through singular value decomposition of projector matrix , then compute projector matrix by triangulation .

在笛氏齐次坐标的基础上，采用齐次向量的方法，建立二维射影坐标系。

It is shown that the 2_dimensional projective coordinate system can be constructed by homogeneous vector on the basis of the Descartes homogeneous coordinates .

首先结合多体系统理论和齐次坐标变换建立目标机床的误差模型；

The first work was to build an error model of target machine tool by combining the multi-body system theory and homogeneous coordinate transform .

应用刚体运动学理论和齐次坐标变换技术建立了多轴数控加工中心空间误差的通用模型，把加工中心刀具相对工件的终端误差表示为各个误差源和刀具位置的函数。

The final error between the tool and the part on a machine is expressed as functions of the tool location and its elemental errors .

使用齐次坐标变换的方法建立了三轴数控铣床的切削力误差综合数学模型。

The error synthesis model of the cutting force induced errors of a3-axis CNC milling machine was obtained by use of the homogeneous coordinate transformation method .

本文在齐次坐标变换理论和机器人机构运动学以及动力学知识基础上，结合船用起重机的工作特点来解决吊重系统的防摆动问题。

The solution of ship-mounted crane anti-sway is based on robots kinematics , homogeneous coordinates and knowledge of dynamics and Combined with characteristics of ship-mounted crane .

文中对各个阶段的约束条件和运动情况进行了较详细的分析，采用了齐次坐标变换的方法。

The restraint and themovement in these stages had been analysed in detail , and the method of homogeneous coordinate trans-formation had been used in this thesis .

同时对这两种求解方法进行了计算机模拟。结果证明，利用改进的四元数变换矩阵方法的求解速度比利用齐次坐标变换矩阵的方法快一些。

Computer simulations made for the two solution methods proves that the solution speed of improved quaternion matrix arithmetic is faster than that of the coordinate transformation arithmetic .

介绍一种用于复杂空间机构分析的简捷而有效的数学方法&齐次坐标及其变换，阐述了齐次坐标的定义、性质及坐标变换。

The application of homogeneous coordinates in the analysis of complex spatial mechanism is presented . The definition , properties and transformation of the homogeneous coordinates are presented .