Study E.: Geometrie der Dynamen. Leipzip 1903. Home/Search Document Not in Database Summary Related Articles Check |
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Geometries for CAGD - Pottmann, Leopoldseder (Correct)
....sphere geometry can be found in [102] 3. Line Geometry Line geometry investigates the set of lines in three space. There is rich literature on this classical topic of geometry including several monographs [23,34,36,64,89,107,111] Line geometry possesses a close relation to spatial kinematics [11,43,98,101,107], see also chapter . Line geometry enters problems in geometric computing in various ways. A detailed account of the use of line geometry in geometric modeling and related areas is given in a monograph by Pottmann and Wallher [89] In the following, we briefly outline just a few basic principles ....
Study E.: Geometrie der Dynamen. Leipzip 1903.
Hand-Eye Calibration in terms of motion of lines.. - Bayro-Corrochano, .. (Correct)
....the double numbers = 1 and the dual numbers = 0. In case of the dual numbers the term b is called the real part and c the dual part. In the famous paper P reliminary sketch of biquaternions [3] Clifford introduced the motors or biquaternions for representing screw motion. Later on Study [9] used the dual numbers to represent the relative position of two skew lines in space, i.e. d. The real part indicates the difference of the line orientation angles and the dual part the distance between both lines. This paper uses dual numbers and only for comparison purposes the ....
Study E. Geometrie der Dynamen. Leipsig 1903.
Pose And Motion Estimation From Vision Using Dual.. - Goddard (1997) (Correct)
....about its real part has a particularly simple form: f(a #b) f(a) #bf # . 2.19) This property is useful in the expansion of commonly used functions. For example, sin( #) sin(#) #d cos(#) 2.20) 39 where # = # #d. Dual numbers were first proposed by Cli#ord [86] and developed by Study [87]. Study represented the dual angle of two skew lines in 3 D space as a dual number. The dual angle is # = # #d (2.21) where # is the angle between the line vectors, and d is the shortest distance between the lines. 2.4 Dual Number Quaternions The dual number concept may be applied to ....
E. Study, Geometrie der Dynamen, Leipzig, 1903.
On the Geometry of Spatial Polygons and Screw Polygons - Mavroidis, Roth (1997) (Correct)
....of the parameters are to be determined. 2 Knowing how to solve the polygons is important, since many different types of kinematics problems can be formulated in terms of spatial or screw polygons. Spatial polygons, as geometric elements in kinematics, were first defined by Yang (1963) Earlier, Study (1903) had briefly studied the spatial triangle, i.e. the spatial 3 gon. Roth (1967) using a concept originated by Halphen (1882) developed the screw triangle as a tool in kinematics to study three positions of a rigid body in space. The screw triangle concept was extended to screw polygons for the ....
Study E., 1903, Geometrie der Dynamen, Verlag Teubner, Leipzig.
On the Geometry of Spatial Polygons and Screw Polygons - Mavroidis (1996) (Correct)
....of the parameters are to be determined. Knowing how to solve the polygons is important, since many different types of kinematics problems can be formulated in terms of spatial or screw polygons. Spatial polygons, as geometric elements in kinematics, were first defined by Yang (1963) Earlier, Study (1903) had briefly studied the spatial triangle, i.e. the spatial 3 gon. Roth (1967) using a concept originated by Halphen (1882) developed the screw triangle as a tool in kinematics to study three positions of a rigid body in space. The screw triangle concept was extended to screw polygons for the ....
Study E., 1903, Geometrie der Dynamen, Verlag Teubner, Leipzig.
Hand-Eye Calibration in terms of motion of lines.. - Bayro-Corrochano, .. (Correct)
....double numbers 2 = 1 and the dual numbers 2 = 0. In case of the dual numbers the term b is called the real part and c the dual part. In the famous paper P reliminary sketch of biquaternions [3] Clifford introduced the motors or biquaternions for representing screw motion. Later on Study [9] used the dual numbers to represent the relative position of two skew lines in space, i.e. d. The real part indicates the difference of the line orientation angles and the dual part the distance between both lines. This paper uses dual numbers and only for comparison purposes the ....
Study E. Geometrie der Dynamen. Leipsig 1903.
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