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Form Analysis of cone with FormFittingToolbox (Geodäsie/Vermessung)

MichaeL ⌂, Bad Vilbel, Thursday, 26.01.2012, 18:01 (vor 3962 Tagen) @ SarhatAdam
bearbeitet von MichaeL, Friday, 27.01.2012, 08:48

Hi SarhatAdam,

first, please don't send an email to the forum-adress. You got this mail, because you enabled the notification-option.

Can I ask what Nx, Ny, Nz, α are refer to cause I know that Mx, My, & Mz is the centre of the cone.

The vector n = \begin{pmatrix}n_x & n_y & n_z \end{pmatrix}^T is the rotation-axis of the cone. This vector is also an unit-vector. The point m = \begin{pmatrix}m_x & m_y & m_z \end{pmatrix}^T lies on n. The angle \alpha describes the angle between the vector n and the curved surface area of the cone. Therefore, the formula describes a cone with infinite length.

Are there any formula for cone in 3D space

There are some other ones e.g. in Sung Joon Ahn: Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space.

I need to understand the matrix how it was build in to least square solution.

I used a so-called rigorous Gauss-Helmert model (general least-squares) e.g. Charles D. Ghilani, Paul R. Wolf: Adjustment Computations - Spatial Data Analysis.

kind regards
Micha

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applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

Tags:
Cone, FormFittingToolbox, Form Analysis, Gauss-Helmert-Modell, least-squares


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