Parallel point sampling for 3D bodies

2020 ◽  
Author(s):  
Urban Duh ◽  
Matjaz Depolli ◽  
Jure Slak ◽  
Gregor Kosec
Keyword(s):  
Point Sampling

Fitting Weighted Total Least-Squares Planes and Parallel Planes to Support Tolerancing Standards

2012 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Point Contact ◽  
Coordinate Measuring Machine ◽  
Total Least Squares ◽  
Point Sampling ◽  
Least Squares Fitting ◽  
Weighted Total Least Squares ◽  
Measuring Machine ◽  
Fitting In ◽  
Value Decomposition

We present elegant algorithms for fitting a plane, two parallel planes (corresponding to a slot or a slab) or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3×3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we demonstrate that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

2003 ◽  
Vol 33 (8) ◽  
pp. 1587-1590 ◽  
Author(s):  
J H Gove
Keyword(s):  
Size Distribution ◽  
Graphical Representation ◽  
Basal Area ◽  
Distribution Theory ◽  
Harmonic Mean ◽  
Quadratic Mean ◽  
Point Sampling ◽  
The Relationship ◽  
Horizontal Point Sampling ◽  
Biased Distribution

This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased distribution theory. Second, a new result, which may prove most valuable in viewing the graphical representation of assumed distributions, is also derived. The results are also shown to apply to the basal area – size distribution, providing a unique duality between the two means.

Identification of Shopping Districts by Using Point-sampling-data and Changes of Their Scopes

1991 ◽  
Vol 26 (0) ◽  
pp. 103-108
Author(s):  
Ichiro Sakamoto ◽  
Shigeki Muramatsu ◽  
Hideoki Takatsuji ◽  
Norihiro Nakai
Keyword(s):  
Point Sampling

Kriging-based unconstrained global optimization through multi-point sampling

2019 ◽  
Vol 52 (6) ◽  
pp. 1082-1095 ◽  
Author(s):  
Yaohui Li ◽  
Shuting Wang ◽  
Yizhong Wu
Keyword(s):  
Global Optimization ◽  
Point Sampling

scholarly journals Double Sampling Saves Time When Cruising Appalachian Hardwoods

1996 ◽  
Vol 13 (3) ◽  
pp. 116-118 ◽  
Author(s):  
Paul R. Merten ◽  
Harry V. Wiant ◽  
John C. Rennie
Keyword(s):  
Standard Errors ◽  
Double Sampling ◽  
Point Sampling ◽  
Significant Bias ◽  
Volume Estimates ◽  
Appalachian Hardwoods

Abstract Simulations based on data collected in five Appalachian hardwood sawtimber-size stands indicate double sampling using point sampling (BAF 10 and 20) compared to conventional point sampling would save 24 to 47% of time in the field. There was no significant bias in volume estimates using double sampling, and standard errors were within about 1% of those obtained with conventional point sampling. North. J. Appl. For. 13(3):116-118.

Sign in / Sign up

Export Citation Format

Share Document