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Multiple articles in the category 'Math' on website 3D Game Engine Programming

Extendable linearised adjustment model for deformation analysis

Author supplied: "This paper gives a linearised adjustment model for the affine, similarity and congruence transformations in 3D that is easily extendable with other parameters to describe deformations. The model considers all coordinates stochastic. Full positive semi-definite covariance matrices and correlation between epochs can be handled. The determination of transformation parameters between two or more coordinate sets, determined by geodetic monitoring measurements, can be handled as a least squares adjustment problem. It can be solved without linearisation of the functional model, if it concerns an affine, similarity or congruence transformation in one-, two- or three-dimensional space. If the functional model describes more than such a transformation, it is hardly ever possible to find a direct solution for the transformation parameters. Linearisation of the functional model and applying least squares formulas is then an appropriate mode of working. The adjustment model is given as a model of observation equations with constraints on the parameters. The starting point is the affine transformation, whose parameters are constrained to get the parameters of the similarity or congruence transformation. In this way the use of Euler angles is avoided. Because the model is linearised, iteration is necessary to get the final solution. In each iteration step approximate coordinates are necessary that fulfil the constraints. For the affine transformation it is easy to get approximate coordinates. For the similarity and congruence transformation the approximate coordinates have to comply to constraints. To achieve this, use is made of the singular value decomposition of the rotation matrix. To show the effectiveness of the proposed adjustment model total station measurements in two epochs of monitored buildings are analysed. Coordinate sets with full, rank deficient covariance matrices are determined from the measurements and adjusted with the proposed model. Testing the adjustment for deformations results in detection of the simulated deformations."

Digital Twins of the ocean : autogenerated 3D environments for validating offshore wind farm operations.

Within the context of the Iliad project, the authors present technical challenges and the first results of having valid 3D scenes of (non-)existing offshore wind farms procedurally and automatically generated within either the Unreal or Unity game engine. The Iliad – Digital Twins of the Ocean project (EU Horizon 2020) aims to develop a ‘system of systems’ for creating cutting-edge digital twins of specific sea and ocean areas for diverse purposes related to their sustainable use and protection. One of the Iliad pilots addresses the topic of offshore floating wind farm construction or maintenance scenario testing and validation using the Unity 3D game engine. This work will speed up the development of these scenarios by procedurally and automatically creating the Unity 3D scene rather than manually (which is done at present). The main technical challenges concern the data-driven approach, in which a JSON configuration file drives the scene creation. The first results show a base wind farm running in Unreal 5.1. The final product will be able to handle environmental conditions, biological conditions, and specific human activities as input parameters.

The 3D additivist cookbook

The 3D Additivist Cookbook, devised and edited by Morehshin Allahyari & Daniel Rourke, is a free compendium of imaginative, provocative works from over 100 world-leading artists, activists and theorists. The 3D Additivist Cookbook contains .obj and .stl files for the 3D printer, as well as critical and fictional texts, templates, recipes, (im)practical designs and methodologies for living in this most contradictory of times.

Fashion Design and Presentation using 3D Digital Prototyping

The short-term aim of this R&D project (financed by the Centre of Expertise Creative Industries) is to develop a virtually simulated textile database that renders 3D visual representations of these fabrics. The idea is for this database to be open source and be able to interface with 3D design applications such as those of Lectra. The textile database will include a number of different digital datasets per textile that contain information about the fabric’s drape, weight, flexibility etc., to virtually render prototypes in a 3D simulated environment. As such, in building garments via a 3D software design application, designers will be able to see how a garment changes as new textiles are applied, and how textiles behave when constructed as different garments. This will take place on 3D avatars, which may be bespoke body scans, and will allow for coordinated and precise fitting and grading.

Time Series Analysis of 3D Coordinates Using Nonstochastic Observations

From the article: Abstract Adjustment and testing of a combination of stochastic and nonstochastic observations is applied to the deformation analysis of a time series of 3D coordinates. Nonstochastic observations are constant values that are treated as if they were observations. They are used to formulate constraints on the unknown parameters of the adjustment problem. Thus they describe deformation patterns. If deformation is absent, the epochs of the time series are supposed to be related via affine, similarity or congruence transformations. S-basis invariant testing of deformation patterns is treated. The model is experimentally validated by showing the procedure for a point set of 3D coordinates, determined from total station measurements during five epochs. The modelling of two patterns, the movement of just one point in several epochs, and of several points, is shown. Full, rank deficient covariance matrices of the 3D coordinates, resulting from free network adjustments of the total station measurements of each epoch, are used in the analysis.