Modeling the forming surfaces of wood trunks using spline functions

• Main Authors: Yuriy Hrytsiuk, Svitlana Yatsyshyn
• Format: Article
• Language: English
• Published: Ukrainian National Forestry University 2018-10-01
• Series: Наукові праці Лісівничої академії наук України
• Subjects: information technology; software design; tree trunk; cross-section of the log; forming surface; annual rings; cutting scheme; timber; technological equipment; resource-saving process
• Online Access: http://fasu.nltu.edu.ua/index.php/nplanu/article/view/243
• ISSN: 1991-606X; 2616-5015

It was developed the methodology for modeling complex geometric surfaces of natural origin – a tree trunk using spline functions. It allows to increase the accuracy and reliability of wood assessment in different dimensional characteristics, as well as sawn timber in the field of woodworking. It was found that the method of constructing mathematical models of forming the cross-sectional surface of logs and their surfaces along the axis allows based on a single theoretical approach to describe the dimensions and shape of the axes, as well as external surfaces. It is based on the measurement of coordinates certain amount of the cross-section of a tree trunk points along its length and the subsequent interpolation point basis. It was found that the mathematical implementation – interpolating cubic splines, constructed on a small number of surface points, allow to determine with sufficient accuracy, the dimensional indices logs and incorporate features of the form of timber barrel (curvature, convergence, ovality). The cubic splines are also the adequate individual models to account for the logs as an industrial raw material and timber sawn from them. It was determined that the main objectives of software devel-opment is the construction of the cross-sectional surfaces forming logs cubic splines, scale forming butt logs for the construction of the annual rings and calculating his area and the output of sawed sawn timber for different cutting patterns. The software for constructing forming surfaces of complex shape of trunks of wood, which makes it possible to build models of surfaces logs by spline functions was implemented. The algorithms accounting for wood barrel and some algorithms schemes cutting logs for timbers are given. It is proved that the output of sawn timber after the implementation of mathematical modelling is significantly increased in comparison with the traditional methods of modelling the surfaces of logs. It was found that the method of individual models of trunks of wood, their mathematical, software and hardware support in the form of mathematical models, algorithms, implementation and software, the results and conclusions of the presented research can be used in the design of production and processing of wood systems, the establishment of appropriate resource-saving technological processes on the basis of modern technology and measuring equipment, methods and information tech-nology models.