Numerical Methods for solving globally convergent nonlinear polynomial system of equations. Pathfinder part 1
There are many applications to solving a set of nonlinear system of equations problem in biology, economics, physics, engineering, geometry (intersection of surfaces) and of course mathematics and we have not found a numerical methods for solving it yet. Because of the existence of several roots, and that these usually are dispersed to unknown positions in N-dimensional space, efficient numerical methods are hard to develop. This posts presents three basics approach in solving this kind of problems and contains one simple example of kinematic chain that is helpful in general understanding of the main problem.
The post presents review of book “Fundamentals of Three-Dimensional Digital Image Processing” by Junichiro Toriwaki and Hiroyuki Yoshida I’ve prepared for my talk at my university. I have read this book and the review is part of report that is possible to read on my blog. Depsite the post doesn’t present the pure CAD/CAM content the 3D imaging has many application, I decided to publish it here and spend some time on reading this book. It’s a very interesting domain of knowledge and for sure 3D digital image processing is very important task with much more applications than in medicine.
3D Image processing. Report and Power Point presentation that describes the basics of 3D medical images
This post presents auxiliary materials to the talk I gave at my university about processing of 3D medical images. The rapid development of medical devices allowed for processing its results digitally. I am discussing the basic problems of image digitization and the process of creating 3D image. An survey about data structures and algorithms that plays major role in medical imaging has been published. The power point presentation, videos, and full text of report is available for downloading. It’s based on Fundamentals of Three-dimensional Digital Image Processing book by Springer.
This post explains how differential constraints can be used to implement automatic car parking system. A geometry of parking has been described and explained. Short introduction to mathematical task of deriving differential constraints and solving this problem has been proposed.
This post explains how differential constraints that are widely used in CAD/CAM can be combined with classical mechanics to produce car ESP system that will be manufactured serially and mounted in modern vehicles. Main problems of constraints and conditions of ESP system are explained.
This post presents piston move animation according to Hamilton mechanics with full real-life physics support solved using C# and WPF. An in-depth derivation of motion equation has been published to help understanding of Hamiliton mechanics. This is tutorial is helpful start-on in various mechanical simulation. Full source code, executable and explanatory pictures are downloadable. As a result easy to use educational animation has been produced that facilitates understanding of piston work and movement.
I received an ask for a help to get the properties of a points. The post explains how to get properties of NX points objects and work with them. The post presents a real world CFD problem with a solution.
The post show how to retrieve programatically the user selected curve’s point coordinates. A very simple NX GUI has been provided. An short introductory video that shows the result of NX customization code has been published. Source code has been included.
There are numerous examples of normal ray casting. Almost everyone has heard about CSG. Each computer graphics book has printed a csg ray traced image. Performing Constructive Solid Geometrical operations is crucial in CAD/CAM and almost in every computer graphics application. I’m going to explain you some main ideas on csg ray casting that will help you to develop your own code. The article covers only implicit representation of surfaces does not present any knowledge about parametrical. Source code is included.
This post describes how to execute unmanaged C++ OpenGL drawing on windows forms and WPF to achieve very fast and reliable graphics rendering over stunning GUI done in WPF or Windows Forms. There other tasks that use this kind of cross-platform rendering like digitall sculpturing programs, CUDA simulations which requires speed, sophisticated graphics performance or special usage of special technology like CUDA and nice UI that would allow for controlling the process that is going in behind. So it’s important to know how to combine those technologies and really worth doing! Two solutions to this problem have been meticulously described and discussed.