Web-system for modeling surfaces based on Catmull-Rom patches


  • A. Demchyshyn
  • Y. Burienkov


Hermite surface, Ketmal-Roma spline, NURBS, Single Page Application, surface smoothness


Today, surfaces play an important role in the work of designers, scientists, artists, sur-geons and other professionals involved in creating innovative products. Development of uten-sils, furniture, automobile chassis, phones, clothes, buildings, even human bodies involves geometrical modeling of surfaces. NURBS modeling is the technology of non-uniform rational B-splines creating smooth forms and models that have no sharp edges. The characteristic makes NURBS as the analytical model of choice in Autodesk 3ds Max, Blender, Autodesk Ma-ya, ZBrush, and other modeling systems. A generalizing characteristic of the given software systems is the use of a monolithic architectural style of software development, which is typical for desktop applications. Desktop software systems require installation on a local computer, which in turn binds the user to a specific operating system. NURBS accurately describe conical surfaces. Although each control has its own weight, and each weight has a local effect on the surface, a change in the weight of one vertex leads to a change in the entire surface. One of the main requirements for 3D object modeling software is the ability to change the shape of the surface freely as it passes through all control points. An algorithmic model of the Hermit surface construction under the Catmull-Rom condition and nonzero surface torsion vectors is obtained. It is shown that the Catmull-Rom condition makes it possible to glue individual patches with first-order smoothness, which is a guarantee of ergonomic surfaces. It is shown that a single control point has a local effect on the surface, namely on the 12 sur-rounding patches. The development of a software system for modeling the surfaces of objects with the client part in the form of a web application, which is based on the architectural style of SPA, showed that the user experience of such an application is close to the experience of using a desktop program. At the same time, the SPA application does not require installation and successfully runs on both stationary and mobile devices.


Yamaguchi F. Curves and Surfaces in Computer Aided Geometric Design / F. Ya-maguchi. – Springer, 2014. – 396 p.

Salomon D. The Computer Graphics Manual / D. Salomon. – Springer, 2011. – 1526 p.

Agoston Max K. Computer Graphics and Geometric Modelling / Max K. Agoston. Springer, 2005. – P. 524.

Tickoo S. Autodesk 3ds Max 2019: A Comrehensive Guide / S. Tickoo. – CADCIM Technologies, 2018. – 720 p.

Skolski P. Single-page application vs. multiple-page application / P. Skolski – Source: https://medium.com/@NeotericEU/single-page-application-vs-multiple-page-application-2591588efe58

Rogers D., Adams J. A. Mathematical Elements for Computer Graphics / D. Rogers, J. A. Adams. McGraw-Hill Science/Engineering/Math, 1989. – 512p.

Farin G. Curves and Surfaces for CAGD: A Practical Guide / G. Farin. Morgan Kaufmann, 2001. – P. 291.

Zhou Xi-jun G2 Continuity Algorithms between Adjacent NURBS Patches along Common Cubic Boundary Curve / Xi-jun Zhou. - Chinese Journal of Aero-nautics 16(4), 2003. – P. 241-246. DOI: 10.1016/S1000-9361(11)60191-X

Geometric continuity constraints for adjacent NURBS patches in shape optimisa-tion / X. Zhang, Y. Wang, M. Gugala, J.-D. Muller. ECCOMAS Congress 2016. – P 1-14. DOI:10.7712/100016.2086.9316

Abramowitz M., Stegun I. Handbook of Mathematical Functions: with For-mulas, Graphs, and Mathematical Tables M. Abramowitz, I. A. Stegun. Dover Publi-cations, 1972. – P. 884.