E.O. Deryugina – Ph.D.(Eng.), Associate Professor, 

Department «Information Systems and Networks», Kaluga branch of the Bauman MSTU

E-mail: syvorova_eo@mail.ru

N.A. Borsuk – Ph.D.(Eng.), Associate Professor, 

Department «Information Systems and Networks», Kaluga branch of the Bauman MSTU

E-mail: borsuk.65@yandex.ru

E.V. Vasina – Student, 

Department «Information Systems and Networks», Kaluga branch of the Bauman MSTU Е-mail: liz.vasina@gmail.ru

The article describes the approach of mathematical modeling for the software component for building a 3D model using multimedia technologies as an example of the Museum of the History of Cosmonautics named after K.E. Tsiolkovsky.

Automation of the stages of building a 3D model from a series of images of an object, or from photographs, or from a digitized image with lost fragments - this direction is relevant when using the capabilities of 3D modeling when reconstructing lost historical and cultural values and digitizing existing museum exhibits with complex surface geometry or too large, hard to see.

Modern computer technologies provide a wide range of opportunities for data visualization and access to a wide audience. One of the directions in this area: the use of 3D-modeling to create information objects in bulk digital form. As the initial data for creating a 3D model, drawings, sketches, descriptions, photographs, and real objects can be used.

To create a mathematical model of a software component, we initially consider general methods for converting two-dimensional space into three-dimensional. Then advancing in the matter of constructing a mathematical model of a software component, we construct a mathematical model of the camera, which is called the «projective camera». The experiment, testing of the model is carried out in the Open Computer Vision (OpenCV) library. The obtained data (matrices) are used for the second step or block of the mathematical model. In the second block, we decided to use the principles of stereo vision to automate the process of building a 3D model. Internet research has shown that such a trip is not implemented in any well-known product. In our case, when scanning photographs or images of lost objects, either an insufficiently informative copy due to a poor image or a limited number of images for building 3D models can be obtained. The mathematical model of stereo vision is based on elements of epipolar geometry. Therefore, we use elements of epipolar geometry, taking into account the distortions that are introduced by average cameras. The distortion coefficients are calculated in Matlab. The process of creating a 3D model is proposed to be divided into two stages: on the first, we build the frame of the main elements of the object, on the second, we build the surface of the 3D model. Surface construction is performed using the Delaunay triangulation algorithm. These steps are also simulated in Matlab. An experiment to test the resulting mathematical model was also conducted at Matlab for the museum exhibit, for two photographs. The entire process is described in detail in the article.

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