GENERIC COORDINATE SYSTEMS IN THE COMPUTER GEOMETRY COURSE
Journal Title: Современные информационные технологии и ИТ-образование - Year 2018, Vol 14, Issue 4
Abstract
The article presents an approach to describe generic coordinate systems as a part of the course “Computer Geometry and Geometric Modeling”, which is taught to third-year students majoring in mathematics at the Lobachevsky State University of Nizhni Novgorod. Describing geometric mappings using coordinates and using transitions to other coordinate systems are the main tools in drawing images on the computer screen. The mathematical foundation of these operations come from analytic geometry and linear algebra courses, which mathematics majors take during their first year. However, many computer graphics textbooks do not make full use of theoretical concepts from these courses and do not provide proofs of correctness of coordinate transformations. Even when these proofs are present, they use linear algebra methods, which often consist of manipulating nested sums and numerous indices. This article demonstrates that the mains facts studied in linear algebra and used in constructing computer images can be generalized to arbitrary coordinate systems. The proofs of these facts use commutative diagrams. The helps abstract away from unnecessary details and clarify the main idea of the proof. We also advocate an approach that actively uses material covered by earlier mathematical courses and provides proofs that coordinate transformations used in drawing computer images are correct.
Authors and Affiliations
Evgeny Makarov
Keywords
Related Articles
- EP ID EP521923
- DOI 10.25559/SITITO.14.201804.833-841
- Views 80
- Downloads 0
ARTIFICIAL INTELLIGENT INTRUSION DETECTION SYSTEMS: PERSPECTIVES OF INNOVATIVE TECHNOLOGIES
The most popular development tools of the quantum cryptography technology are compared, the structure and the basic principles of its work is considered. In article the significance in the modern information society of t...
PARALLEL IMPLEMENTATION OF SYMMETRIC HORIZONTAL DISTRIBUTION OF DATA ON THE NETWORK TECHNOLOGIES BASIS
The approach to the construction of software and hardware complexes for implementing a symmetric horizontal distribution of tables in relational databases is considered. To solve this problem, we propose to use standard...
HASH ALGORITHM WITH THE CONTROLLING TREE-LIKE STRUCTURE AND THE METHOD OF ITS IMPLEMENTATION ON PARALLEL ARCHITECTURES
The article is devoted to research and development of new hashing methods that have the ability to adapt to increased requirements for cryptographic stability, and also support parallelization of computations, which is e...
THE ESTIMATIONS OF THE PARAMETERS OF THE DISTRIBUTION OF THE LOGARITHM OF THE COMPLEXITY OF TSP
The complexity of the individual traveling salesman problem was analyzed by means of mathematical statistics. The complexity is defined as a number of nodes of the decision tree created by the branch and bound algorithm....
MODIFICATION OF THE ANT COLONY OPTIMIZATION FOR THE DEVELOPMENT OF SOFTWARE FOR SOLVING MULTI-CRITERION SUPPLY MANAGEMENT PROBLEMS
The article proposes three modifications of the Ant Colony Optimization, for finding multi-criterion solutions for the task of supplying spare parts for aviation equipment. A peculiarity of modifications is the weights m...