Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
An application of number theory to the organization of raster-graphics memory
Journal of the ACM (JACM) - The MIT Press scientific computation series
Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Tilings and patterns
Intersection algorithms for lines and circles
ACM Transactions on Graphics (TOG)
Hierarchical representations of collections of small rectangles
ACM Computing Surveys (CSUR)
The Euclidean algorithm strikes again
American Mathematical Monthly
ACM Transactions on Graphics (TOG)
Common LISP: the language (2nd ed.)
Common LISP: the language (2nd ed.)
Number systems with a complex base: a fractal tool for teaching topology
American Mathematical Monthly
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
Computing A*B (mod N) efficiently in ANSI C
ACM SIGPLAN Notices
On the permutations of a vector obtainable through the restructure and transpose functions of APL
ACM SIGAPL APL Quote Quad
A ``Binary'' System for Complex Numbers
Journal of the ACM (JACM)
Anti-Aliasing through the Use of Coordinate Transformations
ACM Transactions on Graphics (TOG)
Curve Fitting with Conic Splines
ACM Transactions on Graphics (TOG)
Algorithm 467: matrix transposition in place [F1]
Communications of the ACM
Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Structure of Computers and Computations
Structure of Computers and Computations
APL '81 Proceedings of the international conference on APL
Principal values and branch cuts in complex APL
APL '81 Proceedings of the international conference on APL
| Hi-index | 0.00 |
Some recent computer languages incorporate rational numbers, complex numbers, and rational complex numbers. We extend these numeric facilities to deal properly with Gaussian integers---i.e., complex numbers whose real and imaginary parts are both ordinary (rational) integers. In addition to their intrinsic mathematical interest, such extensions also raise interesting questions regarding polymorphism and multiple inheritance.Since Gaussian integers are the coordinates of discrete square pixels in the complex plane, complex operations can be used to implement 2-D graphics operations. Many 2-D algorithms are more elegant in complex number form---e.g., one can envision a 2-D spreadsheet for scientific applications whose coordinates are Gaussian integers.