Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Communications of the ACM
An efficient new algorithm for 2-D line clipping: Its development and analysis
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Program Transformation Systems
ACM Computing Surveys (CSUR)
Using program transformations to derive line-drawing algorithms
ACM Transactions on Graphics (TOG)
Proceedings of an International Workshop on Advanced Programming Environments
Proceedings of an International Workshop on Advanced Programming Environments
Analysis of the nicholl-lee-nicholl algorithm
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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Problems in geometry often possess symmetry properties that may be exploited in order to develop solutions. Algorithms based on these symmetry properties will frequently use geometric transformations to transform one case into another (symmetric) case. One advantage of this approach is that the algorithm avoids enumeration of cases and thus is shorter and generally easier to read. One disadvantage is that some additional execution time is required to perform these transformations. We describe how simple program equivalences may be used as program transformations to eliminate this additional execution time from programs that use geometric transformations. This approach has been used to develop an efficient implementation of a new algorithm for the two-dimensional line-clipping problem.