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The implementation of reliable and efficient geometric algorithms is achallenging task. The reason is the following conflict: On the one hand,computing with rounded arithmetic may question the reliability of programswhile, on the other hand, computing with exact arithmetic may be too expensiveand hence inefficient. One solution is the implementation of controlledperturbation algorithms which combine the speed of floating-point arithmeticwith a protection mechanism that guarantees reliability, nonetheless.  This paper is concerned with the performance analysis of controlledperturbation algorithms in theory. We answer this question with thepresentation of a general analysis tool box. This tool box is separated intoindependent components which are presented individually with their interfaces.This way, the tool box supports alternative approaches for the derivation ofthe most crucial bounds. We present three approaches for this task.Furthermore, we have thoroughly reworked the concept of controlled perturbationin order to include rational function based predicates into the theory;polynomial based predicates are included anyway. Even more we introduceobject-preserving perturbations. Moreover, the tool box is designed such thatit reflects the actual behavior of the controlled perturbation algorithm athand without any simplifying assumptions.

General Analysis Tool Box for Controlled Perturbation