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**1 - 3**of**3**### Making geometry visible: An introduction to the animation of geometric algorithms

- In Handbook on Computational Geometry, J.-R. Sack and
, 1997

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### IN CANDIDACY FOR THE DEGREE

, 2001

"... ii This thesis looks at animation as a means of explaining software and algorithms, and considers human and computer factors that come into play. Understanding software is critical, because it enters so many aspects of our lives. Of course, students need to learn algorithms and programming technique ..."

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ii This thesis looks at animation as a means of explaining software and algorithms, and considers human and computer factors that come into play. Understanding software is critical, because it enters so many aspects of our lives. Of course, students need to learn algorithms and programming techniques, but even experienced practicioners find that aspects of the programs they have written can exceed their understanding. For this reason, explanatory tools are sorely needed. By considering the types of uses that algorithm animation may be put to, we establish that it resembles visual arts, but, just as importantly, that there is little hope for automatic systems that can produce a useful animation based on a pseudocode description of an algorithm. Animation demands human guidance. Hence a good AA system must be interactive, and we establish a thorough list of requirements for such a system. We propose a portable web-based system. One important requirement is that algorithms and animations must run as separate

### An Interactive Fibonacci Heap Applet

"... A Fibonacci heap (F-heap) is a collection of heap-ordered trees. F-heaps are the type of data structure in which the work that must be done to reorder the structure is postponed until the very last possible moment. F-heaps are useful for algorithms involving graph data structures, such as those used ..."

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A Fibonacci heap (F-heap) is a collection of heap-ordered trees. F-heaps are the type of data structure in which the work that must be done to reorder the structure is postponed until the very last possible moment. F-heaps are useful for algorithms involving graph data structures, such as those used for computing shortest paths in computer networks [5]. The common operations supported by F-heaps are insert, minimum, extract-min, union, decrease-key, and delete. These operations are described below. • Insert: A new node is inserted into the heap by simply adding the node to the root list and updating the pointer to the minimum node if necessary. • Minimum: This operation simply returns the node in the heap with the minimum key. This node is constantly referenced, so no real work must be done here. • Extract-Min: First, each of the minimum node’s children is added to the root list and the minimum node itself is deleted from the list. Finally, roots of equal degree in the root list are combined until at most one root of each