# zero or one or .... parameters

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Hi I am reading a book about geometry and computer graphics . It says that : " The common theme that unifies the analysis of the queries is that the objects can be parametrized by zero ( point ) , one ( segment ) ,two ( triangle , rectangle ) , or three ( tetradedra , box ) parameters. " I can't understand what is zero or one or two or three parameter . Please tell me that what it means . thanks

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Precise answer: the number of parameters for those objects is the smallest dimensionality n such that the object can be bijectively and continuously mapped to a subset of Rn.

Hand-waving answer: parameters are used to represent movement inside the object.
You can't move inside a point (because there's nowhere to go except stay on the point), therefore there are no movement parameters. When on a segment, you can move from one end to the other, and so you can represent your position by a single parameter (for instance, the distance from one of the segment edges). When on a triangle, rectangle or other surface, you can move both in the north-south direction and the east-west direction (or any combination of the two), and you cannot represent both movements with a single parameter—but two parameters (latitude, longitude) are enough to represent any position on a surface. Finally, when inside a volume, using only two parameters will let you position yourself in a horizontal plane, but you would still need to specify the altitude of that plane, and so you need three parameters (left-right, forward-backward, up-down).

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