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CTK Exchange
alexb
Charter Member
1523 posts |
May-11-05, 10:22 AM (EST) |
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1. "RE: Closed curve"
In response to message #0
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>What is the criteria to decide a curve is What do you mean by critera? If any exists, it may depend on how your curve is defined. In what form do you have a curve? |
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sfwc
Member since Jun-19-03
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May-12-05, 01:23 PM (EST) |
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3. "RE: Closed curve"
In response to message #2
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Is the equation parametric (for example, x = sin(t), y = cos(t)) or is the curve instead specified as the solution set of an equation (for example x^2 + y^2 = 1). Or is it given in a different form again? In the parametric case, suppose the curve (x(t), y(t)) is specified on some interval . Then the curve is closed iff x(a) = x(b) and y(a) = y(b) and non-intersecting iff for s and t in In the solution set case, the curve is usually closed if it is bounded. It is almost certainly nonintersecting if the defining function (in the above case x^2 + y^2 - 1) has nondegenrate derivative on the curve, but it is harder to give an all inclusive condition.Thankyou sfwc
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