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Some Possible Solutions--2

Explicit curves (form y = f(x))

• Polynomials, e.g.,

• y = ax3 + bx2 + cx + d

• Problem: has to maintain properties of a continuous function with y dependent on x

  • can't have multiple y's for one x

  • is not a rotationally invariant type of description: can't guarantee that it will remain a function when rotated

  • curves with vertical tangents hard to represent,
    slope =

Implicit Curves (form f(x,y) = 0)

• 
  
  E.g., for a circle x2 + y2 = c2, c a constant

• Problem: how to model half a circle?

• Difficult to join sequences of implicit functions

Animation - 10 MAY 95

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