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Advantage of Parametric vs. Explicit Line Definition

• Explicit line definition:

• y = mx + b, m = dx/dy; how best to deal with

  • vertical slope?

  • finite lines (line segments)?
    
    

• Parametric:

• x = (1 - t) x1 + tx2,

• y = (1 - t) y1 + ty2, 0 t 1

  • for vertical slope

  • for t = 0, x = x1, y = y1

  • for t = 1, x = x2, y = y2

  • restricted range of t defines a segment, not a whole line:

  • t < 0, (x, y) lies "before" it

  • t > 0, (x, y) lies "after" it

Animation - 10 MAY 95

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