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Re: [svg-developers] Conics to Bezier curves... how?

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  • Bernhard Herzog
    ... They can t. As the mathworld page says, only *rational* Bezier curves can represent conics exactly. SVG only support non-rational quadratic and cubic
    Message 1 of 3 , Aug 24, 2000
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      "Alexander J. Vincent" <ajvincent@...> writes:

      > Okay, now I know that somehow, something in my previous message here was
      > partly incorrect. According to Mathworld @ Wolfram, a Bezier curve can
      > represent a conic section exactly.
      >
      > http://mathworld.wolfram.com/BezierCurve.html
      >
      > (MathWorld is one of the better math references out there)
      >
      > But how?

      They can't. As the mathworld page says, only *rational* Bezier curves
      can represent conics exactly. SVG only support non-rational quadratic
      and cubic bezier curves which can only approximate them.

      --
      Bernhard Herzog | Sketch, a drawing program for Unix
      herzog@... | http://sketch.sourceforge.net/
    • Chris Lilley
      ... Correct. If a particular implementation wanted to represent all geometry internally as one type, it could do so by translating them all to rational
      Message 2 of 3 , Aug 31, 2000
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        Bernhard Herzog wrote:
        >
        > "Alexander J. Vincent" <ajvincent@...> writes:
        >
        > > Okay, now I know that somehow, something in my previous message here was
        > > partly incorrect. According to Mathworld @ Wolfram, a Bezier curve can
        > > represent a conic section exactly.
        > > http://mathworld.wolfram.com/BezierCurve.html

        > They can't. As the mathworld page says, only *rational* Bezier curves
        > can represent conics exactly. SVG only support non-rational quadratic
        > and cubic bezier curves which can only approximate them.

        Correct. If a particular implementation wanted to represent all geometry
        internally as one type, it could do so by translating them all to rational
        beziers, NURBS, or whatever.

        Congratulations on the 0.6.8 release of Sketch, by the way!

        --
        Chris
      • Dave & Jocelyn Corstorphan
        About 20 years ago I used a fortran program which actually approximated this extremly well, we used it on a cartogrphic project with considerable success. But
        Message 3 of 3 , Aug 31, 2000
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          About 20 years ago I used a fortran program which actually approximated this
          extremly well, we used it on a cartogrphic project with considerable
          success. But I have misplaced the fortran subroutine. If I find it, I will
          post it to the forum. It was not a very difficult formula.

          Cheers

          Dave Corstorphan
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