Interval Bisection: General Formula?

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SUMMARY

The discussion centers on the concept of interval bisection and its relation to linear interpolation in three-dimensional space. The point that bisects the interval from (x_0, y_0, z_0) to (x_1, y_1, z_1) is calculated using the formula ((x_0 + x_1)/2, (y_0 + y_1)/2, (z_0 + z_1)/2). This formula is derived from the principles of averaging coordinates and does not require re-derivation for each application. The user initially confused interval bisection with linear interpolation, seeking a general formula for the latter.

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  • Understanding of three-dimensional coordinate systems
  • Familiarity with linear interpolation concepts
  • Basic knowledge of mathematical averaging techniques
  • Experience with geometric principles, specifically similar triangles
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  • Study the mathematical derivation of interval bisection formulas
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Mathematicians, computer graphics developers, and anyone involved in geometric computations or interpolation methods will benefit from this discussion.

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Is there any general formula for interval bisection, rather than consider two similar triangles each time?

Thanks
 
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I must be misunderstanding what you mean by "interval bisection". The point bisecting the interval from [itex](x_0,y_0,z_0)[/itex] to [itex](x_1, y_1, z_1)[/itex], in 3 dimensions, is [itex]((x_0+ x_1)/2, (y_0+ y_1)/2, (z_0+ z_1)/2)[/itex], "averaging" the coordinates. That can be derived by using 'similar triangles' but you surely don't have to rederive it for each application.
 
Thanks for the reply. Sorry, I meant linear interpolation, not interval bisection - is there a general formula for this?

Thanks
 

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