Kochanek–Bartels spline - Alchetron, the free social encyclopedia

In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents.

Given n + 1 knots,

p₀, ..., p_n,

to be interpolated with n cubic Hermite curve segments, for each curve we have a starting point p_i and an ending point p_i+1 with starting tangent d_i and ending tangent d_i+1 defined by

d i = ( 1 − t ) ( 1 + b ) ( 1 + c ) 2 ( p i − p i − 1 ) + ( 1 − t ) ( 1 − b ) ( 1 − c ) 2 ( p i + 1 − p i ) d i + 1 = ( 1 − t ) ( 1 + b ) ( 1 − c ) 2 ( p i + 1 − p i ) + ( 1 − t ) ( 1 − b ) ( 1 + c ) 2 ( p i + 2 − p i + 1 )

where...

Setting each parameter to zero would give a Catmull–Rom spline.

The source code found here of Steve Noskowicz in 1996 actually describes the impact that each of these values has on the drawn curve:

The code includes matrix summary needed to generate these splines in a BASIC dialect.

References

Kochanek–Bartels spline Wikipedia

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