In mathematics, a KochanekâBartels spline or KochanekâBartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents.
Given n + 1 knots,
to be interpolated with n cubic Hermite curve segments, for each curve we have a starting point pi and an ending point pi+1 with starting tangent di and ending tangent di+1 defined by
where...
t | tension | Changes the length of the tangent vector | |
b | bias | Primarily changes the direction of the tangent vector | |
c | continuity | Changes the sharpness in change between tangents |
Setting each parameter to zero would give a CatmullâRom 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:
Tension | T = +1→ Tight | T = −1→ Round | |
Bias | B = +1→ Post Shoot | B = −1→ Pre shoot | |
Continuity | C = +1→ Inverted corners | C = −1→ Box corners |
The code includes matrix summary needed to generate these splines in a BASIC dialect.
In mathematics, a KochanekâBartels spline or KochanekâBartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents.
Given n + 1 knots,
to be interpolated with n cubic Hermite curve segments, for each curve we have a starting point pi and an ending point pi+1 with starting tangent di and ending tangent di+1 defined by
where...
t | tension | Changes the length of the tangent vector | |
b | bias | Primarily changes the direction of the tangent vector | |
c | continuity | Changes the sharpness in change between tangents |
Setting each parameter to zero would give a CatmullâRom 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:
Tension | T = +1→ Tight | T = −1→ Round | |
Bias | B = +1→ Post Shoot | B = −1→ Pre shoot | |
Continuity | C = +1→ Inverted corners | C = −1→ Box corners |
The code includes matrix summary needed to generate these splines in a BASIC dialect.