Kochanek–Bartels spline on:
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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
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline
In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the correspondi ...
with tension, bias, and continuity parameters defined to change the behavior of the tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
s.
Given ''n'' + 1 knots
A knot is a fastening in rope or interwoven lines.
Knot may also refer to:
Places
* Knot, Nancowry, a village in India
Archaeology
* Knot of Isis (tyet), symbol of welfare/life.
* Minoan snake goddess figurines#Sacral knot
Arts, entertainme ...
,
: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
:
:
where...
Setting each parameter to zero would give a Catmull–Rom spline
In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the correspondin ...
.
Thsource 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
BASIC (Beginners' All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use. The original version was created by John G. Kemeny and Thomas E. Kurtz at Dartmouth College ...
dialect.
External links
* * {{DEFAULTSORT:Kochanek-Bartels spline Splines (mathematics) Interpolation