# 기타 스플라인들

### Kochanek–Bartels (KB) Splines

Same as a Cardinal spline (includes Tension), but with two extra tweaks (usually set on the entire spline).

Bias (from -1 to +1):

A zero bias leaves the velocity vector alone

A positive bias rotates the velocity vector to be more aligned with the point BEFORE this point

A negative bias rotates the velocity vector to be more aligned with the point AFTER this point

Continuity (from -1 to +1):

A zero continuity leaves the velocity vector alone

A positive continuity “poofs out” the corners

A negative continuity “sucks in / squares off” corners

{% hint style="info" %}
역주) Kochanek–Bartels (KB) Splines는 저도 정확히 이해를 못해서 원문 그대로 올립니다.
{% endhint %}

### B-Splines

Stands for “basis spline”.\
Just a generalization of Bezier splines.\
\
The basic idea:\
At any given time, P(t) is a weighted-average blend of 2, 3, 4, or more points in its “neighborhood”.\
\
Equations are usually given in terms of the blend weights for each of the nearby points based on where t is at.

{% hint style="info" %}
역주) B-Splines는 저도 정확히 이해를 못해서 원문 그대로 올립니다.
{% endhint %}

### Splines as filtering/easing functions

스플라인을 이용하여 "easing" 또는 "filtering"함수를 만들 수 있습니다.

예:

"**스무스한 시작**"을 위한 함수( $$t^2$$)는 A지점과 B지점이 겹쳐져 있는 2차 베지어 곡선과 같습니다.

![역주) A=B인 2차 베지어 곡선](/files/-LprPdTPnwaBWw_0xil0)

"**스무스한 종료**"를 위한 함수( $$2t - t^2$$ )는 C지점과 B지점이 겹쳐져 있는 2차 베지어 곡선과 같습니다.

![역주) B=C인 2차 베지어 곡선](/files/-LprPlv8mOW_Zk699EdH)

"**시작과 끝이 모두 스무스한**" 함수( $$3t^2 – 2t^3$$ )는 B=A, C=D인 3차 베지어 곡선과 같습니다.

![역주) A=B, C=D인 3차 베지어 곡선](/files/-LprQ-1Eir3486VgIZ2K)

{% hint style="info" %}
역주) 아래 사이트에 가면 베지어 곡선을 직접 시뮬레이션 해볼 수 있습니다.\
<https://www.jasondavies.com/animated-bezier/>
{% endhint %}

### Curved Surfaces

이 이야기의 범위를 벗어나지만 기본적으로 스플라인을 교차하면 2D곡면을 만들 수 있습니다.

![](/files/-LprFc3ad7Fh89B7LTbw)


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