【MCx几何】在MC中绘制Catmull-Rom平滑曲线【粒子特效基础】

2023-08-05 18:35 作者:On_craft 0人读过 | 我要投稿

前言

众所周知，mc已经被大佬们开发出了许多酷炫的粒子线条，尤其是soma3.0曲线，可以给红石音乐带来非常不错的视觉效果，但弊端是soma3.0缺乏灵活度，只能在平面上进行绘制，这让它在红石音乐以外的领域较难得到应用。这篇专栏就简单讲下更灵活的Catmull-Rom曲线的MC内绘制方法

本专栏只讲怎么写代码，不讲原理! 想知道原理和公式推导请自行搜索

编程语言使用Java 18，其他语言也差不多基本上都是数学计算

粒子生成使用ColorBlock模组，原版一样的

(小学生都能看懂!)

准备工作

1.坐标的表示: x-y-z 分别表示mc的三条坐标轴；P.x表示点P的x轴坐标，y，z也一样

2.方程:

算法矩阵式:

$P(t)%3D%5Cbegin%7Bpmatrix%7Dt%5E3%26t%5E2%26t%261%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D-%5Calpha%262-%5Calpha%26%5Calpha-2%20%26%5Calpha%5C%5C2%5Calpha%26%5Calpha-3%263-2%5Calpha%26-%5Calpha%5C%5C-%5Calpha%260%26%5Calpha%260%5C%5C0%261%260%260%20%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7DP_0%5C%5CP_1%5C%5CP_2%5C%5CP_3%5Cend%7Bpmatrix%7D$

写成小学生都能看懂的形式就是:

$%5Cbegin%7Bcases%7DP_x(t)%3Dt%5E3*%5B-%5Calpha*P_0.x%2B(2-%5Calpha)*P_1.x%2B(%5Calpha-2)*P_2.x%2B%5Calpha*P_3.x%5D%2B%5C%5C%20%5Cqquad%20t%5E2*%5B2%5Calpha*P_0.x%2B(%5Calpha-3)*P_1.x%2B(3-2%5Calpha)*P_2.x-%5Calpha*P_3.x%5D%2B%5C%5C%20%5Cqquad%20t*(-%5Calpha*P_0.x%2B%5Calpha*P_2.x)%2BP_3.x%5C%5CP_y(t)%3Dt%5E3*%5B-%5Calpha*P_0.y%2B(2-%5Calpha)*P_1.y%2B(%5Calpha-2)*P_2.y%2B%5Calpha*P_3.y%5D%2B%5C%5C%20%5Cqquad%20t%5E2*%5B2%5Calpha*P_0.y%2B(%5Calpha-3)*P_1.y%2B(3-2%5Calpha)*P_2.y-%5Calpha*P_3.y%5D%2B%5C%5C%20%5Cqquad%20t*(-%5Calpha*P_0.y%2B%5Calpha*P_2.y)%2BP_3.y%5C%5CP_z(t)%3Dt%5E3*%5B-%5Calpha*P_0.z%2B(2-%5Calpha)*P_1.z%2B(%5Calpha-2)*P_2.z%2B%5Calpha*P_3.z%5D%2B%5C%5C%20%5Cqquad%20t%5E2*%5B2%5Calpha*P_0.z%2B(%5Calpha-3)*P_1.z%2B(3-2%5Calpha)*P_2.z-%5Calpha*P_3.z%5D%2B%5C%5C%20%5Cqquad%20t*(-%5Calpha*P_0.z%2B%5Calpha*P_2.z)%2BP_3.z%5Cend%7Bcases%7D$