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function trigger(el, eventType) {
  if (typeof eventType === 'string' && typeof el[eventType] === 'function') {
    el[eventType]();
  } else {
    const event =
      eventType === 'string'
        ? new Event(eventType, {bubbles: true})
        : eventType;
    el.dispatchEvent(event);
  }

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Let $N$ to be normal of plane decided by $a$ and $b$, where $N$ is at the side so that it has the minimal angle between the input normal. Let $angle$ be the unsigned angle between $a$ and $b$. Around $N$, following the right hand rule, if $a$ can rotate to $b$ in positive $angle$ angle, then the result is $angle$. Otherwise, the result is $-angle$.

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Let $b$ be the inverse of $a$, then for the translation term $T$(Vector), rotation term $Q$(Quaternion), scale term $S$(Vector):

$$\begin{equation} \begin{split} T_(a * b) & = T_b + (Q_b \times (S_b \times T_a) \times Q_b^{-1}) = 0 \\\ T(b) & = -(Q_b \times S_b \times T_a \times Q_b^{-1}) \\\ & = Q_b \times (S_b \times -T_a) \times Q_b^{-1} \end{split} \end{equation}$$

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import bpy

def print(data):
    for window in bpy.context.window_manager.windows:
        screen = window.screen
        for area in screen.areas:
            if area.type == 'CONSOLE':
                override = {'window': window, 'screen': screen, 'area': area}
                bpy.ops.console.scrollback_append(override, text=str(data), type="OUTPUT")
                

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import { clamp, Node, NodeSpace, Quat, Vec3 } from "cc";

/**
 * 解析双骨骼（三关节）的 IK 问题。
 * 三关节分别称为根关节、中间关节和末端关节。例如，分别对应于大腿、膝盖和脚关节。
 * @param root 根关节。
 * @param middle 中间关节。
 * @param end 末端关节。
 * @param target 末端关节要抵达的目标位置（世界空间）。
 * @param hint 中间关节的提示位置（世界空间），用于决定中间关节的朝向。

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export function solveTwoBoneIK(
    a: Node,
    b: Node,
    c: Node,
    target: Vec3,
) {
    const sanityChecker = new TwoBoneIKNodeSanityChecker(a, b, c);

    const pA = Vec3.clone(a.worldPosition);
    const pB = Vec3.clone(b.worldPosition);

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Abstract

In our engine, bones exist in form of scene node. We can't tell if a node denotes a bone or not. This sometimes becomes obstacle in animation system.

Problem Statement

Obstacles

Why do we need to distinguish bone nodes from normal? I'll list some cases.

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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\begin{document}

Let RS(denoted as $R$) be "rotation then scale". \\

RS then translation(denoted as $t$):

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也就是说，下面两种算法是等价的，我们不需要遍历两遍：

// 预先累加权重和
function blend(samples: ReadonlyArray<readonly [value: number, weight: number]>) {
  let result = 0.0;
  let sumWeights = 0.0;
  for (const [v, w] of samples) {

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• elementary

• rudimentary

• feasible

• viable

• impair

• interconnect