# Math Function 中文介绍请跳往下面 **Bring mathematics to life in Minecraft with function-powered projectiles and graphs!** [![License](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0.html) [![GitHub Release](https://img.shields.io/github/v/release/aiLinMc/Math-Function)](https://github.com/aiLinMc/Math-Function/releases) [![GitHub code size in bytes](https://img.shields.io/github/languages/code-size/aiLinMc/Math-Function)](https://github.com/aiLinMc/Math-Function) --- ## 📖 Introduction Math Function is a **Minecraft NeoForge mod** that transforms mathematical expressions into interactive in-game experiences. Whether you want to visualize functions as block graphs or launch projectiles along custom curves, this mod brings the beauty of math directly into your world. ### Two Core Features in One Mod: **1. Block Graph Generation** – Visualize any function as a 3D block structure using a simple command. **2. Function Enchantment** – Apply custom mathematical trajectories to weapons and tools, turning arrows, TNT, fireworks, and even your own flight into controllable function curves! ### Supported Functions | Category | Functions | |----------|-----------| | Basic Arithmetic | `+` `-` `*` `/` | | Power | `^` (e.g. `x^2`) | | Unary Operator | `-x` (negative numbers) | | Trigonometry | `sin(x)` `cos(x)` `tan(x)` | | Logarithms | `log(x)` `ln(x)` `log(base, value)` `log2` `log10` | | Roots | `sqrt(x)` `sqrt(root, value)` (e.g. `sqrt(3, 27)` = cube root) | | Rounding | `floor(x)` (round down), `ceil(x)` (round up), `round(x)` (round to nearest), `trunc(x)` (remove decimal) | | Other | `abs(x)` `exp(x)` `min(a, b)` `max(a, b)` `mod(a, b)` | | Random | `Ran#` (0~1) `RanInt(min, max)` | | Constants | `e` `pi` | | Nesting | `3*x^2 + sin(2*x)` | ### Custom Functions Define your own reusable functions using the `/customfunction` command! This is perfect for complex expressions you use frequently. - **Add**: `/customfunction add ` – e.g. `/customfunction add square x^2` - **List**: `/customfunction list` – show all saved functions - **Get**: `/customfunction get ` – view a function's definition - **Eval**: `/customfunction eval ` – quickly compute a value - **Modify**: `/customfunction modify ` – update a function - **Remove**: `/customfunction remove ` – delete a function - **Remove all**: `/customfunction remove-all` – clear all (operator only) Custom functions are saved to `custom_functions.json` and persist across restarts. They can be used anywhere expressions are accepted: `/fx` commands, anvil renames, and enchantment trajectories. > **Note**: Function names cannot conflict with built-in functions (`sin`, `sqrt`, `log`, etc.), constants (`e`, `pi`), or the reserved name `f` (to avoid conflicts with the `f(x)=` prefix). --- ## 🧪 Block Graph Command ``` /fx "" [scale] [mode] [coordinateSystem] ``` **Parameters** | Parameter | Description | |---------------------|-----------------------------------------------------------------------------| | `expression` | Math expression in terms of `x` (e.g. `"x^2 + 3*x - 5"`). Supports `+ - * / ^ sin cos tan sqrt log ln`. | | `min_x`, `max_x` | Domain of the function (x values). | | `block` | Block to build the graph (e.g. `minecraft:red_concrete`). | | `scale` (optional) | How many blocks represent one unit (default = 1, range 1–10). | | `mode` (optional) | `stand` – vertical graph (Y = f(x)), `floor` – horizontal graph (Z = f(x)).| | `coordinateSystem` (optional) | `true` / `false` – whether to generate a quartz coordinate system (origin at (0,0), shifted 1 block left/down). | **Example** ``` /fx "x^2" -5 5 minecraft:blue_wool 2 stand true ``` > Creates a blue wool parabola from x=-5 to x=5, each unit = 2 blocks, with a coordinate system. --- ## ⚔️ Function Enchantment Rename any compatible item to `f(x)=expression` or `y=expression` (e.g. `f(x)=x^2`) and the enchantment will activate automatically. No command required – just rename the item in an anvil! ### Compatible Items & Behaviors | Item | Effect | |------|--------| | **Bow / Crossbow** | Arrows follow the function curve y = f(x), where x is horizontal distance and y is height relative to launch point. | | **Flint and Steel** | Lit TNT flies along the function curve before exploding. | | **Firework Rocket** | Fireworks glide along the curve and explode upon hitting blocks or entities. | | **Trident (with Riptide)** | Player flies along the function curve during water/rain dash – press jump key to stop anytime! | ### Example Usage 1. Get a bow and enchant it with the **Math Function** enchantment or obtain it via commands. 2. Rename the bow in an anvil to `f(x)=sin(x)*2`. 3. Shoot an arrow – it will fly in a beautiful sine wave! 4. For TNT: rename flint and steel to `y=cos(x)` and ignite TNT. 5. For tridents: rename a riptide trident to `f(x)=x^2/10` and dash through water! ### Technical Details - Initial height automatically set to f(0), ensuring constant functions work correctly. - Real-time numerical differentiation computes tangent velocity for smooth motion. - Collision detection prevents projectiles from going through blocks. - Cleanly reverts to vanilla physics when out of range, duration, or upon impact. - Supported since version 2.0, continuously improved with each release. --- ## ✨ Features - **Real‑time expression parsing** – Fast and reliable, no external libraries. - **Continuous graph lines** – Bresenham’s line algorithm fills gaps between sample points. - **Automatic discontinuity handling** – Breaks at invalid points (e.g. `1/x` near 0, `tan(x)` at asymptotes). - **Axis‑aligned placement** – Graph extends along the nearest cardinal direction based on where you look. - **Projectile trajectory** – Full function-based flight with particle trails and collision. - **Multi-shot compatibility** – Arrows spread slightly when using the Multishot enchantment. - **Safe by default** – Prevents rendering outside world height or exceeding performance limits. - **Player feedback** – Chat messages show expression, block name, execution time and origin coordinates. - **Custom functions** – Define and reuse your own math functions with the `/customfunction` command. --- ## 🧩 Requirements - **Minecraft**: 1.21.1 (NeoForge) - **NeoForge**: 21.1.176 or later --- ## 📦 Installation 1. Download the latest JAR from [Modrinth](https://modrinth.com/mod/math-function/versions) or [GitHub Releases](https://github.com/aiLinMc/Math-Function/releases). 2. Place it into your `mods` folder. 3. Launch Minecraft with NeoForge installed. 4. Start building graphs or launching function-powered projectiles! --- ## ⚖️ License This mod is released under the **GNU General Public License v3.0**. You may freely use, modify, and redistribute it, provided you share your changes under the same license. See the [LICENSE](https://github.com/aiLinMc/Math-Function/blob/main/LICENSE) file for details. --- ## 🔗 Links - [GitHub Repository](https://github.com/aiLinMc/Math-Function) - [Issue Tracker](https://github.com/aiLinMc/Math-Function/issues) - Releases: [GitHub](https://github.com/aiLinMc/Math-Function/releases), [Modrinth](https://modrinth.com/mod/math-function/versions) ---
# 中文介绍 ## 📖 概述 **Math Function** 是一个 Minecraft NeoForge 模组，将数学表达式转化为游戏中的交互体验。无论是用方块生成函数图像，还是让弹射物沿自定义曲线飞行，这个模组都能让数学的美丽直接展现在你的世界里。 ### 一个模组，两大核心功能： **1. 方块图像生成** – 通过简单的命令，将任意函数可视化为 3D 方块结构。 **2. 函数附魔** – 为武器和工具赋予数学轨迹，让箭矢、TNT、烟花火箭甚至你自身的飞行都变成可控的函数曲线！ ### 支持的函数 | 类别 | 函数 | |------|------| | 基础运算 | `+` `-` `*` `/` | | 幂运算 | `^`（如 `x^2`） | | 一元负号 | `-x`（负数） | | 三角函数 | `sin(x)` `cos(x)` `tan(x)` | | 对数 | `log(x)` `ln(x)` `log(底数, 真数)` `log2` `log10` | | 根号 | `sqrt(x)` `sqrt(根指数, 被开方数)`（如 `sqrt(3, 27)` = 27 的立方根） | | 取整 | `floor(x)`（向下取整），`ceil(x)`（向上取整），`round(x)`（四舍五入），`trunc(x)`（截断小数） | | 其他 | `abs(x)` `exp(x)` `min(a, b)` `max(a, b)` `mod(a, b)` | | 随机数 | `Ran#`（0~1 随机小数）`RanInt(min, max)`（指定范围随机整数） | | 常数 | `e` `pi` | | 嵌套 | `3*x^2 + sin(2*x)` | ### 自定义函数使用 `/customfunction` 命令创建自己的可复用函数！非常适合经常使用的复杂表达式。 - **添加**：`/customfunction add <名称> <表达式>` – 例如 `/customfunction add square x^2` - **列表**：`/customfunction list` – 显示所有已保存的函数 - **查看**：`/customfunction get <名称>` – 查看函数定义 - **计算**：`/customfunction eval <名称> ` – 快速计算函数值 - **修改**：`/customfunction modify <名称> <新表达式>` – 更新函数 - **删除**：`/customfunction remove <名称>` – 删除函数 - **全部删除**：`/customfunction remove-all` – 清空所有（需管理员权限）自定义函数保存在 `custom_functions.json` 文件中，重启后依然保留。它们可以在任何接受表达式的地方使用：`/fx` 命令、铁砧命名和附魔轨迹。 > **注意**：函数名称不能与内置函数（`sin`、`sqrt`、`log` 等）、常数（`e`、`pi`）或保留名称 `f`（避免与 `f(x)=` 前缀冲突）重名。 --- ## 🧪 方块图像命令 ``` /fx "<表达式>" <最小值_x> <最大值_x> <方块> [缩放] [模式] [坐标系] ``` **参数说明** | 参数 | 说明 | |----------------------|----------------------------------------------------------------------| | `表达式` | 以 `x` 为自变量的数学表达式，支持 `+ - * / ^ sin cos tan sqrt log ln` | | `最小值_x`，`最大值_x` | 定义域（x 的取值范围） | | `方块` | 构建图像所用的方块（如 `minecraft:red_concrete`） | | `缩放`（可选） | 1 个单位长度对应多少格，默认 1，范围 1~10 | | `模式`（可选） | `stand` – 竖立图像（Y = f(x)），`floor` – 平铺图像（Z = f(x)） | | `坐标系`（可选） | `true` / `false`，是否生成石英块坐标轴（原点位于 (0,0)，向左/下偏移 1 格） | **示例** ``` /fx "x^2" -5 5 minecraft:blue_wool 2 stand true ``` > 生成从 x=-5 到 x=5 的蓝色羊毛抛物线，每单位长度 = 2 格，并显示坐标系。 --- ## ⚔️ 函数附魔将任意兼容物品重命名为 `f(x)=表达式` 或 `y=表达式`（例如 `f(x)=x^2`），附魔会自动激活。无需命令，只需在铁砧中重命名即可！ ### 兼容物品与效果 | 物品 | 效果 | |------|------| | **弓 / 弩** | 箭矢沿函数曲线 y = f(x) 飞行，其中 x 为水平距离，y 为相对发射点的高度。 | | **打火石** | 点燃的 TNT 沿函数曲线飞行，碰撞后爆炸。 | | **烟花火箭** | 烟花沿曲线滑翔，碰到方块或实体时爆炸。 | | **三叉戟（激流附魔）** | 玩家在水中/雨中冲刺时沿函数曲线飞行 – 按下跳跃键可随时停止！ | | **其他弹射物（如雪球、鸡蛋等）** | 同样支持函数轨迹，重命名对应物品即可！ | ### 使用示例 1. 获取一把弓，并为其附魔**函数**或通过命令获取。 2. 在铁砧中将弓重命名为 `f(x)=sin(x)*2`。 3. 射出箭矢 – 它将沿美丽的正弦波飞行！ 4. TNT 用法：将打火石重命名为 `y=cos(x)`，然后点燃 TNT。 5. 三叉戟用法：将带有激流附魔的三叉戟重命名为 `f(x)=x^2/10`，在水中冲刺！ 6. 雪球用法：将雪球重命名为 `f(x)=sqrt(25-x^2)`，扔出后它会沿半圆形轨迹飞行！ ### 技术细节 - 起始高度自动设为 f(0)，确保常函数也能正常工作。 - 实时数值微分计算切线速度，实现平滑运动。 - 碰撞检测防止弹射物穿透方块。 - 超出范围、超时或撞击后自动恢复原版物理。 - 自 2.0 版本起支持，持续迭代优化。 --- ## ✨ 特色功能 - **实时表达式解析** – 快速可靠，无需外部库。 - **连续曲线图像** – 使用 Bresenham 直线算法填充采样点间隙。 - **自动处理间断点** – 遇到无效点（如 `1/x` 在 0 附近、`tan(x)` 的渐近线）自动断开。 - **沿轴向放置** – 图像根据玩家面朝方向自动对齐东南西北。 - **弹射物轨迹** – 完整的函数飞行，带有粒子尾迹和碰撞处理。 - **多重射击兼容** – 使用多重射击附魔时箭矢会略微分散。 - **默认安全机制** – 限制超出世界高度或性能开销过大的情况。 - **玩家反馈** – 聊天栏显示表达式、方块名称、执行耗时和原点坐标。 - **自定义函数** – 使用 `/customfunction` 命令定义和复用你自己的数学函数。 --- ## 🧩 运行要求 - **Minecraft 版本**：1.21.1（NeoForge） - **NeoForge 版本**：21.1.176 或更高 --- ## 📦 安装方法 1. 从 [Modrinth](https://modrinth.com/mod/math-function/versions) 或 [GitHub Releases](https://github.com/aiLinMc/Math-Function/releases) 下载最新 JAR 文件。 2. 放入你的 Minecraft `mods` 文件夹。 3. 确保已安装 NeoForge 并启动游戏。 4. 开始生成函数图像或发射函数弹射物！ --- ## ⚖️ 法律信息本模组采用 **GNU 通用公共许可证 v3.0** 发布。你可以自由使用、修改和重新分发，但必须同样以 GPLv3 许可证公开你的修改。详见 [LICENSE](https://github.com/aiLinMc/Math-Function/blob/main/LICENSE) 文件。 --- ## 🔗 相关链接 - [GitHub 仓库](https://github.com/aiLinMc/Math-Function) - [问题反馈](https://github.com/aiLinMc/Math-Function/issues) - 版本发布：[GitHub](https://github.com/aiLinMc/Math-Function/releases)，[Modrinth](https://modrinth.com/mod/math-function/versions)