《用MATLAB玩转游戏开发》打砖块：向量反射与实时物理模拟MATLAB教程

《用MATLAB玩转游戏开发：从零开始打造你的数字乐园》基础篇（2D图形交互）-《打砖块：向量反射与实时物理模拟》MATLAB教程 🎮

引言：从游戏到物理模拟

还记得小时候玩过的打砖块游戏吗？🎯 一个小球在屏幕上弹来弹去，击碎各种砖块，同时玩家控制一块挡板防止小球掉落。这看似简单的游戏背后，其实蕴含着丰富的物理和数学原理！今天，我们就用MATLAB来实现这个经典游戏，并深入探讨其中的向量反射和实时物理模拟技术。

通过本教程，你将学到：

• 向量运算在游戏物理中的应用
• 实时碰撞检测的实现方法
• MATLAB动画和交互式图形编程
• 游戏状态管理和逻辑控制

准备好你的MATLAB环境(2016b版本)，让我们开始这场有趣的编程之旅吧！🚀

1. 设计思路与游戏概述 🧠

打砖块游戏(Breakout/Arkanoid)是经典的街机游戏，包含以下核心元素：

• 一个由玩家控制的挡板(paddle)
• 一个运动的球(ball)
• 由砖块组成的墙(bricks)
• 边界(walls)

游戏目标是用挡板反弹球，消除所有砖块。每次球碰到砖块，砖块消失，玩家得分。

1.1 物理模型关键点 ⚛️

1. 碰撞检测：判断球与边界、挡板、砖块的接触
2. 反射计算：球碰到物体后的运动方向变化
3. 实时渲染：游戏画面的流畅更新
4. 游戏逻辑：得分、生命、胜负判断

2. 核心原理详解 🔍

2.1 向量反射原理 📐

球碰到平面后的反射遵循"入射角=反射角"原则。数学上可以用向量运算表示：

给定：

• 入射向量 v = [vx, vy]
• 法向量 n = [nx, ny] (垂直于反射平面)

反射向量 r 的计算公式为：
$$r=v-2(v\cdot n)n$$

在MATLAB中实现：

function reflectedVec = reflectVector(inVec, normalVec)% 归一化法向量normalVec = normalVec / norm(normalVec);% 计算反射向量reflectedVec = inVec - 2 * dot(inVec, normalVec) * normalVec;
end

2.2 碰撞检测原理 🔄

我们需要检测球与以下物体的碰撞：

1. 边界：比较球心坐标与边界位置
2. 挡板：判断球是否在挡板的矩形区域内
3. 砖块：类似挡板，但需要考虑砖块是否已被消除

2.3 游戏循环结构 🔁

标准游戏循环包含以下步骤：

1. 初始化：创建游戏对象和变量
2. 输入处理：读取玩家操作
3. 状态更新：计算物理和游戏逻辑
4. 渲染：绘制游戏画面
5. 循环控制：控制帧率和退出条件

3. 完整流程图 📊

4. 分步实现教程 🛠️

4.1 初始化设置

function breakoutGame()% 清除工作区和图形窗口clc; clear; close all;% 游戏参数设置gameParams = struct(...'paddleWidth', 100, ...    % 挡板宽度'paddleHeight', 15, ...    % 挡板高度'ballRadius', 10, ...      % 球半径'brickRows', 5, ...        % 砖块行数'brickCols', 10, ...       % 砖块列数'brickWidth', 60, ...      % 砖块宽度'brickHeight', 20, ...     % 砖块高度'brickOffsetTop', 50, ...  % 砖块顶部偏移'brickPadding', 5, ...     % 砖块间距'ballSpeed', 8, ...        % 球初始速度'lives', 3, ...            % 初始生命数'score', 0 ...             % 初始得分);% 创建图形窗口fig = figure('Name', 'MATLAB打砖块', ...'NumberTitle', 'off', ...'Position', [100, 100, 800, 600], ...'KeyPressFcn', @keyDown, ...'KeyReleaseFcn', @keyUp, ...'WindowButtonDownFcn', @mouseClick);% 创建坐标轴ax = axes('Parent', fig, ...'Position', [0.05, 0.05, 0.9, 0.9], ...'XLim', [0, 800], ...'YLim', [0, 600], ...'Color', [0.1, 0.1, 0.3], ...'XTick', [], ...'YTick', []);hold(ax, 'on');axis equal;

4.2 创建游戏对象

    % 创建挡板paddle = rectangle('Parent', ax, ...'Position', [350, 30, gameParams.paddleWidth, gameParams.paddleHeight], ...'FaceColor', [0.8, 0.2, 0.2], ...'EdgeColor', 'none', ...'Curvature', [0.2, 0.2]);% 创建球theta = rand * 2 * pi;  % 随机初始角度ballVel = [gameParams.ballSpeed * cos(theta), gameParams.ballSpeed * sin(theta)];ball = rectangle('Parent', ax, ...'Position', [400, 200, gameParams.ballRadius*2, gameParams.ballRadius*2], ...'FaceColor', [0.9, 0.9, 0.1], ...'EdgeColor', 'none', ...'Curvature', [1, 1]);% 创建砖块bricks = gobjects(gameParams.brickRows, gameParams.brickCols);brickColors = hsv(gameParams.brickRows);  % 每行不同颜色for r = 1:gameParams.brickRowsfor c = 1:gameParams.brickColsbrickX = (c-1) * (gameParams.brickWidth + gameParams.brickPadding);brickY = 550 - (r-1) * (gameParams.brickHeight + gameParams.brickPadding);bricks(r,c) = rectangle('Parent', ax, ...'Position', [brickX, brickY, gameParams.brickWidth, gameParams.brickHeight], ...'FaceColor', brickColors(r,:), ...'EdgeColor', 'w');endend% 创建文本显示scoreText = text(ax, 20, 580, sprintf('得分: %d', gameParams.score), ...'Color', 'w', 'FontSize', 12);livesText = text(ax, 700, 580, sprintf('生命: %d', gameParams.lives), ...'Color', 'w', 'FontSize', 12);startText = text(ax, 400, 300, '点击开始游戏', ...'Color', 'w', 'FontSize', 24, ...'HorizontalAlignment', 'center');

4.3 游戏主循环

    % 游戏状态变量gameState = struct(...'isRunning', false, ...    % 游戏是否进行中'paddleDir', 0, ...        % 挡板移动方向 (-1:左, 0:停止, 1:右)'paddleSpeed', 15, ...     % 挡板移动速度'activeBricks', true(gameParams.brickRows, gameParams.brickCols) ... % 活跃砖块);% 键盘控制回调函数function keyDown(~, event)switch event.Keycase 'leftarrow'gameState.paddleDir = -1;case 'rightarrow'gameState.paddleDir = 1;case 'escape'gameState.isRunning = false;endendfunction keyUp(~, event)switch event.Keycase {'leftarrow', 'rightarrow'}gameState.paddleDir = 0;endend% 鼠标点击开始游戏function mouseClick(~, ~)if ~gameState.isRunninggameState.isRunning = true;delete(startText);startText = [];endend% 主游戏循环while ishandle(fig)if gameState.isRunning% 更新挡板位置paddlePos = get(paddle, 'Position');newX = paddlePos(1) + gameState.paddleSpeed * gameState.paddleDir;% 限制挡板不超出边界newX = max(0, min(newX, 800 - gameParams.paddleWidth));set(paddle, 'Position', [newX, paddlePos(2), paddlePos(3), paddlePos(4)]);% 更新球位置ballPos = get(ball, 'Position');newBallX = ballPos(1) + ballVel(1);newBallY = ballPos(2) + ballVel(2);% 检测碰撞[ballVel, gameParams, gameState] = checkCollisions(...[newBallX, newBallY], ballVel, gameParams, gameState, paddle, bricks);% 更新球位置set(ball, 'Position', [newBallX, newBallY, ballPos(3), ballPos(4)]);% 更新文本显示set(scoreText, 'String', sprintf('得分: %d', gameParams.score));set(livesText, 'String', sprintf('生命: %d', gameParams.lives));% 检查游戏结束条件if newBallY < 0  % 球落到底部gameParams.lives = gameParams.lives - 1;if gameParams.lives <= 0gameState.isRunning = false;text(ax, 400, 300, '游戏结束!', ...'Color', 'r', 'FontSize', 36, ...'HorizontalAlignment', 'center');else% 重置球位置set(ball, 'Position', [400, 200, gameParams.ballRadius*2, gameParams.ballRadius*2]);theta = rand * 2 * pi;ballVel = [gameParams.ballSpeed * cos(theta), gameParams.ballSpeed * sin(theta)];pause(1);endend% 检查胜利条件if ~any(gameState.activeBricks(:))gameState.isRunning = false;text(ax, 400, 300, '恭喜通关!', ...'Color', 'g', 'FontSize', 36, ...'HorizontalAlignment', 'center');endend% 控制帧率pause(0.02);end

4.4 碰撞检测函数

function [newVel, gameParams, gameState] = checkCollisions(ballPos, ballVel, gameParams, gameState, paddle, bricks)% 获取球参数ballX = ballPos(1) + gameParams.ballRadius;ballY = ballPos(2) + gameParams.ballRadius;% 边界碰撞检测if ballX <= gameParams.ballRadius || ballX >= 800 - gameParams.ballRadiusballVel(1) = -ballVel(1);  % 水平反转endif ballY >= 600 - gameParams.ballRadiusballVel(2) = -ballVel(2);  % 垂直反转end% 挡板碰撞检测paddlePos = get(paddle, 'Position');if ballY <= paddlePos(2) + paddlePos(4) + gameParams.ballRadius && ...ballY >= paddlePos(2) && ...ballX >= paddlePos(1) - gameParams.ballRadius && ...ballX <= paddlePos(1) + paddlePos(3) + gameParams.ballRadius% 计算碰撞点相对于挡板中心的位置 (-1到1)hitPos = (ballX - (paddlePos(1) + paddlePos(3)/2)) / (paddlePos(3)/2);% 根据碰撞点调整反射角度maxAngle = pi/3;  % 最大反射角度 (60度)angle = hitPos * maxAngle;% 计算新速度向量speed = norm(ballVel);ballVel = [speed * sin(angle), speed * cos(angle)];% 增加一点速度让游戏更有挑战性ballVel = ballVel * 1.02;end% 砖块碰撞检测for r = 1:gameParams.brickRowsfor c = 1:gameParams.brickColsif gameState.activeBricks(r,c)brickPos = get(bricks(r,c), 'Position');% 检查球是否与砖块相交if ballX + gameParams.ballRadius > brickPos(1) && ...ballX - gameParams.ballRadius < brickPos(1) + brickPos(3) && ...ballY + gameParams.ballRadius > brickPos(2) && ...ballY - gameParams.ballRadius < brickPos(2) + brickPos(4)% 确定碰撞边 (简化版)if ballY < brickPos(2) || ballY > brickPos(2) + brickPos(4)ballVel(2) = -ballVel(2);  % 上下碰撞elseballVel(1) = -ballVel(1);  % 左右碰撞end% 标记砖块为不活跃并隐藏gameState.activeBricks(r,c) = false;set(bricks(r,c), 'Visible', 'off');% 增加分数gameParams.score = gameParams.score + 10;% 只需要处理一次碰撞break;endendendendnewVel = ballVel;
end

5. 完整可运行代码 🏆

将以下所有代码段按顺序组合成一个.m文件即可运行：

function breakoutGame()% 清除工作区和图形窗口clc; clear; close all;% 游戏参数设置gameParams = struct(...'paddleWidth', 100, ...    % 挡板宽度'paddleHeight', 15, ...    % 挡板高度'ballRadius', 10, ...      % 球半径'brickRows', 5, ...        % 砖块行数'brickCols', 10, ...       % 砖块列数'brickWidth', 60, ...      % 砖块宽度'brickHeight', 20, ...     % 砖块高度'brickOffsetTop', 50, ...  % 砖块顶部偏移'brickPadding', 5, ...     % 砖块间距'ballSpeed', 8, ...        % 球初始速度'lives', 3, ...            % 初始生命数'score', 0 ...             % 初始得分);% 创建图形窗口fig = figure('Name', 'MATLAB打砖块', ...'NumberTitle', 'off', ...'Position', [100, 100, 800, 600], ...'KeyPressFcn', @keyDown, ...'KeyReleaseFcn', @keyUp, ...'WindowButtonDownFcn', @mouseClick);% 创建坐标轴ax = axes('Parent', fig, ...'Position', [0.05, 0.05, 0.9, 0.9], ...'XLim', [0, 800], ...'YLim', [0, 600], ...'Color', [0.1, 0.1, 0.3], ...'XTick', [], ...'YTick', []);hold(ax, 'on');axis equal;% 创建挡板paddle = rectangle('Parent', ax, ...'Position', [350, 30, gameParams.paddleWidth, gameParams.paddleHeight], ...'FaceColor', [0.8, 0.2, 0.2], ...'EdgeColor', 'none', ...'Curvature', [0.2, 0.2]);% 创建球theta = rand * 2 * pi;  % 随机初始角度ballVel = [gameParams.ballSpeed * cos(theta), gameParams.ballSpeed * sin(theta)];ball = rectangle('Parent', ax, ...'Position', [400, 200, gameParams.ballRadius*2, gameParams.ballRadius*2], ...'FaceColor', [0.9, 0.9, 0.1], ...'EdgeColor', 'none', ...'Curvature', [1, 1]);% 创建砖块bricks = gobjects(gameParams.brickRows, gameParams.brickCols);brickColors = hsv(gameParams.brickRows);  % 每行不同颜色for r = 1:gameParams.brickRowsfor c = 1:gameParams.brickColsbrickX = (c-1) * (gameParams.brickWidth + gameParams.brickPadding);brickY = 550 - (r-1) * (gameParams.brickHeight + gameParams.brickPadding);bricks(r,c) = rectangle('Parent', ax, ...'Position', [brickX, brickY, gameParams.brickWidth, gameParams.brickHeight], ...'FaceColor', brickColors(r,:), ...'EdgeColor', 'w');endend% 创建文本显示scoreText = text(ax, 20, 580, sprintf('得分: %d', gameParams.score), ...'Color', 'w', 'FontSize', 12);livesText = text(ax, 700, 580, sprintf('生命: %d', gameParams.lives), ...'Color', 'w', 'FontSize', 12);startText = text(ax, 400, 300, '点击开始游戏', ...'Color', 'w', 'FontSize', 24, ...'HorizontalAlignment', 'center');% 游戏状态变量gameState = struct(...'isRunning', false, ...    % 游戏是否进行中'paddleDir', 0, ...        % 挡板移动方向 (-1:左, 0:停止, 1:右)'paddleSpeed', 15, ...     % 挡板移动速度'activeBricks', true(gameParams.brickRows, gameParams.brickCols) ... % 活跃砖块);% 键盘控制回调函数function keyDown(~, event)switch event.Keycase 'leftarrow'gameState.paddleDir = -1;case 'rightarrow'gameState.paddleDir = 1;case 'escape'gameState.isRunning = false;endendfunction keyUp(~, event)switch event.Keycase {'leftarrow', 'rightarrow'}gameState.paddleDir = 0;endend% 鼠标点击开始游戏function mouseClick(~, ~)if ~gameState.isRunninggameState.isRunning = true;delete(startText);startText = [];endend% 主游戏循环while ishandle(fig)if gameState.isRunning% 更新挡板位置paddlePos = get(paddle, 'Position');newX = paddlePos(1) + gameState.paddleSpeed * gameState.paddleDir;% 限制挡板不超出边界newX = max(0, min(newX, 800 - gameParams.paddleWidth));set(paddle, 'Position', [newX, paddlePos(2), paddlePos(3), paddlePos(4)]);% 更新球位置ballPos = get(ball, 'Position');newBallX = ballPos(1) + ballVel(1);newBallY = ballPos(2) + ballVel(2);% 检测碰撞[ballVel, gameParams, gameState] = checkCollisions(...[newBallX, newBallY], ballVel, gameParams, gameState, paddle, bricks);% 更新球位置set(ball, 'Position', [newBallX, newBallY, ballPos(3), ballPos(4)]);% 更新文本显示set(scoreText, 'String', sprintf('得分: %d', gameParams.score));set(livesText, 'String', sprintf('生命: %d', gameParams.lives));% 检查游戏结束条件if newBallY < 0  % 球落到底部gameParams.lives = gameParams.lives - 1;if gameParams.lives <= 0gameState.isRunning = false;text(ax, 400, 300, '游戏结束!', ...'Color', 'r', 'FontSize', 36, ...'HorizontalAlignment', 'center');else% 重置球位置set(ball, 'Position', [400, 200, gameParams.ballRadius*2, gameParams.ballRadius*2]);theta = rand * 2 * pi;ballVel = [gameParams.ballSpeed * cos(theta), gameParams.ballSpeed * sin(theta)];pause(1);endend% 检查胜利条件if ~any(gameState.activeBricks(:))gameState.isRunning = false;text(ax, 400, 300, '恭喜通关!', ...'Color', 'g', 'FontSize', 36, ...'HorizontalAlignment', 'center');endend% 控制帧率pause(0.02);end% 碰撞检测函数function [newVel, gameParams, gameState] = checkCollisions(ballPos, ballVel, gameParams, gameState, paddle, bricks)% 获取球参数ballX = ballPos(1) + gameParams.ballRadius;ballY = ballPos(2) + gameParams.ballRadius;% 边界碰撞检测if ballX <= gameParams.ballRadius || ballX >= 800 - gameParams.ballRadiusballVel(1) = -ballVel(1);  % 水平反转endif ballY >= 600 - gameParams.ballRadiusballVel(2) = -ballVel(2);  % 垂直反转end% 挡板碰撞检测paddlePos = get(paddle, 'Position');if ballY <= paddlePos(2) + paddlePos(4) + gameParams.ballRadius && ...ballY >= paddlePos(2) && ...ballX >= paddlePos(1) - gameParams.ballRadius && ...ballX <= paddlePos(1) + paddlePos(3) + gameParams.ballRadius% 计算碰撞点相对于挡板中心的位置 (-1到1)hitPos = (ballX - (paddlePos(1) + paddlePos(3)/2)) / (paddlePos(3)/2);% 根据碰撞点调整反射角度maxAngle = pi/3;  % 最大反射角度 (60度)angle = hitPos * maxAngle;% 计算新速度向量speed = norm(ballVel);ballVel = [speed * sin(angle), speed * cos(angle)];% 增加一点速度让游戏更有挑战性ballVel = ballVel * 1.02;end% 砖块碰撞检测for r = 1:gameParams.brickRowsfor c = 1:gameParams.brickColsif gameState.activeBricks(r,c)brickPos = get(bricks(r,c), 'Position');% 检查球是否与砖块相交if ballX + gameParams.ballRadius > brickPos(1) && ...ballX - gameParams.ballRadius < brickPos(1) + brickPos(3) && ...ballY + gameParams.ballRadius > brickPos(2) && ...ballY - gameParams.ballRadius < brickPos(2) + brickPos(4)% 确定碰撞边 (简化版)if ballY < brickPos(2) || ballY > brickPos(2) + brickPos(4)ballVel(2) = -ballVel(2);  % 上下碰撞elseballVel(1) = -ballVel(1);  % 左右碰撞end% 标记砖块为不活跃并隐藏gameState.activeBricks(r,c) = false;set(bricks(r,c), 'Visible', 'off');% 增加分数gameParams.score = gameParams.score + 10;% 只需要处理一次碰撞break;endendendendnewVel = ballVel;end
end

来看看我这个菜鸡玩了一局的效果，屏幕前的你也可以试试看看能的多少分～

6. 游戏操作说明 🎮

• 左右箭头键：移动挡板
• ESC键：退出游戏
• 鼠标点击：开始游戏

7. 扩展思路 💡

如果你想进一步提升这个游戏，可以考虑：

1. 增加音效：使用audioplayer添加碰撞音效
2. 多种砖块：不同颜色砖块需要多次击中才能消除
3. 特殊道具：球碰到某些砖块会掉落道具，如加长挡板、额外生命等
4. 关卡设计：设计不同布局的砖块排列
5. 粒子效果：砖块消除时添加爆炸效果

希望你喜欢这个MATLAB打砖块游戏教程！通过这个项目，你不仅学会了向量反射的原理，还掌握了实时物理模拟和游戏开发的基本技巧。Happy coding! 🚀