feat(football): implement World Cup 2026 simulator and Empirical-Poisson Mixture Model

- Implement dynamic SEO meta tags and sitemap.xml for toolbox.pengzhan.dev
- Fix SPA title/meta refresh issue in layout.html
- Address golangci-lint findings:
  - Refactor switch-case for tool path and SVG token parsing
  - Replace math.Pow with direct multiplication for performance
  - Fix unhandled error returns and unused imports
  - Omit redundant type declarations

.gitignore

@@ -1,4 +1,5 @@
 # Binaries
+build/
 toolbox
 *.exe
 *.exe~

cmd/toolbox/main.go

@@ -4,6 +4,7 @@ import (
 	"bytes"
 	"embed"
 	"flag"
+	"fmt"
 	"html/template"
 	"io/fs"
 	"log"
@@ -12,6 +13,7 @@ import (
 	"sort"
 	"strconv"
 	"toolbox/pkg/base"
+	_ "toolbox/pkg/football"
 	_ "toolbox/pkg/learnnumber"
 	_ "toolbox/pkg/zitie" // 匿名导入以触发 init()
 
@@ -56,6 +58,23 @@ func main() {
 	subFS, _ := fs.Sub(webFS, "web")
 	r.StaticFS("/static", http.FS(subFS))
 
+	// 2.5 SEO 静态文件映射
+	r.GET("/robots.txt", func(c *gin.Context) {
+		c.String(http.StatusOK, "User-agent: *\nAllow: /\nSitemap: https://toolbox.pengzhan.dev/sitemap.xml\n")
+	})
+	r.GET("/sitemap.xml", func(c *gin.Context) {
+		var buf bytes.Buffer
+		buf.WriteString("<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n")
+		buf.WriteString("<urlset xmlns=\"http://www.sitemaps.org/schemas/sitemap/0.9\">\n")
+		buf.WriteString("  <url><loc>https://toolbox.pengzhan.dev/</loc><priority>1.0</priority></url>\n")
+
+		// 动态根据注册的工具生成路由
+		for id := range base.Registry {
+			fmt.Fprintf(&buf, "  <url><loc>https://toolbox.pengzhan.dev/%s</loc><priority>0.8</priority></url>\n", id)
+		}
+		buf.WriteString("</urlset>")
+		c.Data(http.StatusOK, "application/xml; charset=utf-8", buf.Bytes())
+	})
 	// 3. 模板引擎初始化
 	// 递归加载 web 目录下所有的 .html 文件
 	tmpl, err := template.ParseFS(subFS, "layout.html", "index.html", "tools/*.html")
@@ -65,9 +84,34 @@ func main() {
 
 	// 通用页面渲染函数
 	serveIndex := func(c *gin.Context) {
+		path := c.Request.URL.Path
+		title := "探索工具箱"
+		desc := "基于 Go 语言构建的模块化个人工具箱，提供汉字字帖生成、数字学习等多种实用生产力工具。"
+		keywords := "个人工具箱, 汉字字帖生成, 书法练习, 数字学习, Own-Tools"
+		baseURL := "https://toolbox.pengzhan.dev"
+		canonical := baseURL + path
+		// 针对不同路径设置 SEO 标签
+		switch path {
+		case "/zitie":
+			title = "汉字字帖生成器 - 教学方格与步进式分解"
+			desc = "在线生成 2x3 教学方格字帖和 9 列步进式笔顺分解字帖，支持多种书法字体和古风排版。"
+			keywords = "字帖生成, 笔顺分解, 汉字教学, 书法字帖, 练字"
+		case "/learn-number":
+			title = "趣味数字学习工具"
+			desc = "为儿童设计的数字学习与计数练习工具，生动活泼，寓教于乐。"
+			keywords = "数字学习, 儿童计数, 幼小衔接"
+		case "/football":
+			title = "2026世界杯小组出线模拟器 - 蒙特卡洛预测"
+			desc = "使用蒙特卡洛算法模拟2026年美加墨世界杯小组赛出线概率，支持自定义比赛概率、小组球队及已有赛果。"
+			keywords = "2026世界杯, 小组出线概率, 蒙特卡洛模拟, 足球预测"
+		}
+
 		data := gin.H{
-			"Title": "Own-Tools",
-			"GA_ID": gaID,
+			"Title":        title,
+			"Description":  desc,
+			"Keywords":     keywords,
+			"CanonicalURL": canonical,
+			"GA_ID":        gaID,
 		}
 
 		var buf bytes.Buffer
@@ -78,12 +122,13 @@ func main() {
 		}
 		c.Data(http.StatusOK, "text/html; charset=utf-8", buf.Bytes())
 	}
-
 	r.GET("/", serveIndex)
 	r.GET("/api/tools", func(c *gin.Context) {
 		var list []map[string]string
 		ids := make([]string, 0, len(base.Registry))
-		for id := range base.Registry { ids = append(ids, id) }
+		for id := range base.Registry {
+			ids = append(ids, id)
+		}
 		sort.Strings(ids)
 
 		for _, id := range ids {

cmd/toolbox/main_test.go

@@ -0,0 +1,160 @@
+package main
+
+import (
+	"bytes"
+	"encoding/json"
+	"fmt"
+	"net/http"
+	"os"
+	"os/exec"
+	"testing"
+	"time"
+)
+
+const (
+	testPort = "9999"
+	baseURL  = "http://localhost:" + testPort
+)
+
+func TestToolboxE2E(t *testing.T) {
+	// 1. Build the binary
+	fmt.Println("--- Step 1: Building binary... ---")
+	_ = os.MkdirAll("build", 0755)
+	buildPath := "build/toolbox_test_bin"
+	buildCmd := exec.Command("go", "build", "-o", buildPath, "main.go")
+	if err := buildCmd.Run(); err != nil {
+		t.Fatalf("Failed to build binary: %v", err)
+	}
+	defer func() { _ = os.Remove(buildPath) }()
+
+	// 2. Start the server
+	fmt.Println("--- Step 2: Starting server... ---")
+	serverCmd := exec.Command("./"+buildPath, "-port", testPort)
+	if err := serverCmd.Start(); err != nil {
+		t.Fatalf("Failed to start server: %v", err)
+	}
+	defer func() {
+		if serverCmd.Process != nil {
+			_ = serverCmd.Process.Kill()
+		}
+	}()
+
+	// 3. Wait for server to be ready
+	fmt.Println("--- Step 3: Waiting for server readiness... ---")
+	ready := false
+	for i := 0; i < 10; i++ {
+		resp, err := http.Get(baseURL + "/api/tools")
+		if err == nil && resp.StatusCode == http.StatusOK {
+			ready = true
+			_ = resp.Body.Close()
+			break
+		}
+		time.Sleep(500 * time.Millisecond)
+	}
+	if !ready {
+		t.Fatal("Server failed to become ready in time")
+	}
+
+	// 4. Test endpoints
+	fmt.Println("--- Step 4: Testing tool endpoints... ---")
+
+	testOutputDir, err := os.MkdirTemp("", "toolbox_test_output_*")
+	if err != nil {
+		t.Fatalf("Failed to create temp dir: %v", err)
+	}
+	fmt.Printf("--- Test Artifacts will be saved to: %s ---\n", testOutputDir)
+
+	tests := []struct {
+		name     string
+		path     string
+		method   string
+		fileName string
+		body     interface{}
+	}{
+		{
+			name:     "Zitie Teaching",
+			path:     "/api/zitie/teaching",
+			method:   "POST",
+			fileName: "zitie_teaching.pdf",
+			body:     map[string]string{"chars": "永和九年", "paper_size": "A4"},
+		},
+		{
+			name:     "Zitie Step",
+			path:     "/api/zitie/step",
+			method:   "POST",
+			fileName: "zitie_step.pdf",
+			body:     map[string]string{"chars": "永", "paper_size": "A4"},
+		},
+		{
+			name:     "Zitie Manuscript",
+			path:     "/api/zitie/manuscript",
+			method:   "POST",
+			fileName: "zitie_manuscript.pdf",
+			body:     map[string]string{"chars": "天道酬勤", "paper_size": "A4", "font_type": "kaiti"},
+		},
+		{
+			name:     "Learn Number Counting",
+			path:     "/api/learn-number/counting",
+			method:   "POST",
+			fileName: "counting.pdf",
+			body:     map[string]interface{}{"page_count": 1, "paper_size": "A4"},
+		},
+		{
+			name:     "Learn Number Writing",
+			path:     "/api/learn-number/writing",
+			method:   "POST",
+			fileName: "writing.pdf",
+			body:     map[string]interface{}{"start_num": 1, "end_num": 5, "paper_size": "A4"},
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			var resp *http.Response
+			var err error
+
+			if tt.method == "POST" {
+				b, _ := json.Marshal(tt.body)
+				resp, err = http.Post(baseURL+tt.path, "application/json", bytes.NewBuffer(b))
+			} else {
+				resp, err = http.Get(baseURL + tt.path)
+			}
+
+			if err != nil {
+				t.Errorf("%s failed: %v", tt.name, err)
+				return
+			}
+			defer func() { _ = resp.Body.Close() }()
+
+			if resp.StatusCode != http.StatusOK {
+				t.Errorf("%s returned status %d", tt.name, resp.StatusCode)
+				return
+			}
+
+			contentType := resp.Header.Get("Content-Type")
+			if contentType != "application/pdf" {
+				t.Errorf("%s expected application/pdf, got %s", tt.name, contentType)
+			} else {
+				// Save PDF to temp directory for human review
+				outPath := testOutputDir + "/" + tt.fileName
+				f, err := os.Create(outPath)
+				if err != nil {
+					t.Errorf("Failed to create output file: %v", err)
+					return
+				}
+				defer func() { _ = f.Close() }()
+
+				_, err = f.ReadFrom(resp.Body)
+
+				if err != nil {
+					t.Errorf("Failed to save PDF: %v", err)
+					return
+				}
+
+				fmt.Printf("[PASS] %s: Saved to %s\n", tt.name, outPath)
+			}
+		})
+	}
+
+	fmt.Printf("\n--- ALL TESTS DONE. PLEASE REVIEW PDFS IN: %s ---\n", testOutputDir)
+}

cmd/toolbox/web/index.html

@@ -14,6 +14,7 @@
 <!-- Tools Panels Containers -->
 {{template "zitie" .}}
 {{template "learn_number" .}}
+{{template "football" .}}
 
 <script>
     // 首页 Tile 渲染

cmd/toolbox/web/layout.html

@@ -4,6 +4,24 @@
     <meta charset="UTF-8">
     <meta name="viewport" content="width=device-width, initial-scale=1.0">
     <title>{{.Title}} | Own-Tools</title>
+    <meta name="description" content="{{.Description}}">
+    <meta name="keywords" content="{{.Keywords}}">
+    <link rel="canonical" href="{{.CanonicalURL}}">
+
+    <!-- Open Graph / Facebook -->
+    <meta property="og:type" content="website">
+    <meta property="og:url" content="{{.CanonicalURL}}">
+    <meta property="og:title" content="{{.Title}} | Own-Tools">
+    <meta property="og:description" content="{{.Description}}">
+    <meta property="og:image" content="/static/og-image.png">
+
+    <!-- Twitter -->
+    <meta property="twitter:card" content="summary_large_image">
+    <meta property="twitter:url" content="{{.CanonicalURL}}">
+    <meta property="twitter:title" content="{{.Title}} | Own-Tools">
+    <meta property="twitter:description" content="{{.Description}}">
+    <meta property="twitter:image" content="/static/og-image.png">
+
     <link rel="icon" type="image/svg+xml" href="data:image/svg+xml,<svg xmlns=%22http://www.w3.org/2000/svg%22 viewBox=%220 0 100 100%22><text y=%22.9em%22 font-size=%2290%22>🖋️</text></svg>">
     
     {{if .GA_ID}}
@@ -126,10 +144,46 @@
             renderCurrentPath();
         }
 
+        const metaConfig = {
+            'welcome': {
+                title: '探索工具箱',
+                desc: '基于 Go 语言构建的模块化个人工具箱，提供汉字字帖生成、数字学习等多种实用生产力工具。',
+                keywords: '个人工具箱, 汉字字帖生成, 书法练习, 数字学习, Own-Tools'
+            },
+            'zitie': {
+                title: '汉字字帖生成器 - 教学方格与步进式分解',
+                desc: '在线生成 2x3 教学方格字帖和 9 列步进式笔顺分解字帖，支持多种书法字体和古风排版。',
+                keywords: '字帖生成, 笔顺分解, 汉字教学, 书法字帖, 练字'
+            },
+            'learn-number': {
+                title: '趣味数字学习工具',
+                desc: '为儿童设计的数字学习与计数练习工具，生动活泼，寓教力乐。',
+                keywords: '数字学习, 儿童计数, 幼小衔接'
+            },
+            'football': {
+                title: '2026世界杯小组出线模拟器',
+                desc: '使用蒙特卡洛算法模拟2026年美加墨世界杯小组赛出线概率，支持自定义比赛概率、小组球队及已有赛果。',
+                keywords: '2026世界杯, 小组出线概率, 蒙特卡洛模拟, 足球预测'
+            }
+        };
+
         function renderCurrentPath() {
             const path = window.location.pathname.replace('/', '') || 'welcome';
             
-            // 隐藏所有面板
+            // 1. 更新标题与元数据
+            const meta = metaConfig[path] || metaConfig['welcome'];
+            document.title = `${meta.title} | Own-Tools`;
+            document.querySelector('meta[name="description"]').setAttribute('content', meta.desc);
+            document.querySelector('meta[name="keywords"]').setAttribute('content', meta.keywords);
+            
+            // 更新 Open Graph 标签 (可选，社交分享主要看服务端渲染)
+            const canonical = `https://toolbox.pengzhan.dev/${path === 'welcome' ? '' : path}`;
+            document.querySelector('link[rel="canonical"]').setAttribute('href', canonical);
+            document.querySelector('meta[property="og:title"]').setAttribute('content', `${meta.title} | Own-Tools`);
+            document.querySelector('meta[property="og:description"]').setAttribute('content', meta.desc);
+            document.querySelector('meta[property="og:url"]').setAttribute('content', canonical);
+
+            // 2. 隐藏所有面板
             document.querySelectorAll('.tool-panel').forEach(p => p.classList.remove('active'));
             
             // 显示目标面板

pkg/football/logic/models.go

@@ -0,0 +1,44 @@
+package logic
+
+// Team represents a football team.
+type Team struct {
+	Name  string `json:"name"`
+	Group string `json:"group"` // e.g., "A", "B", ..., "L"
+}
+
+// Match represents a group stage match between two teams.
+type Match struct {
+	TeamA       string `json:"team_a"`
+	TeamB       string `json:"team_b"`
+	IsCompleted bool   `json:"is_completed"`
+	ScoreA      int    `json:"score_a"`
+	ScoreB      int    `json:"score_b"`
+}
+
+// ScoreOutcome represents a possible match score and its probability.
+type ScoreOutcome struct {
+	ScoreA      int     `json:"score_a"`
+	ScoreB      int     `json:"score_b"`
+	Probability float64 `json:"probability"`
+}
+
+// TeamStats holds the metrics used to rank teams within a group or across third-place teams.
+type TeamStats struct {
+	TeamName       string
+	Points         int
+	GoalDifference int
+	GoalsScored    int
+	// Fields used for tie-breaking comparison within the group
+	H2HPoints int
+	H2HGD     int
+	H2HGS     int
+}
+
+// TeamProbability represents the calculated qualification probabilities for a single team.
+type TeamProbability struct {
+	TeamName       string  `json:"team_name"`
+	Group          string  `json:"group"`
+	DirectQualProb float64 `json:"direct_qual_prob"`
+	ThirdQualProb  float64 `json:"third_qual_prob"`
+	TotalQualProb  float64 `json:"total_qual_prob"`
+}

pkg/football/logic/score_model.go

@@ -0,0 +1,191 @@
+package logic
+
+import (
+	"math"
+	"math/rand"
+	"sync"
+)
+
+// RawScoreRecord represents the raw statistics for a scoreline in football history.
+type RawScoreRecord struct {
+	GoalsA int `json:"goals_a"`
+	GoalsB int `json:"goals_b"`
+	Count  int `json:"count"`
+}
+
+// WorldCupRawScores represents the actual historical frequencies of scorelines
+// in the FIFA World Cup history (964 matches from 1930 to 2022).
+var WorldCupRawScores = []RawScoreRecord{
+	{GoalsA: 1, GoalsB: 0, Count: 182},
+	{GoalsA: 2, GoalsB: 1, Count: 152},
+	{GoalsA: 2, GoalsB: 0, Count: 111},
+	{GoalsA: 1, GoalsB: 1, Count: 92},
+	{GoalsA: 0, GoalsB: 0, Count: 78},
+	{GoalsA: 3, GoalsB: 1, Count: 68},
+	{GoalsA: 3, GoalsB: 0, Count: 57},
+	{GoalsA: 3, GoalsB: 2, Count: 43},
+	{GoalsA: 2, GoalsB: 2, Count: 35},
+	{GoalsA: 4, GoalsB: 1, Count: 31},
+	{GoalsA: 4, GoalsB: 0, Count: 24},
+	{GoalsA: 4, GoalsB: 2, Count: 17},
+	{GoalsA: 6, GoalsB: 1, Count: 11},
+	{GoalsA: 5, GoalsB: 2, Count: 9},
+	{GoalsA: 5, GoalsB: 0, Count: 7},
+	{GoalsA: 3, GoalsB: 3, Count: 7},
+	{GoalsA: 5, GoalsB: 1, Count: 7},
+	{GoalsA: 6, GoalsB: 0, Count: 5},
+	{GoalsA: 7, GoalsB: 0, Count: 5},
+	{GoalsA: 4, GoalsB: 3, Count: 3},
+	{GoalsA: 7, GoalsB: 1, Count: 3},
+	{GoalsA: 8, GoalsB: 1, Count: 3},
+	{GoalsA: 4, GoalsB: 4, Count: 2},
+	{GoalsA: 6, GoalsB: 3, Count: 2},
+	{GoalsA: 9, GoalsB: 0, Count: 2},
+	{GoalsA: 5, GoalsB: 3, Count: 1},
+	{GoalsA: 6, GoalsB: 2, Count: 1},
+	{GoalsA: 7, GoalsB: 2, Count: 1},
+	{GoalsA: 7, GoalsB: 3, Count: 1},
+	{GoalsA: 6, GoalsB: 5, Count: 1},
+	{GoalsA: 8, GoalsB: 3, Count: 1},
+	{GoalsA: 10, GoalsB: 1, Count: 1},
+	{GoalsA: 7, GoalsB: 5, Count: 1},
+}
+
+// poissonProbability computes the Poisson probability P(k; lambda).
+func poissonProbability(lambda float64, k int) float64 {
+	factorial := 1.0
+	for i := 1; i <= k; i++ {
+		factorial *= float64(i)
+	}
+	return (math.Pow(lambda, float64(k)) * math.Exp(-lambda)) / factorial
+}
+
+// DefaultScoreOutcomes returns the symmetric default probability distribution based on WorldCupRawScores.
+func DefaultScoreOutcomes() []ScoreOutcome {
+	var totalGoals int
+	var totalMatches int
+	for _, r := range WorldCupRawScores {
+		totalGoals += (r.GoalsA + r.GoalsB) * r.Count
+		totalMatches += r.Count
+	}
+
+	if totalMatches == 0 {
+		return []ScoreOutcome{{ScoreA: 1, ScoreB: 1, Probability: 1.0}}
+	}
+
+	// 1. Calculate expected goals per team (lambda)
+	lambda := float64(totalGoals) / (2.0 * float64(totalMatches))
+
+	// 2. Compute Poisson 1D and 2D probabilities (up to MaxGoals = 10)
+	maxGoals := 10
+	poisson1D := make([]float64, maxGoals+1)
+	var sumP float64
+	for g := 0; g <= maxGoals; g++ {
+		p := poissonProbability(lambda, g)
+		poisson1D[g] = p
+		sumP += p
+	}
+	for g := 0; g <= maxGoals; g++ {
+		poisson1D[g] /= sumP
+	}
+
+	// 3. Build Empirical 2D map
+	type scoreKey struct {
+		goalsA int
+		goalsB int
+	}
+	empirical := make(map[scoreKey]float64)
+	for _, r := range WorldCupRawScores {
+		if r.GoalsA <= maxGoals && r.GoalsB <= maxGoals {
+			prob := float64(r.Count) / float64(totalMatches)
+			if r.GoalsA == r.GoalsB {
+				empirical[scoreKey{r.GoalsA, r.GoalsB}] = prob
+			} else {
+				empirical[scoreKey{r.GoalsA, r.GoalsB}] = prob / 2.0
+				empirical[scoreKey{r.GoalsB, r.GoalsA}] = prob / 2.0
+			}
+		}
+	}
+
+	// 4. Combine into Mixture Model (alpha = 0.99)
+	alpha := 0.99
+	var outcomes []ScoreOutcome
+	for ga := 0; ga <= maxGoals; ga++ {
+		for gb := 0; gb <= maxGoals; gb++ {
+			pPoisson := poisson1D[ga] * poisson1D[gb]
+			pEmpirical := empirical[scoreKey{ga, gb}]
+			pMix := alpha*pEmpirical + (1.0-alpha)*pPoisson
+
+			outcomes = append(outcomes, ScoreOutcome{
+				ScoreA:      ga,
+				ScoreB:      gb,
+				Probability: pMix,
+			})
+		}
+	}
+
+	// Normalize just in case of float64 precision drift
+	var sumMix float64
+	for _, o := range outcomes {
+		sumMix += o.Probability
+	}
+	for i := range outcomes {
+		outcomes[i].Probability /= sumMix
+	}
+
+	return outcomes
+}
+
+// ScoreModel holds the probability distribution used to sample random scores.
+type ScoreModel struct {
+	Outcomes []ScoreOutcome
+	mu       sync.RWMutex
+}
+
+// NewScoreModel creates a ScoreModel from custom score outcomes.
+// If customOutcomes is empty, it uses DefaultScoreOutcomes().
+func NewScoreModel(customOutcomes []ScoreOutcome) *ScoreModel {
+	sm := &ScoreModel{}
+	if len(customOutcomes) > 0 {
+		// Normalize custom outcomes to ensure they sum to 1.0
+		var sum float64
+		for _, o := range customOutcomes {
+			sum += o.Probability
+		}
+		if sum > 0 {
+			normalized := make([]ScoreOutcome, len(customOutcomes))
+			for i, o := range customOutcomes {
+				normalized[i] = ScoreOutcome{
+					ScoreA:      o.ScoreA,
+					ScoreB:      o.ScoreB,
+					Probability: o.Probability / sum,
+				}
+			}
+			sm.Outcomes = normalized
+			return sm
+		}
+	}
+	sm.Outcomes = DefaultScoreOutcomes()
+	return sm
+}
+
+// RandomScore samples a random score outcome based on the probability distribution.
+func (sm *ScoreModel) RandomScore(r *rand.Rand) ScoreOutcome {
+	sm.mu.RLock()
+	outcomes := sm.Outcomes
+	sm.mu.RUnlock()
+
+	if len(outcomes) == 0 {
+		return ScoreOutcome{ScoreA: 0, ScoreB: 0, Probability: 1.0}
+	}
+
+	p := r.Float64()
+	var cumulative float64
+	for _, outcome := range outcomes {
+		cumulative += outcome.Probability
+		if p <= cumulative {
+			return outcome
+		}
+	}
+	return outcomes[len(outcomes)-1]
+}

pkg/football/logic/simulator.go

@@ -0,0 +1,125 @@
+package logic
+
+import (
+	"math/rand"
+	"sort"
+	"time"
+)
+
+// RunMonteCarlo runs a Monte Carlo simulation of the remaining matches.
+// Returns a slice of TeamProbability sorted by Group and then by TotalQualProb descending.
+func RunMonteCarlo(teams []Team, matches []Match, scoreOutcomes []ScoreOutcome, numSimulations int) []TeamProbability {
+	if numSimulations <= 0 {
+		numSimulations = 50000
+	}
+	r := rand.New(rand.NewSource(time.Now().UnixNano()))
+	sm := NewScoreModel(scoreOutcomes)
+
+	// Map teams to groups
+	teamGroups := make(map[string]string)
+	groupsTeams := make(map[string][]string)
+	for _, t := range teams {
+		teamGroups[t.Name] = t.Group
+		groupsTeams[t.Group] = append(groupsTeams[t.Group], t.Name)
+	}
+
+	directCounts := make(map[string]int)
+	thirdCounts := make(map[string]int)
+
+	// Separate completed and uncompleted matches
+	var completed []Match
+	var uncompleted []Match
+	for _, m := range matches {
+		if m.IsCompleted {
+			completed = append(completed, m)
+		} else {
+			uncompleted = append(uncompleted, m)
+		}
+	}
+
+	for sim := 0; sim < numSimulations; sim++ {
+		// Clone completed matches and simulate uncompleted ones
+		simMatches := make([]Match, len(completed)+len(uncompleted))
+		copy(simMatches, completed)
+
+		for i, m := range uncompleted {
+			outcome := sm.RandomScore(r)
+			simMatches[len(completed)+i] = Match{
+				TeamA:       m.TeamA,
+				TeamB:       m.TeamB,
+				IsCompleted: true,
+				ScoreA:      outcome.ScoreA,
+				ScoreB:      outcome.ScoreB,
+			}
+		}
+
+		// Calculate standings for each group
+		thirdPlaced := make([]*TeamStats, 0, 12)
+		for grp, grpTeams := range groupsTeams {
+			var grpMatches []Match
+			for _, m := range simMatches {
+				if teamGroups[m.TeamA] == grp && teamGroups[m.TeamB] == grp {
+					grpMatches = append(grpMatches, m)
+				}
+			}
+
+			// Shuffle group teams to randomize tie-breaks in SortGroupStandings
+			shuffledGrpTeams := make([]string, len(grpTeams))
+			copy(shuffledGrpTeams, grpTeams)
+			r.Shuffle(len(shuffledGrpTeams), func(i, j int) {
+				shuffledGrpTeams[i], shuffledGrpTeams[j] = shuffledGrpTeams[j], shuffledGrpTeams[i]
+			})
+
+			standings := CalculateStandings(shuffledGrpTeams, grpMatches)
+			// Top 2 qualify directly
+			if len(standings) > 0 {
+				directCounts[standings[0].TeamName]++
+			}
+			if len(standings) > 1 {
+				directCounts[standings[1].TeamName]++
+			}
+			// 3rd placed team goes to the pool
+			if len(standings) > 2 {
+				thirdPlaced = append(thirdPlaced, standings[2])
+			}
+		}
+
+		// Shuffle third-placed list to randomize cross-group tie-breaks in CompareThirdPlaced
+		r.Shuffle(len(thirdPlaced), func(i, j int) {
+			thirdPlaced[i], thirdPlaced[j] = thirdPlaced[j], thirdPlaced[i]
+		})
+
+		CompareThirdPlaced(thirdPlaced)
+		limit := 8
+		if len(thirdPlaced) < limit {
+			limit = len(thirdPlaced)
+		}
+		for i := 0; i < limit; i++ {
+			thirdCounts[thirdPlaced[i].TeamName]++
+		}
+	}
+
+	// Build result slice
+	res := make([]TeamProbability, 0, len(teams))
+	for _, t := range teams {
+		dQual := float64(directCounts[t.Name]) / float64(numSimulations)
+		tQual := float64(thirdCounts[t.Name]) / float64(numSimulations)
+		res = append(res, TeamProbability{
+			TeamName:       t.Name,
+			Group:          t.Group,
+			DirectQualProb: dQual,
+			ThirdQualProb:  tQual,
+			TotalQualProb:  dQual + tQual,
+		})
+	}
+
+	// Sort results by Group name first, then by TotalQualProb descending
+	sort.Slice(res, func(i, j int) bool {
+		if res[i].Group != res[j].Group {
+			return res[i].Group < res[j].Group
+		}
+		return res[i].TotalQualProb > res[j].TotalQualProb
+	})
+
+	return res
+}

pkg/football/logic/simulator_test.go

@@ -0,0 +1,54 @@
+package logic
+
+import (
+	"testing"
+)
+
+func TestCalculateStandings(t *testing.T) {
+	teams := []string{"MEX", "RSA", "KOR", "CZE"}
+	matches := []Match{
+		{TeamA: "MEX", TeamB: "RSA", IsCompleted: true, ScoreA: 2, ScoreB: 0}, // MEX: 3 pts, RSA: 0 pts
+		{TeamA: "KOR", TeamB: "CZE", IsCompleted: true, ScoreA: 2, ScoreB: 1}, // KOR: 3 pts, CZE: 0 pts
+	}
+
+	standings := CalculateStandings(teams, matches)
+	if len(standings) != 4 {
+		t.Fatalf("expected 4 teams, got %d", len(standings))
+	}
+
+	// MEX and KOR should be top 2
+	if standings[0].TeamName != "MEX" && standings[0].TeamName != "KOR" {
+		t.Errorf("expected MEX or KOR as first, got %s", standings[0].TeamName)
+	}
+}
+
+func TestRunMonteCarlo(t *testing.T) {
+	teams := []Team{
+		{Name: "MEX", Group: "A"},
+		{Name: "RSA", Group: "A"},
+		{Name: "KOR", Group: "A"},
+		{Name: "CZE", Group: "A"},
+	}
+	matches := []Match{
+		{TeamA: "MEX", TeamB: "RSA", IsCompleted: true, ScoreA: 2, ScoreB: 0},
+		{TeamA: "KOR", TeamB: "CZE", IsCompleted: true, ScoreA: 2, ScoreB: 1},
+		{TeamA: "CZE", TeamB: "RSA", IsCompleted: false},
+		{TeamA: "MEX", TeamB: "KOR", IsCompleted: false},
+		{TeamA: "MEX", TeamB: "CZE", IsCompleted: false},
+		{TeamA: "KOR", TeamB: "RSA", IsCompleted: false},
+	}
+
+	// We only simulate Group A here (4 teams, 6 matches total).
+	// Note: 3rd place comparison won't succeed in putting any team to top 8 of third placed
+	// unless there are other groups, but it shouldn't crash.
+	probs := RunMonteCarlo(teams, matches, nil, 100)
+	if len(probs) != 4 {
+		t.Fatalf("expected probabilities for 4 teams, got %d", len(probs))
+	}
+
+	for _, p := range probs {
+		if p.TotalQualProb < 0 || p.TotalQualProb > 1.0 {
+			t.Errorf("invalid total qual probability for %s: %f", p.TeamName, p.TotalQualProb)
+		}
+	}
+}

pkg/football/logic/standings.go

@@ -0,0 +1,161 @@
+package logic
+
+import (
+	"sort"
+)
+
+// CalculateStandings computes the stats for each team in a group given the match results.
+func CalculateStandings(teams []string, matches []Match) []*TeamStats {
+	statsMap := make(map[string]*TeamStats)
+	for _, t := range teams {
+		statsMap[t] = &TeamStats{TeamName: t}
+	}
+
+	for _, m := range matches {
+		if !m.IsCompleted {
+			continue
+		}
+		sa, sb := statsMap[m.TeamA], statsMap[m.TeamB]
+		if sa == nil || sb == nil {
+			continue
+		}
+
+		sa.GoalsScored += m.ScoreA
+		sa.GoalDifference += m.ScoreA - m.ScoreB
+		sb.GoalsScored += m.ScoreB
+		sb.GoalDifference += m.ScoreB - m.ScoreA
+
+		if m.ScoreA > m.ScoreB {
+			sa.Points += 3
+		} else if m.ScoreA < m.ScoreB {
+			sb.Points += 3
+		} else {
+			sa.Points += 1
+			sb.Points += 1
+		}
+	}
+
+	res := make([]*TeamStats, 0, len(teams))
+	for _, s := range statsMap {
+		res = append(res, s)
+	}
+
+	// Sort the standings
+	SortGroupStandings(res, matches)
+	return res
+}
+
+// SortGroupStandings sorts the teams in a group based on the tie-breaking rules.
+func SortGroupStandings(teams []*TeamStats, matches []Match) {
+	sort.Slice(teams, func(i, j int) bool {
+		ti, tj := teams[i], teams[j]
+
+		// 1. Points
+		if ti.Points != tj.Points {
+			return ti.Points > tj.Points
+		}
+
+		// 2. Goal Difference
+		if ti.GoalDifference != tj.GoalDifference {
+			return ti.GoalDifference > tj.GoalDifference
+		}
+
+		// 3. Goals Scored
+		if ti.GoalsScored != tj.GoalsScored {
+			return ti.GoalsScored > tj.GoalsScored
+		}
+
+		// 4-6. Head-to-Head (H2H)
+		// We dynamically compute H2H stats for all teams that are tied on Points, GD, and GS.
+		// Since we are sorting, we can check the relationship between ti and tj.
+		// First find all teams tied with ti and tj.
+		tiedTeams := []string{}
+		for _, t := range teams {
+			if t.Points == ti.Points && t.GoalDifference == ti.GoalDifference && t.GoalsScored == ti.GoalsScored {
+				tiedTeams = append(tiedTeams, t.TeamName)
+			}
+		}
+
+		if len(tiedTeams) > 1 {
+			h2hStats := computeH2H(tiedTeams, matches)
+			h2hi := h2hStats[ti.TeamName]
+			h2hj := h2hStats[tj.TeamName]
+
+			if h2hi != nil && h2hj != nil {
+				// H2H Points
+				if h2hi.Points != h2hj.Points {
+					return h2hi.Points > h2hj.Points
+				}
+				// H2H GD
+				if h2hi.GoalDifference != h2hj.GoalDifference {
+					return h2hi.GoalDifference > h2hj.GoalDifference
+				}
+				// H2H GS
+				if h2hi.GoalsScored != h2hj.GoalsScored {
+					return h2hi.GoalsScored > h2hj.GoalsScored
+				}
+			}
+		}
+
+		// 7. No fallback (retains the shuffled input order to randomize tie-breaks in Monte Carlo)
+		return false
+	})
+}
+
+// computeH2H calculates Points, GD, and GS only considering matches between the specified tied teams.
+func computeH2H(tiedTeams []string, matches []Match) map[string]*TeamStats {
+	statsMap := make(map[string]*TeamStats)
+	isTied := make(map[string]bool)
+	for _, t := range tiedTeams {
+		statsMap[t] = &TeamStats{TeamName: t}
+		isTied[t] = true
+	}
+
+	for _, m := range matches {
+		if !m.IsCompleted {
+			continue
+		}
+		if isTied[m.TeamA] && isTied[m.TeamB] {
+			sa, sb := statsMap[m.TeamA], statsMap[m.TeamB]
+			sa.GoalsScored += m.ScoreA
+			sa.GoalDifference += m.ScoreA - m.ScoreB
+			sb.GoalsScored += m.ScoreB
+			sb.GoalDifference += m.ScoreB - m.ScoreA
+
+			if m.ScoreA > m.ScoreB {
+				sa.Points += 3
+			} else if m.ScoreA < m.ScoreB {
+				sb.Points += 3
+			} else {
+				sa.Points += 1
+				sb.Points += 1
+			}
+		}
+	}
+	return statsMap
+}
+
+// CompareThirdPlaced ranks the third-placed teams across groups.
+func CompareThirdPlaced(thirdTeams []*TeamStats) {
+	sort.Slice(thirdTeams, func(i, j int) bool {
+		ti, tj := thirdTeams[i], thirdTeams[j]
+
+		// 1. Points
+		if ti.Points != tj.Points {
+			return ti.Points > tj.Points
+		}
+
+		// 2. Goal Difference
+		if ti.GoalDifference != tj.GoalDifference {
+			return ti.GoalDifference > tj.GoalDifference
+		}
+
+		// 3. Goals Scored
+		if ti.GoalsScored != tj.GoalsScored {
+			return ti.GoalsScored > tj.GoalsScored
+		}
+
+		// 4. No fallback (retains the shuffled input order to randomize tie-breaks in Monte Carlo)
+		return false
+	})
+}

pkg/football/tool.go

@@ -0,0 +1,211 @@
+package football
+
+import (
+	"fmt"
+	"net/http"
+	"toolbox/pkg/base"
+	"toolbox/pkg/football/logic"
+
+	"github.com/gin-gonic/gin"
+)
+
+type footballTool struct{}
+
+func init() {
+	base.Register(&footballTool{})
+}
+
+func (t *footballTool) ID() string   { return "football" }
+func (t *footballTool) Name() string { return "足球概率模拟" }
+func (t *footballTool) Description() string {
+	return "使用蒙特卡洛算法模拟2026年美加墨世界杯小组赛阶段的出线概率"
+}
+func (t *footballTool) Emoji() string { return "⚽" }
+
+func (t *footballTool) Init() error {
+	fmt.Println("Initializing Football Tool...")
+	return nil
+}
+
+func (t *footballTool) RegisterRoutes(r *gin.RouterGroup) {
+	r.GET("/defaults", t.handleDefaults)
+	r.POST("/simulate", t.handleSimulate)
+}
+
+type SimulateRequest struct {
+	Groups           map[string][]string  `json:"groups"`
+	CompletedMatches []logic.Match        `json:"completed_matches"`
+	ScoreOutcomes    []logic.ScoreOutcome `json:"score_outcomes"`
+	Simulations      int                  `json:"simulations"`
+}
+
+func (t *footballTool) handleDefaults(c *gin.Context) {
+	defaultGroups := map[string][]string{
+		"A": {"MEX", "RSA", "KOR", "CZE"},
+		"B": {"CAN", "QAT", "SUI", "BIH"},
+		"C": {"BRA", "MAR", "HAI", "SCO"},
+		"D": {"USA", "PAR", "AUS", "TUR"},
+		"E": {"GER", "CUW", "CIV", "ECU"},
+		"F": {"NED", "JPN", "TUN", "SWE"},
+		"G": {"BEL", "EGY", "IRN", "NZL"},
+		"H": {"ESP", "KSA", "URU", "CPV"},
+		"I": {"FRA", "SEN", "IRQ", "NOR"},
+		"J": {"ARG", "ALG", "AUT", "JOR"},
+		"K": {"POR", "COL", "UZB", "COD"},
+		"L": {"ENG", "CRO", "GHA", "PAN"},
+	}
+
+	defaultMatches := []logic.Match{
+		// === ROUND 1 ===
+		{TeamA: "MEX", TeamB: "RSA", IsCompleted: true, ScoreA: 2, ScoreB: 0}, // Group A
+		{TeamA: "KOR", TeamB: "CZE", IsCompleted: true, ScoreA: 2, ScoreB: 1}, // Group A
+		{TeamA: "CAN", TeamB: "BIH", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group B
+		{TeamA: "USA", TeamB: "PAR", IsCompleted: true, ScoreA: 4, ScoreB: 1}, // Group D
+		{TeamA: "QAT", TeamB: "SUI", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group B
+		{TeamA: "BRA", TeamB: "MAR", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group C
+		{TeamA: "SCO", TeamB: "HAI", IsCompleted: true, ScoreA: 1, ScoreB: 0}, // Group C
+		{TeamA: "AUS", TeamB: "TUR", IsCompleted: true, ScoreA: 2, ScoreB: 0}, // Group D
+		{TeamA: "GER", TeamB: "CUW", IsCompleted: true, ScoreA: 7, ScoreB: 1}, // Group E
+		{TeamA: "NED", TeamB: "JPN", IsCompleted: true, ScoreA: 2, ScoreB: 2}, // Group F
+		{TeamA: "CIV", TeamB: "ECU", IsCompleted: true, ScoreA: 1, ScoreB: 0}, // Group E
+		{TeamA: "SWE", TeamB: "TUN", IsCompleted: true, ScoreA: 5, ScoreB: 1}, // Group F
+		{TeamA: "ESP", TeamB: "CPV", IsCompleted: true, ScoreA: 0, ScoreB: 0}, // Group H
+		{TeamA: "BEL", TeamB: "EGY", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group G
+		{TeamA: "KSA", TeamB: "URU", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group H
+		{TeamA: "IRN", TeamB: "NZL", IsCompleted: true, ScoreA: 2, ScoreB: 2}, // Group G
+		{TeamA: "FRA", TeamB: "SEN", IsCompleted: true, ScoreA: 3, ScoreB: 1}, // Group I
+		{TeamA: "IRQ", TeamB: "NOR", IsCompleted: true, ScoreA: 1, ScoreB: 4}, // Group I
+		{TeamA: "ARG", TeamB: "ALG", IsCompleted: true, ScoreA: 3, ScoreB: 0}, // Group J
+		{TeamA: "AUT", TeamB: "JOR", IsCompleted: true, ScoreA: 3, ScoreB: 1}, // Group J
+		{TeamA: "POR", TeamB: "COD", IsCompleted: true, ScoreA: 1, ScoreB: 1}, // Group K
+		{TeamA: "ENG", TeamB: "CRO", IsCompleted: true, ScoreA: 4, ScoreB: 2}, // Group L
+		{TeamA: "GHA", TeamB: "PAN", IsCompleted: true, ScoreA: 1, ScoreB: 0}, // Group L
+		{TeamA: "UZB", TeamB: "COL", IsCompleted: true, ScoreA: 1, ScoreB: 3}, // Group K
+
+		// === ROUND 2 ===
+		{TeamA: "CZE", TeamB: "RSA", IsCompleted: true, ScoreA: 1, ScoreB: 1},  // Group A
+		{TeamA: "SUI", TeamB: "BIH", IsCompleted: true, ScoreA: 4, ScoreB: 1},  // Group B
+		{TeamA: "CAN", TeamB: "QAT", IsCompleted: true, ScoreA: 6, ScoreB: 0},  // Group B
+		{TeamA: "MEX", TeamB: "KOR", IsCompleted: true, ScoreA: 1, ScoreB: 0},  // Group A
+		{TeamA: "USA", TeamB: "AUS", IsCompleted: true, ScoreA: 2, ScoreB: 0},  // Group D
+		{TeamA: "SCO", TeamB: "MAR", IsCompleted: false, ScoreA: 0, ScoreB: 1}, // Group C
+		{TeamA: "BRA", TeamB: "HAI", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group C
+		{TeamA: "TUR", TeamB: "PAR", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group D
+		{TeamA: "NED", TeamB: "SWE", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group F
+		{TeamA: "GER", TeamB: "CIV", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group E
+		{TeamA: "ECU", TeamB: "CUW", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group E
+		{TeamA: "TUN", TeamB: "JPN", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group F
+		{TeamA: "ESP", TeamB: "KSA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group H
+		{TeamA: "BEL", TeamB: "IRN", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group G
+		{TeamA: "URU", TeamB: "CPV", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group H
+		{TeamA: "NZL", TeamB: "EGY", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group G
+		{TeamA: "ARG", TeamB: "AUT", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group J
+		{TeamA: "FRA", TeamB: "IRQ", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group I
+		{TeamA: "NOR", TeamB: "SEN", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group I
+		{TeamA: "JOR", TeamB: "ALG", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group J
+		{TeamA: "POR", TeamB: "UZB", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group K
+		{TeamA: "ENG", TeamB: "GHA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group L
+		{TeamA: "PAN", TeamB: "CRO", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group L
+		{TeamA: "COL", TeamB: "COD", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group K
+
+		// === ROUND 3 ===
+		{TeamA: "SUI", TeamB: "CAN", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group B
+		{TeamA: "BIH", TeamB: "QAT", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group B
+		{TeamA: "SCO", TeamB: "BRA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group C
+		{TeamA: "MAR", TeamB: "HAI", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group C
+		{TeamA: "CZE", TeamB: "MEX", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group A
+		{TeamA: "RSA", TeamB: "KOR", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group A
+		{TeamA: "CUW", TeamB: "CIV", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group E
+		{TeamA: "ECU", TeamB: "GER", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group E
+		{TeamA: "JPN", TeamB: "SWE", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group F
+		{TeamA: "TUN", TeamB: "NED", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group F
+		{TeamA: "TUR", TeamB: "USA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group D
+		{TeamA: "PAR", TeamB: "AUS", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group D
+		{TeamA: "NOR", TeamB: "FRA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group I
+		{TeamA: "SEN", TeamB: "IRQ", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group I
+		{TeamA: "CPV", TeamB: "KSA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group H
+		{TeamA: "URU", TeamB: "ESP", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group H
+		{TeamA: "EGY", TeamB: "IRN", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group G
+		{TeamA: "NZL", TeamB: "BEL", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group G
+		{TeamA: "PAN", TeamB: "ENG", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group L
+		{TeamA: "CRO", TeamB: "GHA", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group L
+		{TeamA: "COL", TeamB: "POR", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group K
+		{TeamA: "COD", TeamB: "UZB", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group K
+		{TeamA: "ALG", TeamB: "AUT", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group J
+		{TeamA: "JOR", TeamB: "ARG", IsCompleted: false, ScoreA: 0, ScoreB: 0}, // Group J
+	}
+
+	c.JSON(http.StatusOK, gin.H{
+		"groups":            defaultGroups,
+		"completed_matches": defaultMatches,
+		"score_outcomes":    logic.DefaultScoreOutcomes(),
+	})
+}
+
+func (t *footballTool) handleSimulate(c *gin.Context) {
+	var req SimulateRequest
+	if err := c.ShouldBindJSON(&req); err != nil {
+		c.JSON(http.StatusBadRequest, gin.H{"error": err.Error()})
+		return
+	}
+
+	if len(req.Groups) == 0 {
+		c.JSON(http.StatusBadRequest, gin.H{"error": "Groups map cannot be empty"})
+		return
+	}
+
+	// Reconstruct Teams
+	var teams []logic.Team
+	for grp, grpTeams := range req.Groups {
+		for _, teamName := range grpTeams {
+			teams = append(teams, logic.Team{Name: teamName, Group: grp})
+		}
+	}
+
+	// Generate all group matches (completed + uncompleted)
+	var allMatches []logic.Match
+	for _, grpTeams := range req.Groups {
+		for i := 0; i < len(grpTeams); i++ {
+			for j := i + 1; j < len(grpTeams); j++ {
+				tA := grpTeams[i]
+				tB := grpTeams[j]
+
+				// Check if this match is completed in input
+				isCompleted := false
+				scoreA, scoreB := 0, 0
+				for _, cm := range req.CompletedMatches {
+					if !cm.IsCompleted {
+						continue
+					}
+					if cm.TeamA == tA && cm.TeamB == tB {
+						isCompleted = true
+						scoreA = cm.ScoreA
+						scoreB = cm.ScoreB
+						break
+					} else if cm.TeamA == tB && cm.TeamB == tA {
+						isCompleted = true
+						scoreA = cm.ScoreB
+						scoreB = cm.ScoreA
+						break
+					}
+				}
+
+				allMatches = append(allMatches, logic.Match{
+					TeamA:       tA,
+					TeamB:       tB,
+					IsCompleted: isCompleted,
+					ScoreA:      scoreA,
+					ScoreB:      scoreB,
+				})
+			}
+		}
+	}
+
+	sims := req.Simulations
+	if sims <= 0 {
+		sims = 50000
+	}
+
+	results := logic.RunMonteCarlo(teams, allMatches, req.ScoreOutcomes, sims)
+	c.JSON(http.StatusOK, results)
+}

pkg/football/tool_test.go

@@ -0,0 +1,87 @@
+package football
+
+import (
+	"bytes"
+	"encoding/json"
+	"net/http"
+	"net/http/httptest"
+	"testing"
+	"toolbox/pkg/football/logic"
+
+	"github.com/gin-gonic/gin"
+)
+
+func TestFootballToolRoutes(t *testing.T) {
+	// Set Gin to test mode
+	gin.SetMode(gin.TestMode)
+
+	// Create test router and register routes
+	r := gin.New()
+	api := r.Group("/api/football")
+	tool := &footballTool{}
+	tool.RegisterRoutes(api)
+
+	// 1. Test /api/football/defaults
+	reqDefaults, _ := http.NewRequest(http.MethodGet, "/api/football/defaults", nil)
+	respDefaults := httptest.NewRecorder()
+	r.ServeHTTP(respDefaults, reqDefaults)
+
+	if respDefaults.Code != http.StatusOK {
+		t.Fatalf("expected status 200 OK for defaults, got %d", respDefaults.Code)
+	}
+
+	var defaults struct {
+		Groups           map[string][]string  `json:"groups"`
+		CompletedMatches []logic.Match        `json:"completed_matches"`
+		ScoreOutcomes    []logic.ScoreOutcome `json:"score_outcomes"`
+	}
+
+	if err := json.Unmarshal(respDefaults.Body.Bytes(), &defaults); err != nil {
+		t.Fatalf("failed to parse defaults JSON response: %v", err)
+	}
+
+	if len(defaults.Groups) != 12 {
+		t.Errorf("expected 12 groups, got %d", len(defaults.Groups))
+	}
+	if len(defaults.CompletedMatches) == 0 {
+		t.Errorf("expected completed matches in default configuration")
+	}
+
+	// 2. Test /api/football/simulate
+	simReq := SimulateRequest{
+		Groups:           defaults.Groups,
+		CompletedMatches: defaults.CompletedMatches,
+		ScoreOutcomes:    defaults.ScoreOutcomes,
+		Simulations:      100, // run a small number for fast test
+	}
+
+	reqBody, _ := json.Marshal(simReq)
+	reqSim, _ := http.NewRequest(http.MethodPost, "/api/football/simulate", bytes.NewBuffer(reqBody))
+	reqSim.Header.Set("Content-Type", "application/json")
+	respSim := httptest.NewRecorder()
+	r.ServeHTTP(respSim, reqSim)
+
+	if respSim.Code != http.StatusOK {
+		t.Fatalf("expected status 200 OK for simulate, got %d. Body: %s", respSim.Code, respSim.Body.String())
+	}
+
+	var results []logic.TeamProbability
+	if err := json.Unmarshal(respSim.Body.Bytes(), &results); err != nil {
+		t.Fatalf("failed to parse simulate JSON response: %v", err)
+	}
+
+	if len(results) != 48 {
+		t.Errorf("expected 48 team probabilities, got %d", len(results))
+	}
+
+	// Sum of TotalQualProb across all 48 teams should be exactly 32.0
+	var sum float64
+	for _, r := range results {
+		sum += r.TotalQualProb
+	}
+
+	// Because of floating point representation it should be extremely close to 32.0
+	if sum < 31.9 || sum > 32.1 {
+		t.Errorf("expected sum of probabilities to be 32.0, got %f", sum)
+	}
+}

pkg/learnnumber/logic/counting.go

@@ -7,7 +7,6 @@ import (
 	"regexp"
 	"strconv"
 	"strings"
-	"time"
 	"toolbox/pkg/learnnumber/data"
 
 	"github.com/signintech/gopdf"
@@ -33,15 +32,20 @@ type PathResult struct {
 var reSVGToken = regexp.MustCompile(`[a-zA-Z]|-?\d+\.?\d*`)
 
 func GenerateCountingPDF(req CountingRequest) ([]byte, error) {
-	rand.Seed(time.Now().UnixNano())
 	pdf := &gopdf.GoPdf{}
 	rect := gopdf.Rect{W: 595.28, H: 841.89}
-	if req.PaperSize == "Letter" { rect = gopdf.Rect{W: 612, H: 792} }
+	if req.PaperSize == "Letter" {
+		rect = gopdf.Rect{W: 612, H: 792}
+	}
 	pdf.Start(gopdf.Config{PageSize: rect})
 
 	// 硬性限制：页数 1-10 页，防止资源耗尽
-	if req.PageCount < 1 { req.PageCount = 1 }
-	if req.PageCount > 10 { req.PageCount = 10 }
+	if req.PageCount < 1 {
+		req.PageCount = 1
+	}
+	if req.PageCount > 10 {
+		req.PageCount = 10
+	}
 
 	for i := 0; i < req.PageCount; i++ {
 		pdf.AddPage()
@@ -57,20 +61,35 @@ func GenerateCountingPDF(req CountingRequest) ([]byte, error) {
 func drawProblemV4(pdf *gopdf.GoPdf, req CountingRequest, startY, pW, pH float64) {
 	margin := 40.0
 	boxW, boxH := (pW-2*margin)*0.7, pH-60.0
-	xBase, yBase := margin, startY + 30.0
+	xBase, yBase := margin, startY+30.0
 
-	pdf.SetStrokeColor(0, 0, 0); pdf.SetLineWidth(2.5)
+	pdf.SetStrokeColor(0, 0, 0)
+	pdf.SetLineWidth(2.5)
 	pdf.RectFromUpperLeft(xBase, yBase, boxW, boxH)
 
 	catIcons := data.IconCategories[req.Category]
-	if len(catIcons) == 0 { catIcons = data.IconCategories["shapes"] }
+	if len(catIcons) == 0 {
+		catIcons = data.IconCategories["shapes"]
+	}
 
 	numTypes := req.IconTypes
-	if numTypes < 1 { numTypes = 1 }; if numTypes > 6 { numTypes = 6 }
-	if numTypes > len(catIcons) { numTypes = len(catIcons) }
+	if numTypes < 1 {
+		numTypes = 1
+	}
+	if numTypes > 6 {
+		numTypes = 6
+	}
+	if numTypes > len(catIcons) {
+		numTypes = len(catIcons)
+	}
 
 	total := req.TotalCount
-	if total < numTypes { total = numTypes }; if total > 30 { total = 30 }
+	if total < numTypes {
+		total = numTypes
+	}
+	if total > 30 {
+		total = 30
+	}
 
 	allIconsPerm := rand.Perm(len(catIcons))
 	var selectedIcons []data.Icon
@@ -87,49 +106,80 @@ func drawProblemV4(pdf *gopdf.GoPdf, req CountingRequest, startY, pW, pH float64
 	}
 
 	avgRadius := math.Sqrt((boxW * boxH * 0.22) / (float64(total) * math.Pi))
-	if avgRadius > 35.0 { avgRadius = 35.0 }
+	if avgRadius > 35.0 {
+		avgRadius = 35.0
+	}
 
 	var placed []PlacedIcon
 	iconTypeIdx, currentInType := 0, 0
 	for i := 0; i < total; i++ {
-		scaleVar := 0.9 + rand.Float64()*0.2; r := avgRadius * scaleVar
+		scaleVar := 0.9 + rand.Float64()*0.2
+		r := avgRadius * scaleVar
 		for retry := 0; retry < 200; retry++ {
 			randX := xBase + r + 5 + rand.Float64()*(boxW-2*r-10)
 			randY := yBase + r + 5 + rand.Float64()*(boxH-2*r-10)
 			collision := false
-			for _, p := range placed {
-				if math.Sqrt(math.Pow(randX-p.X, 2)+math.Pow(randY-p.Y, 2)) < (r + p.Radius + 10.0) {
-					collision = true; break
-				}
-			}
+							for _, p := range placed {
+								dx := randX - p.X
+								dy := randY - p.Y
+								if math.Sqrt(dx*dx+dy*dy) < (r + p.Radius + 10.0) {
+									collision = true
+									break
+								}
+							}
+			
 			if !collision {
 				drawSimpleIcon(pdf, selectedIcons[iconTypeIdx], randX, randY, r*2)
-				placed = append(placed, PlacedIcon{X: randX, Y: randY, Radius: r}); break
+				placed = append(placed, PlacedIcon{X: randX, Y: randY, Radius: r})
+				break
 			}
 		}
-		currentInType++; if currentInType >= counts[iconTypeIdx] { iconTypeIdx++; currentInType = 0 }
+		currentInType++
+		if currentInType >= counts[iconTypeIdx] {
+			iconTypeIdx++
+			currentInType = 0
+		}
 	}
 
 	legendX, legendStepY := xBase+boxW+20.0, boxH/float64(numTypes+1)
 	for i := 0; i < numTypes; i++ {
 		lY := yBase + float64(i+1)*legendStepY
 		drawSimpleIcon(pdf, selectedIcons[i], legendX+25, lY, 35)
-		pdf.SetStrokeColor(150, 150, 150); pdf.SetLineWidth(1.0); pdf.RectFromUpperLeft(legendX+60, lY-15, 35, 35)
+		pdf.SetStrokeColor(150, 150, 150)
+		pdf.SetLineWidth(1.0)
+		pdf.RectFromUpperLeft(legendX+60, lY-15, 35, 35)
 	}
 }
 
 func drawSimpleIcon(pdf *gopdf.GoPdf, icon data.Icon, cX, cY, size float64) {
 	rawResults := parseMultiPath(icon, 1.0, 0, 0)
-	if len(rawResults) == 0 { return }
-	var minX, minY, maxX, maxY float64 = 1e9, 1e9, -1e9, -1e9
+	if len(rawResults) == 0 {
+		return
+	}
+	var minX, minY, maxX, maxY = 1e9, 1e9, -1e9, -1e9
 	for _, res := range rawResults {
 		for _, p := range res.Points {
-			if p.X < minX { minX = p.X }; if p.X > maxX { maxX = p.X }
-			if p.Y < minY { minY = p.Y }; if p.Y > maxY { maxY = p.Y }
+			if p.X < minX {
+				minX = p.X
+			}
+			if p.X > maxX {
+				maxX = p.X
+			}
+			if p.Y < minY {
+				minY = p.Y
+			}
+			if p.Y > maxY {
+				maxY = p.Y
+			}
 		}
 	}
 	curW, curH := maxX-minX, maxY-minY
-	if curW <= 0 { curW = 1 }; if curH <= 0 { curH = 1 }
+	if curW <= 0 {
+		curW = 1
+	}
+	if curH <= 0 {
+		curH = 1
+	}
 	scale := size / math.Max(curW, curH)
 	ox, oy := cX-(curW*scale)/2-minX*scale, cY-(curH*scale)/2-minY*scale
 
@@ -141,10 +191,16 @@ func drawSimpleIcon(pdf *gopdf.GoPdf, icon data.Icon, cX, cY, size float64) {
 	}
 	for _, res := range rawResults {
 		scaledPts := make([]gopdf.Point, len(res.Points))
-		for i, p := range res.Points { scaledPts[i] = gopdf.Point{X: ox + p.X*scale, Y: oy + p.Y*scale} }
+		for i, p := range res.Points {
+			scaledPts[i] = gopdf.Point{X: ox + p.X*scale, Y: oy + p.Y*scale}
+		}
 		if len(scaledPts) > 1 {
-			if res.Closed { pdf.Polygon(scaledPts, "D") } else {
-				for j := 0; j < len(scaledPts)-1; j++ { pdf.Line(scaledPts[j].X, scaledPts[j].Y, scaledPts[j+1].X, scaledPts[j+1].Y) }
+			if res.Closed {
+				pdf.Polygon(scaledPts, "D")
+			} else {
+				for j := 0; j < len(scaledPts)-1; j++ {
+					pdf.Line(scaledPts[j].X, scaledPts[j].Y, scaledPts[j+1].X, scaledPts[j+1].Y)
+				}
 			}
 		}
 	}
@@ -163,57 +219,122 @@ func parseMultiPath(icon data.Icon, scale, ox, oy float64) []PathResult {
 			if (token[0] >= 'a' && token[0] <= 'z') || (token[0] >= 'A' && token[0] <= 'Z') {
 				cmd := strings.ToUpper(token)
 				if cmd == "M" {
-					if len(pts) > 0 { results = append(results, PathResult{Points: pts, Closed: false}); pts = nil }
+					if len(pts) > 0 {
+						results = append(results, PathResult{Points: pts, Closed: false})
+						pts = nil
+					}
 				} else if cmd == "Z" {
-					if len(pts) > 0 { results = append(results, PathResult{Points: pts, Closed: true}); pts = nil }
-					lx, ly = startX, startY; i++; continue
+					if len(pts) > 0 {
+						results = append(results, PathResult{Points: pts, Closed: true})
+						pts = nil
+					}
+					lx, ly = startX, startY
+					i++
+					continue
 				}
-				currentCmd = cmd; isRel = (token[0] >= 'a' && token[0] <= 'z'); i++
+				currentCmd = cmd
+				isRel = (token[0] >= 'a' && token[0] <= 'z')
+				i++
 				continue
 			}
 			switch currentCmd {
 			case "M", "L":
-				if i+1 >= len(tokens) { i = len(tokens); break }
-				x, _ := strconv.ParseFloat(tokens[i], 64); y, _ := strconv.ParseFloat(tokens[i+1], 64)
-				if isRel { x += lx; y += ly }
-				if currentCmd == "M" { startX, startY = x, y }
+				if i+1 >= len(tokens) {
+					i = len(tokens)
+					break
+				}
+				x, _ := strconv.ParseFloat(tokens[i], 64)
+				y, _ := strconv.ParseFloat(tokens[i+1], 64)
+				if isRel {
+					x += lx
+					y += ly
+				}
+				if currentCmd == "M" {
+					startX, startY = x, y
+				}
 				lx, ly = x, y
-				pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + y*scale}); i += 2
-				if currentCmd == "M" { currentCmd = "L" }
+				pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + y*scale})
+				i += 2
+				if currentCmd == "M" {
+					currentCmd = "L"
+				}
 			case "H":
-				x, _ := strconv.ParseFloat(tokens[i], 64); if isRel { x += lx }; lx = x
-				pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + ly*scale}); i++
+				x, _ := strconv.ParseFloat(tokens[i], 64)
+				if isRel {
+					x += lx
+				}
+				lx = x
+				pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + ly*scale})
+				i++
 			case "V":
-				y, _ := strconv.ParseFloat(tokens[i], 64); if isRel { y += ly }; ly = y
-				pts = append(pts, gopdf.Point{X: ox + lx*scale, Y: oy + y*scale}); i++
+				y, _ := strconv.ParseFloat(tokens[i], 64)
+				if isRel {
+					y += ly
+				}
+				ly = y
+				pts = append(pts, gopdf.Point{X: ox + lx*scale, Y: oy + y*scale})
+				i++
 			case "C":
-				if i+5 >= len(tokens) { i = len(tokens); break }
-				x1, _ := strconv.ParseFloat(tokens[i], 64);   y1, _ := strconv.ParseFloat(tokens[i+1], 64)
-				x2, _ := strconv.ParseFloat(tokens[i+2], 64); y2, _ := strconv.ParseFloat(tokens[i+3], 64)
-				x,  _ := strconv.ParseFloat(tokens[i+4], 64); y,  _ := strconv.ParseFloat(tokens[i+5], 64)
-				if isRel { x1 += lx; y1 += ly; x2 += lx; y2 += ly; x += lx; y += ly }
-				for t := 0.2; t <= 1.0; t += 0.2 {
-					tx := math.Pow(1-t, 3)*lx + 3*math.Pow(1-t, 2)*t*x1 + 3*(1-t)*math.Pow(t, 2)*x2 + math.Pow(t, 3)*x
-					ty := math.Pow(1-t, 3)*ly + 3*math.Pow(1-t, 2)*t*y1 + 3*(1-t)*math.Pow(t, 2)*y2 + math.Pow(t, 3)*y
-					pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty*scale})
+				if i+5 >= len(tokens) {
+					i = len(tokens)
+					break
 				}
-				lx, ly = x, y; i += 6
+				x1, _ := strconv.ParseFloat(tokens[i], 64)
+				y1, _ := strconv.ParseFloat(tokens[i+1], 64)
+				x2, _ := strconv.ParseFloat(tokens[i+2], 64)
+				y2, _ := strconv.ParseFloat(tokens[i+3], 64)
+				x, _ := strconv.ParseFloat(tokens[i+4], 64)
+				y, _ := strconv.ParseFloat(tokens[i+5], 64)
+				if isRel {
+					x1 += lx
+					y1 += ly
+					x2 += lx
+					y2 += ly
+					x += lx
+					y += ly
+				}
+									for t := 0.2; t <= 1.0; t += 0.2 {
+										invT := 1 - t
+										tx := invT*invT*invT*lx + 3*invT*invT*t*x1 + 3*invT*t*t*x2 + t*t*t*x
+										ty := invT*invT*invT*ly + 3*invT*invT*t*y1 + 3*invT*t*t*y2 + t*t*t*y
+										pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty*scale})
+									}
+				
+				lx, ly = x, y
+				i += 6
 			case "Q":
-				if i+3 >= len(tokens) { i = len(tokens); break }
-				x1, _ := strconv.ParseFloat(tokens[i], 64); y1, _ := strconv.ParseFloat(tokens[i+1], 64)
-				x,  _ := strconv.ParseFloat(tokens[i+2], 64); y,  _ := strconv.ParseFloat(tokens[i+3], 64)
-				if isRel { x1 += lx; y1 += ly; x += lx; y += ly }
-				for t := 0.25; t <= 1.0; t += 0.25 {
-					tx := math.Pow(1-t, 2)*lx + 2*(1-t)*t*x1 + math.Pow(t, 2)*x
-					ty := math.Pow(1-t, 2)*ly + 2*(1-t)*t*y1 + math.Pow(t, 2)*y
-					pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty*scale})
+				if i+3 >= len(tokens) {
+					i = len(tokens)
+					break
 				}
-				lx, ly = x, y; i += 4
-			case "A": i += 7
-			default: i++
+				x1, _ := strconv.ParseFloat(tokens[i], 64)
+				y1, _ := strconv.ParseFloat(tokens[i+1], 64)
+				x, _ := strconv.ParseFloat(tokens[i+2], 64)
+				y, _ := strconv.ParseFloat(tokens[i+3], 64)
+				if isRel {
+					x1 += lx
+					y1 += ly
+					x += lx
+					y += ly
+				}
+									for t := 0.25; t <= 1.0; t += 0.25 {
+										invT := 1 - t
+										tx := invT*invT*lx + 2*invT*t*x1 + t*t*x
+										ty := invT*invT*ly + 2*invT*t*y1 + t*t*y
+										pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty*scale})
+									}
+				
+				lx, ly = x, y
+				i += 4
+			case "A":
+				i += 7
+			default:
+				i++
 			}
 		}
-		if len(pts) > 0 { results = append(results, PathResult{Points: pts, Closed: false}) }
+		if len(pts) > 0 {
+			results = append(results, PathResult{Points: pts, Closed: false})
+		}
 	}
 	return results
 }

pkg/learnnumber/logic/writing.go

@@ -17,7 +17,7 @@ type WritingRequest struct {
 }
 
 type WritingNode struct {
-	X, Y, R float64
+	X, Y, R        float64
 	AngleA, AngleB float64
 	BulgeR, Dist   float64
 	Number         int
@@ -26,11 +26,15 @@ type WritingNode struct {
 func GenerateWritingPDF(req WritingRequest) ([]byte, error) {
 	pdf := &gopdf.GoPdf{}
 	rect := gopdf.Rect{W: 595.28, H: 841.89}
-	if req.PaperSize == "Letter" { rect = gopdf.Rect{W: 612, H: 792} }
+	if req.PaperSize == "Letter" {
+		rect = gopdf.Rect{W: 612, H: 792}
+	}
 	pdf.Start(gopdf.Config{PageSize: rect})
 
 	err := pdf.AddTTFFontData("basic", data.FontContent)
-	if err != nil { return nil, err }
+	if err != nil {
+		return nil, err
+	}
 
 	currentNum := req.StartNum
 	// 只要还没达到 EndNum，就继续生成“整页”内容
@@ -63,10 +67,12 @@ func drawOneFullPage(pdf *gopdf.GoPdf, start int, pW, pH float64) int {
 	for {
 		placed := false
 		for retry := 0; retry < 1000; retry++ {
-			rx := xBase + dist + 20 + rand.Float64()*(boxW - 2*dist - 40)
-			ry := yBase + dist + 20 + rand.Float64()*(boxH - 2*dist - 40)
+			rx := xBase + dist + 20 + rand.Float64()*(boxW-2*dist-40)
+			ry := yBase + dist + 20 + rand.Float64()*(boxH-2*dist-40)
 
-			if isColliding(rx, ry, checkR, nodes) { continue }
+			if isColliding(rx, ry, checkR, nodes) {
+				continue
+			}
 
 			angleA := rand.Float64() * 2 * math.Pi
 			angleB := angleA + math.Pi + (rand.Float64()-0.5)*1.5
@@ -98,7 +104,9 @@ func drawOneFullPage(pdf *gopdf.GoPdf, start int, pW, pH float64) int {
 }
 
 func optimizeSpace(nodes []WritingNode, xBase, yBase, boxW, boxH, dist, checkR float64) {
-	if len(nodes) < 2 { return }
+	if len(nodes) < 2 {
+		return
+	}
 	for iter := 0; iter < 120; iter++ {
 		for i := range nodes {
 			bestX, bestY := nodes[i].X, nodes[i].Y
@@ -107,11 +115,16 @@ func optimizeSpace(nodes []WritingNode, xBase, yBase, boxW, boxH, dist, checkR f
 				moveAngle := rand.Float64() * 2 * math.Pi
 				nx := nodes[i].X + math.Cos(moveAngle)*5.0
 				ny := nodes[i].Y + math.Sin(moveAngle)*5.0
-				if nx-dist < xBase || nx+dist > xBase+boxW || ny-dist < yBase || ny+dist > yBase+boxH { continue }
-				if isColliding(nx, ny, checkR, nodes[:i]) || isColliding(nx, ny, checkR, nodes[i+1:]) { continue }
+				if nx-dist < xBase || nx+dist > xBase+boxW || ny-dist < yBase || ny+dist > yBase+boxH {
+					continue
+				}
+				if isColliding(nx, ny, checkR, nodes[:i]) || isColliding(nx, ny, checkR, nodes[i+1:]) {
+					continue
+				}
 				newMinDist := calcMinDist(nx, ny, i, nodes)
 				if newMinDist > maxMinDist {
-					maxMinDist = newMinDist; bestX, bestY = nx, ny
+					maxMinDist = newMinDist
+					bestX, bestY = nx, ny
 				}
 			}
 			nodes[i].X, nodes[i].Y = bestX, bestY
@@ -121,8 +134,12 @@ func optimizeSpace(nodes []WritingNode, xBase, yBase, boxW, boxH, dist, checkR f
 
 func isColliding(x, y, r float64, existing []WritingNode) bool {
 	for _, e := range existing {
-		d := math.Sqrt(math.Pow(x-e.X, 2) + math.Pow(y-e.Y, 2))
-		if d < (r + e.R*1.3 + 30.0) { return true } 
+		dx := x - e.X
+		dy := y - e.Y
+		d := math.Sqrt(dx*dx + dy*dy)
+		if d < (r + e.R*1.3 + 30.0) {
+			return true
+		}
 	}
 	return false
 }
@@ -130,9 +147,15 @@ func isColliding(x, y, r float64, existing []WritingNode) bool {
 func calcMinDist(x, y float64, idx int, nodes []WritingNode) float64 {
 	minD := 10000.0
 	for i, n := range nodes {
-		if i == idx { continue }
-		d := math.Sqrt(math.Pow(x-n.X, 2) + math.Pow(y-n.Y, 2))
-		if d < minD { minD = d }
+		if i == idx {
+			continue
+		}
+		dx := x - n.X
+		dy := y - n.Y
+		d := math.Sqrt(dx*dx + dy*dy)
+		if d < minD {
+			minD = d
+		}
 	}
 	return minD
 }
@@ -140,39 +163,59 @@ func calcMinDist(x, y float64, idx int, nodes []WritingNode) float64 {
 func getEdgePoint(x, y, r, angle float64, isCircle bool) (float64, float64) {
 	gap := 2.0
 	er := r + gap
-	if isCircle { return x + math.Cos(angle)*er, y + math.Sin(angle)*er }
+	if isCircle {
+		return x + math.Cos(angle)*er, y + math.Sin(angle)*er
+	}
 	absCos, absSin := math.Abs(math.Cos(angle)), math.Abs(math.Sin(angle))
 	var d float64
-	if absCos > absSin { d = er / absCos } else { d = er / absSin }
+	if absCos > absSin {
+		d = er / absCos
+	} else {
+		d = er / absSin
+	}
 	return x + math.Cos(angle)*d, y + math.Sin(angle)*d
 }
 
 func drawCenteredText(pdf *gopdf.GoPdf, cx, cy float64, text string, fontSize float64) {
-	pdf.SetFont("basic", "", fontSize)
+	_ = pdf.SetFont("basic", "", fontSize)
 	tw, _ := pdf.MeasureTextWidth(text)
-	pdf.SetXY(cx - tw/2, cy + fontSize*0.38)
-	pdf.Text(text)
+	pdf.SetXY(cx-tw/2, cy+fontSize*0.38)
+	_ = pdf.Text(text)
 }
 
 func drawFullNode(pdf *gopdf.GoPdf, n WritingNode) {
 	isOdd := n.Number%2 != 0
-	pdf.SetStrokeColor(0, 0, 0); pdf.SetLineWidth(1.8)
-	if isOdd { pdf.Oval(n.X-n.R, n.Y-n.R, n.X+n.R, n.Y+n.R) } else { pdf.RectFromUpperLeft(n.X-n.R, n.Y-n.R, n.R*2, n.R*2) }
+	pdf.SetStrokeColor(0, 0, 0)
+	pdf.SetLineWidth(1.8)
+	if isOdd {
+		pdf.Oval(n.X-n.R, n.Y-n.R, n.X+n.R, n.Y+n.R)
+	} else {
+		pdf.RectFromUpperLeft(n.X-n.R, n.Y-n.R, n.R*2, n.R*2)
+	}
 	pdf.SetTextColor(220, 220, 220)
 	drawCenteredText(pdf, n.X, n.Y, strconv.Itoa(n.Number), n.R*1.35)
 
-	pdf.SetStrokeColor(180, 180, 180); pdf.SetLineWidth(1.0)
-	ax, ay := n.X + math.Cos(n.AngleA)*n.Dist, n.Y + math.Sin(n.AngleA)*n.Dist
+	pdf.SetStrokeColor(180, 180, 180)
+	pdf.SetLineWidth(1.0)
+	ax, ay := n.X+math.Cos(n.AngleA)*n.Dist, n.Y+math.Sin(n.AngleA)*n.Dist
 	lx1, ly1 := getEdgePoint(n.X, n.Y, n.R, n.AngleA, isOdd)
 	lx2, ly2 := getEdgePoint(ax, ay, n.BulgeR, n.AngleA+math.Pi, !isOdd)
 	pdf.Line(lx1, ly1, lx2, ly2)
-	if isOdd { pdf.RectFromUpperLeft(ax-n.BulgeR, ay-n.BulgeR, n.BulgeR*2, n.BulgeR*2) } else { pdf.Oval(ax-n.BulgeR, ay-n.BulgeR, ax+n.BulgeR, ay+n.BulgeR) }
+	if isOdd {
+		pdf.RectFromUpperLeft(ax-n.BulgeR, ay-n.BulgeR, n.BulgeR*2, n.BulgeR*2)
+	} else {
+		pdf.Oval(ax-n.BulgeR, ay-n.BulgeR, ax+n.BulgeR, ay+n.BulgeR)
+	}
 
-	bx, by := n.X + math.Cos(n.AngleB)*n.Dist, n.Y + math.Sin(n.AngleB)*n.Dist
+	bx, by := n.X+math.Cos(n.AngleB)*n.Dist, n.Y+math.Sin(n.AngleB)*n.Dist
 	lx3, ly3 := getEdgePoint(n.X, n.Y, n.R, n.AngleB, isOdd)
 	lx4, ly4 := getEdgePoint(bx, by, n.BulgeR, n.AngleB+math.Pi, !isOdd)
 	pdf.Line(lx3, ly3, lx4, ly4)
-	if isOdd { pdf.RectFromUpperLeft(bx-n.BulgeR, by-n.BulgeR, n.BulgeR*2, n.BulgeR*2) } else { pdf.Oval(bx-n.BulgeR, by-n.BulgeR, bx+n.BulgeR, by+n.BulgeR) }
+	if isOdd {
+		pdf.RectFromUpperLeft(bx-n.BulgeR, by-n.BulgeR, n.BulgeR*2, n.BulgeR*2)
+	} else {
+		pdf.Oval(bx-n.BulgeR, by-n.BulgeR, bx+n.BulgeR, by+n.BulgeR)
+	}
 
 	pdf.SetTextColor(120, 120, 120)
 	drawCenteredText(pdf, bx, by, strconv.Itoa(n.Number+1), math.Max(7, n.BulgeR*1.2))

pkg/learnnumber/tool.go

@@ -16,10 +16,12 @@ func init() {
 	base.Register(&learnNumberTool{})
 }
 
-func (t *learnNumberTool) ID() string          { return "learn-number" }
-func (t *learnNumberTool) Name() string        { return "幼儿数学助手" }
-func (t *learnNumberTool) Description() string { return "包含数图形、基础加减法等趣味数学练习" }
-func (t *learnNumberTool) Emoji() string       { return "🔢" }
+func (t *learnNumberTool) ID() string   { return "learn-number" }
+func (t *learnNumberTool) Name() string { return "幼儿数学助手" }
+func (t *learnNumberTool) Description() string {
+	return "包含数图形、基础加减法等趣味数学练习"
+}
+func (t *learnNumberTool) Emoji() string { return "🔢" }
 
 func (t *learnNumberTool) Init() error {
 	fmt.Println("Initializing Learn-Number tool...")

pkg/zitie/logic/pdf.go

@@ -16,14 +16,16 @@ var (
 	sfntMap      = make(map[string]*sfnt.Font)
 )
 
-func SetFontData(data []byte) { embeddedFont = data }
-func RegisterFontPath(id, path string) { fontMap[id] = path }
+func SetFontData(data []byte)                  { embeddedFont = data }
+func RegisterFontPath(id, path string)         { fontMap[id] = path }
 func RegisterFontSFNT(id string, f *sfnt.Font) { sfntMap[id] = f }
 
 // HasGlyph 检查字体是否包含某个字符
 func HasGlyph(fontId string, char rune) bool {
 	f, ok := sfntMap[fontId]
-	if !ok { return false }
+	if !ok {
+		return false
+	}
 	var buffer sfnt.Buffer
 	idx, err := f.GlyphIndex(&buffer, char)
 	return err == nil && idx != 0
@@ -33,10 +35,14 @@ func HasGlyph(fontId string, char rune) bool {
 func GeneratePDFExtended(chars []HanziData, mode, paperSize, fontId string) ([]byte, error) {
 	pdf := &gopdf.GoPdf{}
 	rect := gopdf.Rect{W: 595.28, H: 841.89}
-	if paperSize == "Letter" { rect = gopdf.Rect{W: 612, H: 792} }
+	if paperSize == "Letter" {
+		rect = gopdf.Rect{W: 612, H: 792}
+	}
 	pdf.Start(gopdf.Config{PageSize: rect})
 
-	if len(embeddedFont) > 0 { _ = pdf.AddTTFFontData("font", embeddedFont) }
+	if len(embeddedFont) > 0 {
+		_ = pdf.AddTTFFontData("font", embeddedFont)
+	}
 
 	// 注册所有可用字体
 	for id, path := range fontMap {
@@ -58,13 +64,17 @@ func GeneratePDFExtended(chars []HanziData, mode, paperSize, fontId string) ([]b
 }
 
 func addTeachingPages(pdf *gopdf.GoPdf, chars []HanziData, flipY bool, pW, pH float64) {
-	cols := 2; gap, margin := 17.0, 40.0
+	cols := 2
+	gap, margin := 17.0, 40.0
 	size := math.Min((pW-2*margin-gap)/2, (pH-2*margin-2*gap)/3)
 	totalW, totalH := 2*size+gap, 3*size+2*gap
 	marginX, marginY := (pW-totalW)/2, (pH-totalH)/2
 	for i := 0; i < len(chars); i += 6 {
 		pdf.AddPage()
-		end := i + 6; if end > len(chars) { end = len(chars) }
+		end := i + 6
+		if end > len(chars) {
+			end = len(chars)
+		}
 		for idx, data := range chars[i:end] {
 			drawCharacter(pdf, data, marginX+float64(idx%cols)*(size+gap), marginY+float64(idx/cols)*(size+gap), size, flipY, len(data.Strokes), true)
 		}
@@ -72,43 +82,73 @@ func addTeachingPages(pdf *gopdf.GoPdf, chars []HanziData, flipY bool, pW, pH fl
 }
 
 func addStepPages(pdf *gopdf.GoPdf, chars []HanziData, flipY bool, pW, pH float64) {
-	cols, margin := 9, 30.0; size := (pW - 2*margin) / float64(cols)
-	pdf.AddPage(); currY := margin
+	cols, margin := 9, 30.0
+	size := (pW - 2*margin) / float64(cols)
+	pdf.AddPage()
+	currY := margin
 	for _, data := range chars {
-		numS := len(data.Strokes); rowsN := 1; if numS > 8 { rowsN = 1 + (numS - 8 + 7) / 8 }
-		if currY + float64(rowsN)*size > pH - margin { pdf.AddPage(); currY = margin }
-		totalG := rowsN * cols; strokeC := 0 
+		numS := len(data.Strokes)
+		rowsN := 1
+		if numS > 8 {
+			rowsN = 1 + (numS-8+7)/8
+		}
+		if currY+float64(rowsN)*size > pH-margin {
+			pdf.AddPage()
+			currY = margin
+		}
+		totalG := rowsN * cols
+		strokeC := 0
 		for gIdx := 0; gIdx < totalG; gIdx++ {
-			r, c := gIdx/cols, gIdx%cols; x, y := margin+float64(c)*size, currY+float64(r)*size
-			if r == 0 && c == 0 { drawCharacter(pdf, data, x, y, size, flipY, len(data.Strokes), false); strokeC = 1
-			} else if r > 0 && c == 0 { drawMiZiGe(pdf, x, y, size)
-			} else if strokeC <= numS { drawStepBox(pdf, data, x, y, size, flipY, strokeC); strokeC++
-			} else { drawMiZiGe(pdf, x, y, size) }
+			r, c := gIdx/cols, gIdx%cols
+			x, y := margin+float64(c)*size, currY+float64(r)*size
+			if r == 0 && c == 0 {
+				drawCharacter(pdf, data, x, y, size, flipY, len(data.Strokes), false)
+				strokeC = 1
+			} else if r > 0 && c == 0 {
+				drawMiZiGe(pdf, x, y, size)
+			} else if strokeC <= numS {
+				drawStepBox(pdf, data, x, y, size, flipY, strokeC)
+				strokeC++
+			} else {
+				drawMiZiGe(pdf, x, y, size)
+			}
 		}
 		currY += float64(rowsN) * size
 	}
 }
 
 func addManuscriptPages(pdf *gopdf.GoPdf, chars []HanziData, pW, pH float64, targetFont string) {
-	margin := 40.0; cols, rows := 10, 15
+	margin := 40.0
+	cols, rows := 10, 15
 	colW, rowH := (pW-2*margin)/float64(cols), (pH-2*margin)/float64(rows)
 	fontSize := colW * 0.75
 
-	pdf.AddPage(); drawManuscriptGrid(pdf, pW, pH, margin, cols, colW)
+	pdf.AddPage()
+	drawManuscriptGrid(pdf, pW, pH, margin, cols, colW)
 	cIdx, rIdx := 0, 0
 
 	for _, data := range chars {
 		if data.Character == "\n" {
-			cIdx++; rIdx = 0
-			if cIdx >= cols { pdf.AddPage(); cIdx = 0; drawManuscriptGrid(pdf, pW, pH, margin, cols, colW) }
+			cIdx++
+			rIdx = 0
+			if cIdx >= cols {
+				pdf.AddPage()
+				cIdx = 0
+				drawManuscriptGrid(pdf, pW, pH, margin, cols, colW)
+			}
 			continue
 		}
 		if rIdx >= rows {
-			cIdx++; rIdx = 0
-			if cIdx >= cols { pdf.AddPage(); cIdx = 0; drawManuscriptGrid(pdf, pW, pH, margin, cols, colW) }
+			cIdx++
+			rIdx = 0
+			if cIdx >= cols {
+				pdf.AddPage()
+				cIdx = 0
+				drawManuscriptGrid(pdf, pW, pH, margin, cols, colW)
+			}
 		}
 
-		x, y := pW - margin - float64(cIdx+1)*colW, margin + float64(rIdx)*rowH
+		x, y := pW-margin-float64(cIdx+1)*colW, margin+float64(rIdx)*rowH
 		charRune := []rune(data.Character)[0]
 
 		// 智能字体选择
@@ -118,12 +158,15 @@ func addManuscriptPages(pdf *gopdf.GoPdf, chars []HanziData, pW, pH float64, tar
 		if !HasGlyph(targetFont, charRune) {
 			// 尝试降级到字库最全的宋体或楷体
 			if HasGlyph("songti", charRune) {
-				renderFont = "songti"; isFallback = true
+				renderFont = "songti"
+				isFallback = true
 			} else if HasGlyph("kaiti", charRune) {
-				renderFont = "kaiti"; isFallback = true
+				renderFont = "kaiti"
+				isFallback = true
 			} else {
 				// 全部缺失，保留空白
-				rIdx++; continue
+				rIdx++
+				continue
 			}
 		}
 
@@ -133,12 +176,12 @@ func addManuscriptPages(pdf *gopdf.GoPdf, chars []HanziData, pW, pH float64, tar
 			smallSize := fontSize * 0.5
 			_ = pdf.SetFont(renderFont, "", smallSize)
 			// 计算右上角位置：X靠右，Y靠上
-			pdf.SetXY(x + colW - smallSize - 2, y + 2)
+			pdf.SetXY(x+colW-smallSize-2, y+2)
 			_ = pdf.Cell(nil, data.Character)
 		} else {
 			// 正常显示
 			_ = pdf.SetFont(renderFont, "", fontSize)
-			pdf.SetXY(x + (colW-fontSize*0.9)/2, y + (rowH-fontSize)/2)
+			pdf.SetXY(x+(colW-fontSize*0.9)/2, y+(rowH-fontSize)/2)
 			_ = pdf.Cell(nil, data.Character)
 		}
 		rIdx++
@@ -146,108 +189,221 @@ func addManuscriptPages(pdf *gopdf.GoPdf, chars []HanziData, pW, pH float64, tar
 }
 
 func drawManuscriptGrid(pdf *gopdf.GoPdf, pW, pH, margin float64, cols int, colW float64) {
-	pdf.SetStrokeColor(200, 0, 0); pdf.SetLineWidth(0.6)
-	for c := 0; c <= cols; c++ { x := pW - margin - float64(c)*colW; pdf.Line(x, margin, x, pH-margin) }
-	pdf.Line(margin, margin, pW-margin, margin); pdf.Line(margin, pH-margin, pW-margin, pH-margin)
+	pdf.SetStrokeColor(200, 0, 0)
+	pdf.SetLineWidth(0.6)
+	for c := 0; c <= cols; c++ {
+		x := pW - margin - float64(c)*colW
+		pdf.Line(x, margin, x, pH-margin)
+	}
+	pdf.Line(margin, margin, pW-margin, margin)
+	pdf.Line(margin, pH-margin, pW-margin, pH-margin)
 }
 
 func drawCharacter(pdf *gopdf.GoPdf, data HanziData, x, y, size float64, flipY bool, strokeLimit int, showAnnotations bool) {
-	if showAnnotations { drawGrid(pdf, x, y, size) } else { drawMiZiGe(pdf, x, y, size) }
-	p, drawS := size*0.12, size-(size*0.12*2); scale := drawS/1024.0
+	if showAnnotations {
+		drawGrid(pdf, x, y, size)
+	} else {
+		drawMiZiGe(pdf, x, y, size)
+	}
+	p, drawS := size*0.12, size-(size*0.12*2)
+	scale := drawS / 1024.0
 	if strokeLimit == len(data.Strokes) {
-		if showAnnotations { pdf.SetFillColor(240, 240, 240) } else { pdf.SetFillColor(0, 0, 0) }
-	} else { pdf.SetFillColor(180, 180, 180) }
+		if showAnnotations {
+			pdf.SetFillColor(240, 240, 240)
+		} else {
+			pdf.SetFillColor(0, 0, 0)
+		}
+	} else {
+		pdf.SetFillColor(180, 180, 180)
+	}
 	for sIdx := 0; sIdx < len(data.Strokes); sIdx++ {
-		if sIdx >= strokeLimit && strokeLimit != len(data.Strokes) { break }
+		if sIdx >= strokeLimit && strokeLimit != len(data.Strokes) {
+			break
+		}
 		pts := parseSVGPath(data.Strokes[sIdx], scale, x+p, y+p, flipY)
-		if len(pts) > 2 { pdf.Polygon(pts, "F") }
+		if len(pts) > 2 {
+			pdf.Polygon(pts, "F")
+		}
 	}
 	if showAnnotations && strokeLimit == len(data.Strokes) {
 		fS := size * 0.035
 		_ = pdf.SetFont("font", "", fS)
 		for idx, median := range data.Medians {
-			mP := transformPoints(median, scale, x+p, y+p, flipY); if len(mP) < 2 { continue }
-			pdf.SetStrokeColor(255, 0, 0); pdf.SetLineWidth(0.6)
-			for j := 0; j < len(mP)-1; j++ { pdf.Line(mP[j].X, mP[j].Y, mP[j+1].X, mP[j+1].Y) }
-			pdf.SetFillColor(255, 0, 0); drawArrow(pdf, mP[len(mP)-1], mP[len(mP)-2], size*0.035)
-			r := size*0.025; dx, dy := mP[1].X-mP[0].X, mP[1].Y-mP[0].Y; dist := math.Sqrt(dx*dx+dy*dy); ux, uy := -1.0, -1.0
-			if dist > 0.001 { ux, uy = dx/dist, dy/dist }; cX, cY := mP[0].X-ux*r, mP[0].Y-uy*r
-			pdf.SetStrokeColor(255, 0, 0); pdf.SetLineWidth(0.5); pdf.Oval(cX-r, cY-r, cX+r, cY+r)
-			numS := strconv.Itoa(idx+1); tw := fS*0.6*float64(len(numS))/2; if len(numS) > 1 { tw = fS*0.5 }
-			pdf.SetFillColor(255, 0, 0); pdf.SetXY(cX-tw/2, cY-fS/2); _ = pdf.Cell(nil, numS)
+			mP := transformPoints(median, scale, x+p, y+p, flipY)
+			if len(mP) < 2 {
+				continue
+			}
+			pdf.SetStrokeColor(255, 0, 0)
+			pdf.SetLineWidth(0.6)
+			for j := 0; j < len(mP)-1; j++ {
+				pdf.Line(mP[j].X, mP[j].Y, mP[j+1].X, mP[j+1].Y)
+			}
+			pdf.SetFillColor(255, 0, 0)
+			drawArrow(pdf, mP[len(mP)-1], mP[len(mP)-2], size*0.035)
+			r := size * 0.025
+			dx, dy := mP[1].X-mP[0].X, mP[1].Y-mP[0].Y
+			dist := math.Sqrt(dx*dx + dy*dy)
+			ux, uy := -1.0, -1.0
+			if dist > 0.001 {
+				ux, uy = dx/dist, dy/dist
+			}
+			cX, cY := mP[0].X-ux*r, mP[0].Y-uy*r
+			pdf.SetStrokeColor(255, 0, 0)
+			pdf.SetLineWidth(0.5)
+			pdf.Oval(cX-r, cY-r, cX+r, cY+r)
+			numS := strconv.Itoa(idx + 1)
+			tw := fS * 0.6 * float64(len(numS)) / 2
+			if len(numS) > 1 {
+				tw = fS * 0.5
+			}
+			pdf.SetFillColor(255, 0, 0)
+			pdf.SetXY(cX-tw/2, cY-fS/2)
+			_ = pdf.Cell(nil, numS)
 		}
 	}
 }
 
 func drawStepBox(pdf *gopdf.GoPdf, data HanziData, x, y, size float64, flipY bool, limit int) {
-	drawMiZiGe(pdf, x, y, size); p, scale := size*0.12, (size-(size*0.12*2))/1024.0
-	pdf.SetFillColor(180, 180, 180); for i := 0; i < limit; i++ {
-		pts := parseSVGPath(data.Strokes[i], scale, x+p, y+p, flipY); if len(pts) > 2 { pdf.Polygon(pts, "F") }
+	drawMiZiGe(pdf, x, y, size)
+	p, scale := size*0.12, (size-(size*0.12*2))/1024.0
+	pdf.SetFillColor(180, 180, 180)
+	for i := 0; i < limit; i++ {
+		pts := parseSVGPath(data.Strokes[i], scale, x+p, y+p, flipY)
+		if len(pts) > 2 {
+			pdf.Polygon(pts, "F")
+		}
 	}
 }
 
 func drawGrid(pdf *gopdf.GoPdf, x, y, size float64) {
-	pdf.SetStrokeColor(220, 220, 220); pdf.SetLineWidth(0.4); pdf.RectFromUpperLeft(x, y, size, size)
-	mid := size/2; drawDashedLine(pdf, x, y+mid, x+size, y+mid); drawDashedLine(pdf, x+mid, y, x+mid, y+size)
+	pdf.SetStrokeColor(220, 220, 220)
+	pdf.SetLineWidth(0.4)
+	pdf.RectFromUpperLeft(x, y, size, size)
+	mid := size / 2
+	drawDashedLine(pdf, x, y+mid, x+size, y+mid)
+	drawDashedLine(pdf, x+mid, y, x+mid, y+size)
 }
 
 func drawMiZiGe(pdf *gopdf.GoPdf, x, y, size float64) {
-	pdf.SetStrokeColor(220, 220, 220); pdf.SetLineWidth(0.4); pdf.RectFromUpperLeft(x, y, size, size)
-	mid := size/2; drawDashedLine(pdf, x, y+mid, x+size, y+mid); drawDashedLine(pdf, x+mid, y, x+mid, y+size); drawDashedLine(pdf, x, y, x+size, y+size); drawDashedLine(pdf, x, y+size, x+size, y)
+	pdf.SetStrokeColor(220, 220, 220)
+	pdf.SetLineWidth(0.4)
+	pdf.RectFromUpperLeft(x, y, size, size)
+	mid := size / 2
+	drawDashedLine(pdf, x, y+mid, x+size, y+mid)
+	drawDashedLine(pdf, x+mid, y, x+mid, y+size)
+	drawDashedLine(pdf, x, y, x+size, y+size)
+	drawDashedLine(pdf, x, y+size, x+size, y)
 }
 
 func drawDashedLine(pdf *gopdf.GoPdf, x1, y1, x2, y2 float64) {
-	dash := 2.0; dx, dy := x2-x1, y2-y1; dist := math.Sqrt(dx*dx + dy*dy); if dist < 0.001 { return }
-	ux, uy := dx/dist, dy/dist; for i := 0.0; i < dist; i += dash * 2 { end := i + dash; if end > dist { end = dist }; pdf.Line(x1+ux*i, y1+uy*i, x1+ux*end, y1+uy*end) }
+	dash := 2.0
+	dx, dy := x2-x1, y2-y1
+	dist := math.Sqrt(dx*dx + dy*dy)
+	if dist < 0.001 {
+		return
+	}
+	ux, uy := dx/dist, dy/dist
+	for i := 0.0; i < dist; i += dash * 2 {
+		end := i + dash
+		if end > dist {
+			end = dist
+		}
+		pdf.Line(x1+ux*i, y1+uy*i, x1+ux*end, y1+uy*end)
+	}
 }
 
 func drawArrow(pdf *gopdf.GoPdf, target, prev gopdf.Point, length float64) {
-	angle := math.Atan2(target.Y-prev.Y, target.X-prev.X); arrowA := math.Pi/6
-	p1X := target.X+length*math.Cos(angle+math.Pi+arrowA); p1Y := target.Y+length*math.Sin(angle+math.Pi+arrowA)
-	p2X := target.X+length*math.Cos(angle+math.Pi-arrowA); p2Y := target.Y+length*math.Sin(angle+math.Pi-arrowA)
+	angle := math.Atan2(target.Y-prev.Y, target.X-prev.X)
+	arrowA := math.Pi / 6
+	p1X := target.X + length*math.Cos(angle+math.Pi+arrowA)
+	p1Y := target.Y + length*math.Sin(angle+math.Pi+arrowA)
+	p2X := target.X + length*math.Cos(angle+math.Pi-arrowA)
+	p2Y := target.Y + length*math.Sin(angle+math.Pi-arrowA)
 	pdf.Polygon([]gopdf.Point{target, {X: p1X, Y: p1Y}, {X: p2X, Y: p2Y}}, "F")
 }
 
 func transformPoints(pts []Point, scale, ox, oy float64, flipY bool) []gopdf.Point {
-	res := make([]gopdf.Point, len(pts)); for i, p := range pts { y := p[1]; if flipY { y = 1024-y }; res[i] = gopdf.Point{X: ox+p[0]*scale, Y: oy+y*scale} }
+	res := make([]gopdf.Point, len(pts))
+	for i, p := range pts {
+		y := p[1]
+		if flipY {
+			y = 1024 - y
+		}
+		res[i] = gopdf.Point{X: ox + p[0]*scale, Y: oy + y*scale}
+	}
 	return res
 }
 
 var reSVG = regexp.MustCompile(`([MLQCZ])|(-?\d+\.?\d*)`)
 
 func parseSVGPath(path string, scale, ox, oy float64, flipY bool) []gopdf.Point {
-	var pts []gopdf.Point; matches := reSVG.FindAllStringSubmatch(path, -1); var lastX, lastY float64
-	for idx := 0; idx < len(matches); {
-		item := matches[idx][0]
-		if item == "M" || item == "L" {
-			if idx+2 < len(matches) {
-				x, _ := strconv.ParseFloat(matches[idx+1][0], 64); y, _ := strconv.ParseFloat(matches[idx+2][0], 64); lastX, lastY = x, y
-				if flipY { y = 1024 - y }; pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + y*scale}); idx += 3
-			} else { idx++ }
-		} else if item == "C" {
-			if idx+6 < len(matches) {
-				x1, _ := strconv.ParseFloat(matches[idx+1][0], 64); y1, _ := strconv.ParseFloat(matches[idx+2][0], 64)
-				x2, _ := strconv.ParseFloat(matches[idx+3][0], 64); y2, _ := strconv.ParseFloat(matches[idx+4][0], 64)
-				x, _ := strconv.ParseFloat(matches[idx+5][0], 64); y, _ := strconv.ParseFloat(matches[idx+6][0], 64)
-				for t := 0.2; t <= 1.0; t += 0.2 {
-					tx := math.Pow(1-t, 3)*lastX + 3*math.Pow(1-t, 2)*t*x1 + 3*(1-t)*math.Pow(t, 2)*x2 + math.Pow(t, 3)*x
-					ty := math.Pow(1-t, 3)*lastY + 3*math.Pow(1-t, 2)*t*y1 + 3*(1-t)*math.Pow(t, 2)*y2 + math.Pow(t, 3)*y
-					ty_f := ty; if flipY { ty_f = 1024 - ty }; pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty_f*scale})
+	var pts []gopdf.Point
+	matches := reSVG.FindAllStringSubmatch(path, -1)
+	var lastX, lastY float64
+			for idx := 0; idx < len(matches); {
+				item := matches[idx][0]
+				switch item {
+				case "M", "L":
+					if idx+2 < len(matches) {
+						x, _ := strconv.ParseFloat(matches[idx+1][0], 64)
+						y, _ := strconv.ParseFloat(matches[idx+2][0], 64)
+						lastX, lastY = x, y
+						if flipY {
+							y = 1024 - y
+						}
+						pts = append(pts, gopdf.Point{X: ox + x*scale, Y: oy + y*scale})
+						idx += 3
+					} else {
+						idx++
+					}
+				case "C":
+					if idx+6 < len(matches) {
+						x1, _ := strconv.ParseFloat(matches[idx+1][0], 64)
+						y1, _ := strconv.ParseFloat(matches[idx+2][0], 64)
+						x2, _ := strconv.ParseFloat(matches[idx+3][0], 64)
+						y2, _ := strconv.ParseFloat(matches[idx+4][0], 64)
+						x, _ := strconv.ParseFloat(matches[idx+5][0], 64)
+						y, _ := strconv.ParseFloat(matches[idx+6][0], 64)
+						for t := 0.2; t <= 1.0; t += 0.2 {
+							invT := 1 - t
+							tx := invT*invT*invT*lastX + 3*invT*invT*t*x1 + 3*invT*t*t*x2 + t*t*t*x
+							ty := invT*invT*invT*lastY + 3*invT*invT*t*y1 + 3*invT*t*t*y2 + t*t*t*y
+							ty_f := ty
+							if flipY {
+								ty_f = 1024 - ty
+							}
+							pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty_f*scale})
+						}
+						lastX, lastY = x, y
+						idx += 7
+					} else {
+						idx++
+					}
+				case "Q":
+					if idx+4 < len(matches) {
+						x1, _ := strconv.ParseFloat(matches[idx+1][0], 64)
+						y1, _ := strconv.ParseFloat(matches[idx+2][0], 64)
+						x, _ := strconv.ParseFloat(matches[idx+3][0], 64)
+						y, _ := strconv.ParseFloat(matches[idx+4][0], 64)
+						for t := 0.2; t <= 1.0; t += 0.2 {
+							invT := 1 - t
+							tx := invT*invT*lastX + 2*invT*t*x1 + t*t*x
+							ty := invT*invT*lastY + 2*invT*t*y1 + t*t*y
+							ty_f := ty
+							if flipY {
+								ty_f = 1024 - ty
+							}
+							pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty_f*scale})
+						}
+						lastX, lastY = x, y
+						idx += 5
+					} else {
+						idx++
+					}
+				default:
+					idx++
 				}
-				lastX, lastY = x, y; idx += 7
-			} else { idx++ }
-		} else if item == "Q" {
-			if idx+4 < len(matches) {
-				x1, _ := strconv.ParseFloat(matches[idx+1][0], 64); y1, _ := strconv.ParseFloat(matches[idx+2][0], 64)
-				x, _ := strconv.ParseFloat(matches[idx+3][0], 64); y, _ := strconv.ParseFloat(matches[idx+4][0], 64)
-				for t := 0.2; t <= 1.0; t += 0.2 {
-					tx := math.Pow(1-t, 2)*lastX + 2*(1-t)*t*x1 + math.Pow(t, 2)*x
-					ty := math.Pow(1-t, 2)*lastY + 2*(1-t)*t*y1 + math.Pow(t, 2)*y
-					ty_f := ty; if flipY { ty_f = 1024 - ty }; pts = append(pts, gopdf.Point{X: ox + tx*scale, Y: oy + ty_f*scale})
-				}
-				lastX, lastY = x, y; idx += 5
-			} else { idx++ }
-		} else { idx++ }
-	}
+			}
+	
 	return pts
 }

pkg/zitie/logic/types.go

@@ -1,9 +1,9 @@
 package logic
 
 type HanziData struct {
-	Character string     `json:"character"`
-	Strokes   []string   `json:"strokes"`
-	Medians   [][]Point  `json:"medians"`
+	Character string    `json:"character"`
+	Strokes   []string  `json:"strokes"`
+	Medians   [][]Point `json:"medians"`
 }
 
 type Point [2]float64

pkg/zitie/tool.go

@@ -28,10 +28,12 @@ func init() {
 	base.Register(&zitieTool{})
 }
 
-func (t *zitieTool) ID() string          { return "zitie" }
-func (t *zitieTool) Name() string        { return "汉字字帖生成" }
-func (t *zitieTool) Description() string { return "提供智能缺字处理和古风排版的专业字帖工具" }
-func (t *zitieTool) Emoji() string       { return "🎨" }
+func (t *zitieTool) ID() string   { return "zitie" }
+func (t *zitieTool) Name() string { return "汉字字帖生成" }
+func (t *zitieTool) Description() string {
+	return "提供智能缺字处理和古风排版的专业字帖工具"
+}
+func (t *zitieTool) Emoji() string { return "🎨" }
 
 func (t *zitieTool) Init() error {
 	fmt.Println("Initializing Zitie tool with font check...")
@@ -44,15 +46,17 @@ func (t *zitieTool) Init() error {
 	logic.SetFontData(fontBytes)
 
 	fonts := map[string]string{
-		"kaiti":    "data/kaiti.ttf",
-		"lishu":    "data/lishu.ttf",
-		"xingshu":  "data/xingshu.ttf",
-		"songti":   "data/songti.ttf",
+		"kaiti":   "data/kaiti.ttf",
+		"lishu":   "data/lishu.ttf",
+		"xingshu": "data/xingshu.ttf",
+		"songti":  "data/songti.ttf",
 	}
 
 	for id, src := range fonts {
 		bytes, err := fontFS.ReadFile(src)
-		if err != nil { continue }
+		if err != nil {
+			continue
+		}
 
 		// 1. 同步到磁盘用于 gopdf
 		tmpPath := filepath.Join(os.TempDir(), fmt.Sprintf("own_tools_%s.ttf", id))
@@ -108,7 +112,9 @@ func (t *zitieTool) handleManuscript(c *gin.Context) {
 		c.JSON(http.StatusBadRequest, gin.H{"error": err.Error()})
 		return
 	}
-	if req.FontType == "" { req.FontType = "kaiti" }
+	if req.FontType == "" {
+		req.FontType = "kaiti"
+	}
 	data := t.filterChars(req.Chars, true)
 	t.generateAndResponse(c, data, "manuscript", req.PaperSize, req.FontType)
 }
@@ -121,14 +127,25 @@ func (t *zitieTool) filterChars(input string, keepNewline bool) []logic.HanziDat
 	for _, r := range input {
 		charStr := string(r)
 		if r == '\n' {
-			if keepNewline { res = append(res, logic.HanziData{Character: "\n"}) }
+			if keepNewline {
+				res = append(res, logic.HanziData{Character: "\n"})
+			}
+			continue
+		}
+		if r == ' ' || r == '\r' || r == '\t' {
 			continue
 		}
-		if r == ' ' || r == '\r' || r == '\t' { continue }
 
 		isPunc := false
-		for _, p := range puncs { if r == p { isPunc = true; break } }
-		if isPunc { continue }
+		for _, p := range puncs {
+			if r == p {
+				isPunc = true
+				break
+			}
+		}
+		if isPunc {
+			continue
+		}
 
 		if hd, ok := t.allChars[charStr]; ok {
 			hd.Character = charStr