doc: initialize README with initial flow

Author: tiviluson

README.md

@@ -0,0 +1,100 @@
+# LangGraph Implementation with Geometry Visualization
+
+## Key Benefits of Using LangGraph + Visualization:
+
+### 1. **Clear State Management**
+- All application state is centralized in the `TutorState` TypedDict
+- State transitions are explicit and trackable
+- Easy to debug and maintain
+
+### 2. **Modular Node Design**
+- Each function handles a single responsibility
+- Easy to test individual components
+- Simple to add new features or modify existing ones
+
+### 3. **Flexible Workflow Control**
+- Conditional routing based on user input and application state
+- Easy to modify the flow without changing core logic
+- Visual representation of the workflow possible
+
+### 4. **Intelligent Geometry Visualization**
+- **AI-Powered Analysis**: Uses LLM to understand geometry problems
+- **Automatic Plot Generation**: Creates appropriate figures based on problem description
+- **Interactive Visualization**: Users can request plots at any time during problem solving
+- **Multiple Geometry Types**: Supports triangles, circles, quadrilaterals, and combinations
+
+### 5. **Error Handling & Recovery**
+- Each node can handle errors independently
+- Failed operations can route to appropriate recovery nodes
+- Graceful degradation of functionality
+
+### 6. **Scalability**
+- Easy to add new question types or tutoring modes
+- Simple to extend with additional AI agents
+- Can integrate with external tools and APIs
+
+## New Visualization Features:
+
+### **GeometryVisualizationAgent**
+- **Problem Analysis**: Parses geometry problems to extract figure requirements
+- **JSON-based Description**: Structured approach to defining geometric elements
+- **Matplotlib Integration**: Creates professional-looking geometric plots
+- **Fallback Handling**: Provides simple visualizations when complex analysis fails
+
+### **User Interactions**
+| Command | Action |
+|---------|--------|
+| `hint` | Get progressive hints (max 3 per question) |
+| `plot` | Generate and display geometry figure |
+| `Enter` or text | Show solution directly |
+
+## Comparison with Traditional Approach:
+
+| Aspect | Traditional (Class-based) | LangGraph + Visualization |
+|--------|---------------------------|---------------------------|
+| **State Management** | Instance variables | Centralized TypedDict |
+| **Flow Control** | Nested loops & conditionals | Graph-based routing |
+| **Modularity** | Method-based | Node-based functions |
+| **Testing** | Complex mocking | Isolated node testing |
+| **Debugging** | Step-through debugging | State inspection |
+| **Extensibility** | Inheritance/composition | Add nodes & edges |
+| **Visualization** | Manual/external tools | Integrated AI-powered plots |
+
+## Enhanced Workflow Visualization:
+```
+[START] -> Generate Problem -> Setup Question -> Generate Hints 
+              ↓                    ↓                ↓
+         Extract Questions    Display Current    Create 3 Hints
+              ↓              Question            ↓
+              └─────────────────┴─────────→ Get User Input
+                                               ↓
+                                ┌─────────────┼─────────────┐
+                                ↓             ↓             ↓
+                        Process Hint    Generate Plot   Generate Solution
+                                ↓             ↓             ↓
+                        Show Hint (1-3)  Display Figure Show Full Solution
+                                ↓             ↓             ↓
+                                └─────────────┼─────────────┘
+                                              ↓
+                                    ┌─────────┴─────────┐
+                                    ↓                   ↓
+                               Next Question      Ask Continue
+                                    ↓                   ↓
+                               (Back to Setup)    [END or Restart]
+```
+
+## Technical Implementation:
+
+### **Visualization Pipeline**
+1. **Problem Analysis**: LLM analyzes geometry problem text
+2. **Structure Extraction**: Identifies points, lines, circles, angles
+3. **Coordinate Generation**: Creates appropriate coordinate system
+4. **Plot Rendering**: Uses matplotlib to create visual representation
+5. **Display Integration**: Shows plot inline with problem solving flow
+
+### **Supported Geometry Elements**
+- **Points**: Labeled vertices with coordinates
+- **Lines**: Straight lines connecting points
+- **Circles**: With centers, radii, and inscribed/circumscribed relationships
+- **Angles**: Special angle markings and measurements
+- **Special Features**: Tangents, perpendiculars, parallel lines