From 207e283031eb0d66fe231ef1f04ee5116ba3f086 Mon Sep 17 00:00:00 2001 From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com> Date: Mon, 26 Jan 2026 12:37:12 +0000 Subject: [PATCH 1/4] Initial plan From 0ec10928c1ed730cb1b1d902fca2a1b16cd93347 Mon Sep 17 00:00:00 2001 From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com> Date: Mon, 26 Jan 2026 12:42:05 +0000 Subject: [PATCH 2/4] Add comprehensive feature evaluation documents Co-authored-by: SharadhNaidu <185215496+SharadhNaidu@users.noreply.github.com> --- FEATURES_SUMMARY.md | 329 +++++++++++++++++++++++++++ FEATURE_ROADMAP.md | 533 ++++++++++++++++++++++++++++++++++++++++++++ README.md | 40 ++++ 3 files changed, 902 insertions(+) create mode 100644 FEATURES_SUMMARY.md create mode 100644 FEATURE_ROADMAP.md diff --git a/FEATURES_SUMMARY.md b/FEATURES_SUMMARY.md new file mode 100644 index 0000000..2ecd758 --- /dev/null +++ b/FEATURES_SUMMARY.md @@ -0,0 +1,329 @@ +# Visual Calculus - Feature Enhancement Summary + +## Quick Reference: Proposed Features by Category + +This document provides a condensed overview of all proposed features. See [FEATURE_ROADMAP.md](FEATURE_ROADMAP.md) for detailed descriptions and implementation plans. + +--- + +## 📊 Feature Categories + +### 🔴 Core Calculus Features (17 features) + +#### Integration & Area +- [ ] Definite Integrals Visualizer +- [ ] Indefinite Integrals (Antiderivatives) +- [ ] Riemann Sums (Left, Right, Midpoint, Trapezoidal) +- [ ] Volume of Revolution (Disk/Shell Method) with 3D +- [ ] Arc Length Calculator +- [ ] Numerical Integration (Simpson's, Gaussian Quadrature) + +#### Limits & Continuity +- [ ] Limit Calculator (Left/Right Limits) +- [ ] Asymptote Detection (Vertical, Horizontal, Oblique) +- [ ] Continuity Analysis & Discontinuity Classification + +#### Series & Approximations +- [ ] Taylor Series Expansion +- [ ] Maclaurin Series +- [ ] Series Convergence Visualization +- [ ] Fourier Series Decomposition + +#### Advanced Analysis +- [ ] Monotonicity Analysis (Increasing/Decreasing Intervals) +- [ ] Concavity Analysis (Concave Up/Down Regions) +- [ ] Global Extrema Finder +- [ ] Second Derivative Test Visualization + +--- + +### 🎨 Visualization & UI Enhancements (15 features) + +#### Interactive Controls +- [ ] Parameter Sliders (Real-time Function Adjustment) +- [ ] Interactive Tangent Line Tool (Click to Draw) +- [ ] Zoom & Pan Controls (Mouse Wheel, Drag) +- [ ] Dual-Pane Function Comparison +- [ ] Coordinate Display on Hover + +#### Visual Improvements +- [ ] Color-Coded Regions (Increasing/Decreasing, Concave Up/Down) +- [ ] Dark Theme Toggle +- [ ] Customizable Color Schemes +- [ ] High Contrast Accessibility Mode +- [ ] Better Point Markers with Labels +- [ ] Point Classification (Local Max/Min/Saddle) +- [ ] Vector Field Visualization +- [ ] Heatmap Displays + +#### Themes & Layout +- [ ] Responsive Layout (Screen Size Adaptation) +- [ ] Tabbed Organization for Topics +- [ ] Resizable Panels + +--- + +### 📐 Multi-Variable & 3D Calculus (8 features) + +- [ ] Partial Derivatives (∂f/∂x, ∂f/∂y) +- [ ] 3D Surface Plots for z = f(x,y) +- [ ] Contour Plots (Level Curves) +- [ ] Gradient Vector Fields (∇f) +- [ ] Double Integrals (Volume Under Surface) +- [ ] Constrained Optimization (Lagrange Multipliers) +- [ ] Jacobian & Hessian Matrices +- [ ] Polar & Cylindrical Coordinate Support + +--- + +### 🧮 Numerical Methods & Computation (10 features) + +#### Root Finding +- [ ] Newton-Raphson Method (with iteration visualization) +- [ ] Bisection Method +- [ ] Secant Method + +#### Differential Equations +- [ ] Direction (Slope) Fields for dy/dx = f(x,y) +- [ ] Euler's Method +- [ ] Runge-Kutta Methods (RK2, RK4) +- [ ] Solution Families Visualization + +#### Data & Optimization +- [ ] Curve Fitting (Polynomial Regression) +- [ ] Least Squares Fitting +- [ ] Data Import and Analysis + +--- + +### 🎓 Educational & Learning Features (12 features) + +- [ ] Step-by-Step Solution Display +- [ ] Integration Techniques Breakdown +- [ ] Critical Point Classification Explanation +- [ ] Function Library (Pre-built Examples) +- [ ] LaTeX Reference Guide +- [ ] Example Functions by Category +- [ ] Contextual Help & Tooltips +- [ ] Video Tutorial Links +- [ ] Practice Problems Generator +- [ ] Random Problem Generator +- [ ] Difficulty Level Selection +- [ ] Interactive Calculus Exercises + +--- + +### 💾 Export & Productivity (10 features) + +#### Export Formats +- [ ] High-Resolution PNG Export +- [ ] SVG Vector Graphics Export +- [ ] PDF Report Generation +- [ ] LaTeX Code Export +- [ ] CSV Data Export (Plot Coordinates) +- [ ] Copy to Clipboard + +#### Session Management +- [ ] Save Workspace to JSON +- [ ] Load Previous Sessions +- [ ] Import/Export Functionality +- [ ] Undo/Redo Navigation History + +--- + +### 📚 Function Type Support (6 features) + +- [ ] Parametric Curves (x=f(t), y=g(t)) +- [ ] Polar Coordinates (r=f(θ)) +- [ ] Implicit Functions (F(x,y)=0) +- [ ] Piecewise Functions +- [ ] Complex Functions (Real/Imaginary Parts) +- [ ] Vector-Valued Functions + +--- + +### 🎬 Animation & Interactivity (6 features) + +- [ ] Derivative Definition Animation (h→0) +- [ ] Parameter Animation (Play/Pause Controls) +- [ ] Convergence Animation (Series, Riemann Sums) +- [ ] Revolution Animation (Volume of Solids) +- [ ] Export Animation to GIF/Video +- [ ] Timeline Scrubber for Replays + +--- + +### 🔧 Technical & Performance (8 features) + +- [ ] Modular Code Architecture (Separate Files) +- [ ] Abstract Base Classes for Features +- [ ] Configuration File (Settings, Defaults) +- [ ] Computation Caching +- [ ] Asynchronous Plotting (Non-blocking UI) +- [ ] GPU Acceleration for 3D Plots +- [ ] Error Highlighting in LaTeX Input +- [ ] Keyboard Shortcuts + +--- + +### 🌐 Accessibility & Collaboration (6 features) + +- [ ] Screen Reader Support +- [ ] Keyboard Navigation +- [ ] Larger Font Options +- [ ] Share Session via URL/Code +- [ ] Mobile-Responsive Interface +- [ ] Touch-Friendly Controls + +--- + +## 📈 Implementation Priority Summary + +### 🔴 **Phase 1: Critical (Months 1-2)** +**Total: 8 features** + +1. Riemann Sums Visualization ⭐ +2. Taylor Series Expansion ⭐ +3. Interactive Parameter Sliders ⭐ +4. Limits Calculator & Asymptotes ⭐ +5. Dark Theme Toggle +6. Color-Coded Analysis Regions +7. PNG/PDF Export +8. Function Library (Pre-built Examples) + +**Why**: High educational value, quick wins, foundational for future features + +--- + +### 🟡 **Phase 2: High Value (Months 3-5)** +**Total: 12 features** + +1. Volume of Revolution (3D) ⭐ +2. Partial Derivatives & Surface Plots ⭐ +3. Numerical Methods (Newton-Raphson, Bisection) +4. ODE Solvers & Slope Fields +5. Parametric & Polar Curves +6. Concavity/Monotonicity Shading +7. Interactive Tangent Line Tool +8. Zoom & Pan Controls +9. Step-by-Step Solutions +10. Session Save/Load +11. LaTeX Export +12. Definite/Indefinite Integrals Tab + +**Why**: Expands scope to multi-variable calculus, adds professional features + +--- + +### 🟢 **Phase 3: Polish (Months 6-8)** +**Total: 15+ features** + +1. Code Refactoring (Modular Architecture) 🔧 +2. Advanced Series (Fourier, Sequences) +3. Complex Functions +4. Vector Calculus (Line/Surface Integrals) +5. Constrained Optimization +6. Animation Features +7. Data Fitting & Regression +8. Comprehensive Testing Suite +9. Documentation & User Guide +10. Performance Optimization +11. Accessibility Features +12. Collaboration/Sharing Features +13. Practice Problem Generator +14. Multiple Language Support +15. Plugin System + +**Why**: Long-term sustainability, community building, advanced users + +--- + +## 📊 Statistics + +- **Total Features Proposed**: 92+ +- **Core Calculus Features**: 17 +- **UI/UX Enhancements**: 15 +- **Multi-variable Calculus**: 8 +- **Numerical Methods**: 10 +- **Educational Tools**: 12 +- **Export/Productivity**: 10 +- **Function Types**: 6 +- **Animations**: 6 +- **Technical Improvements**: 8 +- **Accessibility**: 6 + +--- + +## 🎯 Top 10 Most Impactful Features (Quick Wins) + +1. **Riemann Sums Visualization** - Essential for integral understanding +2. **Interactive Parameter Sliders** - Transforms user experience +3. **Taylor Series with Convergence** - Core calculus concept +4. **Limits & Asymptote Detection** - Foundational analysis tool +5. **Dark Theme** - Modern UI expectation, easy to implement +6. **Tangent Line Tool** - Interactive learning enhancement +7. **PDF/PNG Export** - High user value for assignments +8. **Color-Coded Intervals** - Visual clarity for analysis +9. **Function Library** - Better onboarding, quick start +10. **Zoom & Pan** - Essential for detailed exploration + +--- + +## 💡 Innovation Opportunities + +### Unique Features (Not in Most Calculators) +- **3D Volume of Revolution Animation** - Rotate surface in real-time +- **Comparative Analysis Mode** - Side-by-side function comparison +- **AI-Powered Step Suggestions** - Intelligent problem-solving hints +- **Collaborative Sessions** - Share and solve problems together +- **Gamification** - Points, badges for solving problems +- **AR Visualization** - View 3D surfaces in augmented reality +- **Voice Input** - Speak equations naturally + +--- + +## 📝 Notes for Developers + +### Quick Start Development +1. Start with Phase 1 features (highest ROI) +2. Focus on one category at a time +3. Maintain backward compatibility +4. Write tests for mathematical operations +5. Document as you go + +### Code Organization +- Keep UI and logic separate +- Use factory pattern for different plot types +- Implement observer pattern for real-time updates +- Cache expensive SymPy computations + +### User Experience Principles +- **Immediate Feedback**: No lag between input and visualization +- **Discoverability**: Features should be easy to find +- **Error Prevention**: Validate input before processing +- **Consistency**: Similar features should work similarly +- **Accessibility**: Support keyboard, screen readers, high contrast + +--- + +## 🔗 Related Documents + +- [FEATURE_ROADMAP.md](FEATURE_ROADMAP.md) - Detailed feature descriptions and implementation plan +- [README.md](README.md) - Project overview +- [requirements.txt](requirements.txt) - Current dependencies + +--- + +## 📞 Contribution Guidelines + +Interested in implementing a feature? +1. Check if the feature is already in progress +2. Create an issue discussing the feature +3. Submit a pull request with tests +4. Update documentation + +--- + +**Last Updated**: January 2026 +**Status**: Proposal Phase +**Maintainer**: Visual Calculus Team diff --git a/FEATURE_ROADMAP.md b/FEATURE_ROADMAP.md new file mode 100644 index 0000000..28b5acf --- /dev/null +++ b/FEATURE_ROADMAP.md @@ -0,0 +1,533 @@ +# Visual Calculus - Feature Roadmap + +## Overview +This document outlines a comprehensive list of features that can be added to the Visual Calculus application to transform it from a basic calculus visualization tool into a professional-grade educational platform. + +## Current Features (v0.1) +- **Function Analyzer**: Plots functions with first and second derivatives, identifies critical points and inflection points +- **Area Between Curves**: Calculates and visualizes the area between two functions over a specified interval + +--- + +## Proposed Features + +### 🔴 High Priority Features + +#### 1. Integration Tools +**Category**: Core Calculus Features + +- **Definite Integrals Visualizer** + - Calculate and display definite integrals ∫[a,b] f(x)dx + - Show the area under the curve with shading + - Display numerical result and symbolic solution + +- **Indefinite Integrals** + - Compute antiderivatives with symbolic representation + - Show family of curves (C parameter) + +- **Riemann Sums Visualization** + - Interactive visualization of approximation methods + - Left endpoint, right endpoint, midpoint, trapezoidal methods + - Slider to control number of rectangles (n) + - Animate convergence as n → ∞ + - Display error compared to exact integral + +#### 2. Limits and Continuity +**Category**: Core Calculus Features + +- **Limit Calculator** + - Compute lim[x→a] f(x) + - Visualize left-hand and right-hand limits + - Identify discontinuities + +- **Asymptote Detection** + - Automatically detect and display vertical asymptotes + - Show horizontal and oblique asymptotes + - Visual representation with dashed lines + +- **Continuity Analysis** + - Highlight points of discontinuity + - Classify discontinuity types (removable, jump, infinite) + +#### 3. Taylor and Maclaurin Series +**Category**: Core Calculus Features + +- **Series Expansion** + - Generate Taylor series up to nth degree + - Maclaurin series (centered at 0) + - Display symbolic expansion + +- **Convergence Visualization** + - Overlay series approximations of different orders + - Animate increasing orders to show convergence + - Show interval of convergence + - Error bounds visualization + +#### 4. Interactive Controls +**Category**: UI/UX Enhancement + +- **Parameter Sliders** + - Real-time adjustment of function coefficients + - Interactive exploration of function families (e.g., ax² + bx + c) + - Immediate plot updates without re-clicking analyze + +- **Tangent Line Tool** + - Click on any point to draw tangent line + - Display slope value and equation of tangent + - Show normal line option + +- **Zoom and Pan Controls** + - Mouse wheel zoom + - Click-and-drag panning + - Reset view button + - Custom axis range quick-set buttons + +#### 5. Visualization Enhancements +**Category**: UI/UX Enhancement + +- **Color-Coded Regions** + - Show increasing/decreasing intervals in different colors + - Highlight concave up/down regions + - Use different colors for f(x), f'(x), f''(x) + +- **Dark Theme** + - Toggle between light and dark modes + - Customizable color schemes + - High contrast option for accessibility + +- **Better Point Markers** + - Label critical points as "Local Max" or "Local Min" + - Show coordinates on hover + - Display second derivative test results + +#### 6. Volume of Revolution +**Category**: Core Calculus Features + +- **3D Visualization** + - Disk method (rotation around x-axis or y-axis) + - Shell method + - Interactive 3D plot with rotation controls + - Calculate volume symbolically and numerically + +- **Cross-Section Display** + - Show representative disk/shell + - Animate the revolution process + +--- + +### 🟡 Medium Priority Features + +#### 7. Multi-Variable Calculus +**Category**: Advanced Calculus + +- **Partial Derivatives** + - Compute ∂f/∂x and ∂f/∂y for z = f(x,y) + - 3D surface plots + - Contour plots (level curves) + +- **Gradient Visualization** + - Vector field showing ∇f + - Gradient at specific points + - Direction of steepest ascent + +- **Double Integrals** + - Calculate volume under surface + - Visualize region of integration + - Polar coordinate support + +#### 8. Numerical Methods +**Category**: Computational Tools + +- **Root Finding** + - Newton-Raphson method with iteration visualization + - Bisection method step-by-step + - Secant method + - Show convergence path on graph + +- **Numerical Integration** + - Simpson's rule + - Gaussian quadrature + - Compare accuracy of different methods + +- **ODE Solvers** + - Direction (slope) fields for dy/dx = f(x,y) + - Euler's method + - Runge-Kutta methods + - Solution curve families + +#### 9. Function Analysis Tools +**Category**: Mathematical Analysis + +- **Monotonicity Analysis** + - Detailed increasing/decreasing intervals + - Sign chart for f'(x) + +- **Concavity Analysis** + - Concave up/down intervals + - Sign chart for f''(x) + - Link to inflection points + +- **Global Extrema** + - Find absolute max/min on closed interval + - Check endpoints and critical points + - Display comparison table + +#### 10. Export and Save Features +**Category**: Productivity + +- **Image Export** + - High-resolution PNG export + - SVG vector graphics export + - Copy to clipboard + +- **PDF Reports** + - Generate PDF with plots and analysis + - Include symbolic expressions + - Formatted for printing + +- **Session Management** + - Save current workspace to JSON + - Load previous sessions + - Export/import functionality + +- **LaTeX Export** + - Export equations to LaTeX code + - Generate full report template + - Copy formatted expressions + +#### 11. Additional Function Types +**Category**: Mathematical Diversity + +- **Parametric Curves** + - Plot x = f(t), y = g(t) + - Show velocity and acceleration vectors + - Calculate arc length + +- **Polar Coordinates** + - Plot r = f(θ) + - Convert to Cartesian + - Calculate area in polar coordinates + +- **Implicit Functions** + - Plot F(x,y) = 0 + - Circle, ellipse, and general implicit curves + +- **Piecewise Functions** + - Support for different definitions on different intervals + - Discontinuity handling + - Conditional notation input + +#### 12. Educational Features +**Category**: Learning Enhancement + +- **Step-by-Step Solutions** + - Show algebraic steps for derivatives + - Integration techniques breakdown + - Critical point classification explanation + +- **Help and Documentation** + - Integrated LaTeX reference guide + - Example functions library + - Contextual tooltips + - Video tutorial links + +- **Function Library** + - Pre-built common functions (sin, cos, polynomials, etc.) + - Click to load and explore + - Categorized by type + +- **Practice Problems** + - Built-in exercises with solutions + - Random problem generator + - Difficulty levels + +--- + +### 🟢 Lower Priority / Future Enhancements + +#### 13. Advanced Calculus Topics +**Category**: Advanced Features + +- **Sequences and Series** + - Convergence tests visualization + - Partial sums + - Geometric and harmonic series + +- **Vector Calculus** + - Line integrals + - Surface integrals + - Green's theorem, Stokes' theorem visualization + +- **Complex Functions** + - Plot real and imaginary parts + - Magnitude and phase plots + - Conformal mapping visualization + +#### 14. Animation Features +**Category**: Interactive Learning + +- **Derivative Animation** + - Animate secant line → tangent line + - Show (f(x+h) - f(x))/h as h → 0 + +- **Parameter Animation** + - Animate function transformation + - Play/pause controls + - Export to GIF or video + +#### 15. Data Analysis Integration +**Category**: Applied Mathematics + +- **Curve Fitting** + - Import data points + - Polynomial regression + - Least squares fitting + - Display R² value + +- **Optimization** + - Constrained optimization problems + - Lagrange multipliers + - Linear programming visualization + +#### 16. Accessibility and Sharing +**Category**: User Experience + +- **Accessibility Mode** + - High contrast themes + - Larger fonts + - Screen reader support + - Keyboard navigation + +- **Collaboration Features** + - Share session via URL/code + - Export classroom-ready presentations + +- **Mobile Responsive** + - Touch-friendly controls + - Simplified mobile interface + +#### 17. Performance Optimization +**Category**: Technical Enhancement + +- **Computation Caching** + - Store expensive symbolic calculations + - Faster re-rendering + +- **Asynchronous Plotting** + - Non-blocking UI during complex calculations + - Progress indicators + +- **GPU Acceleration** + - Hardware acceleration for 3D plots + - Faster rendering of complex surfaces + +--- + +## Implementation Roadmap + +### Phase 1: Essential Enhancements (1-2 months) +**Goal**: Add core missing calculus features and improve UX + +1. **Riemann Sums Visualization** (1 week) + - Most requested educational feature + - High visual impact + +2. **Taylor Series Expansion** (1 week) + - Strong educational value + - Relatively straightforward implementation + +3. **Interactive Sliders** (1 week) + - Significantly improves user experience + - Enables exploration-based learning + +4. **Limits Calculator** (1 week) + - Fundamental calculus concept + - Complements existing features + +5. **Dark Theme** (3 days) + - Quick win for user satisfaction + - Modern UI expectation + +6. **Export to PNG/PDF** (1 week) + - High user value + - Enables sharing and documentation + +### Phase 2: Advanced Features (2-3 months) +**Goal**: Expand to 3D and multi-variable calculus + +1. **Volume of Revolution 3D Visualization** (2 weeks) + - Requires 3D plotting infrastructure + - High educational impact + +2. **Partial Derivatives & 3D Surface Plots** (2 weeks) + - Opens multi-variable calculus + - Foundation for gradient visualization + +3. **Numerical Methods** (2 weeks) + - Root finding (Newton-Raphson, Bisection) + - ODE solvers with slope fields + +4. **Parametric & Polar Curves** (1 week) + - Expands function type support + +5. **Concavity/Monotonicity Shading** (1 week) + - Visual enhancement to existing analysis + +### Phase 3: Polish & Scalability (1-2 months) +**Goal**: Refactor and optimize for maintainability + +1. **Code Refactoring** (2 weeks) + - Split into modules (separate files) + - Create abstract base classes + - Implement plugin architecture + +2. **Function Library & Presets** (1 week) + - Pre-built examples + - Better onboarding experience + +3. **Comprehensive Documentation** (1 week) + - User guide + - API documentation + - Contribution guidelines + +4. **Testing Infrastructure** (1 week) + - Unit tests for calculations + - UI automation tests + +5. **Performance Optimization** (1 week) + - Caching mechanisms + - Asynchronous computations + +### Phase 4: Community & Ecosystem (Ongoing) +**Goal**: Build user base and contribution community + +1. **Online Demo/Web Version** + - Browser-based version (using PyScript or conversion to JavaScript) + +2. **Video Tutorials** + - Screen recordings demonstrating features + +3. **Educational Content** + - Blog posts on calculus concepts + - Integration with curriculum + +4. **Plugin System** + - Allow third-party extensions + - Custom visualization modules + +--- + +## Technical Recommendations + +### Architecture Improvements + +**Current Structure**: Single file (`visual_calculus.py`) + +**Proposed Structure**: +``` +visual_calculus/ +├── __init__.py +├── main.py # Entry point +├── ui/ +│ ├── __init__.py +│ ├── main_window.py # Main application window +│ ├── tabs/ +│ │ ├── function_analyzer.py +│ │ ├── area_between_curves.py +│ │ ├── riemann_sums.py # New +│ │ ├── taylor_series.py # New +│ │ └── ... +│ └── components/ +│ ├── plot_widget.py # Reusable plot component +│ └── slider_control.py # Parameter sliders +├── calculus/ +│ ├── __init__.py +│ ├── symbolic.py # SymPy operations +│ ├── numerical.py # Numerical methods +│ └── analysis.py # Function analysis +├── visualization/ +│ ├── __init__.py +│ ├── plots_2d.py # 2D plotting utilities +│ ├── plots_3d.py # 3D plotting utilities +│ └── themes.py # Color schemes, dark mode +├── utils/ +│ ├── __init__.py +│ ├── latex_parser.py # LaTeX input handling +│ └── export.py # PDF/PNG export +├── config/ +│ ├── settings.json # User preferences +│ └── defaults.py # Default values +└── tests/ + ├── test_symbolic.py + ├── test_numerical.py + └── test_ui.py +``` + +### Dependencies to Consider Adding +- **plotly**: Interactive 3D plots with built-in controls +- **scipy**: Advanced numerical methods +- **Pillow**: Image manipulation for exports +- **reportlab** or **fpdf**: PDF generation +- **PyQt5** or **PyQt6**: More advanced UI framework (future migration) +- **pytest**: Testing framework + +### UI Framework Considerations +- **Current**: Tkinter (simple, cross-platform, included with Python) +- **Alternative**: PyQt5/PySide6 (more modern, better styling, more widgets) +- **Web-based**: PyScript, Streamlit, or Dash (for online version) + +### Best Practices to Implement +1. **Separation of Concerns**: Keep UI, logic, and visualization separate +2. **Configuration Management**: Externalize settings (theme, defaults) +3. **Error Handling**: Graceful degradation and user-friendly error messages +4. **Logging**: Add logging for debugging +5. **Documentation**: Docstrings for all functions and classes +6. **Type Hints**: Use Python type annotations +7. **Testing**: Unit tests for mathematical operations +8. **Version Control**: Semantic versioning + +--- + +## Priority Matrix + +| Feature | Educational Value | Implementation Effort | User Demand | Priority Score | +|---------|------------------|----------------------|-------------|----------------| +| Riemann Sums | Very High | Medium | High | 🔴 Critical | +| Taylor Series | Very High | Medium | High | 🔴 Critical | +| Interactive Sliders | High | Low-Medium | Very High | 🔴 Critical | +| Limits & Asymptotes | Very High | Medium | High | 🔴 Critical | +| Dark Theme | Low | Very Low | High | 🟡 Quick Win | +| Export PNG/PDF | Medium | Medium | Very High | 🟡 High Value | +| Volume of Revolution 3D | High | High | Medium | 🟡 Medium | +| Multi-variable Calculus | High | Very High | Medium | 🟢 Future | +| Numerical Methods | High | Medium-High | Medium | 🟡 Medium | +| ODE Solvers | Medium | High | Low-Medium | 🟢 Future | +| Complex Functions | Low | High | Low | 🟢 Future | + +--- + +## Conclusion + +This roadmap transforms Visual Calculus from a basic tool into a **comprehensive, professional-grade calculus visualization platform**. The features are designed to: + +- **Support learning**: From basic derivatives to advanced multi-variable calculus +- **Enhance exploration**: Interactive controls and real-time feedback +- **Enable sharing**: Export capabilities for assignments and presentations +- **Maintain accessibility**: Clean UI with multiple theme options + +By implementing these features in phases, the application can grow sustainably while continuously delivering value to users. + +**Estimated Total Development Time**: 6-8 months for Phases 1-3 with a single developer + +**Target Audience**: +- High school calculus students +- University undergraduates +- Calculus instructors and educators +- Self-learners and enthusiasts + +**Success Metrics**: +- User engagement time +- Feature adoption rates +- Educational outcomes +- Community contributions +- GitHub stars and forks diff --git a/README.md b/README.md index ed95162..e41ab69 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,44 @@ # Visual-Calculus +A Python-based interactive calculus visualization tool built with Tkinter, SymPy, and Matplotlib. + +## Features + +### Current Features (v0.1) +- **Function Analyzer**: Visualize functions with their first and second derivatives, identify critical points and inflection points +- **Area Between Curves**: Calculate and visualize the area between two functions over a specified interval + ![pic_1](https://github.com/SharadhNaidu/Visual-Calculus/blob/main/Screenshot%202025-10-28%20102631.png) ![pic_2](https://github.com/SharadhNaidu/Visual-Calculus/blob/main/Screenshot%202025-10-28%20102657.png) + +## Installation + +```bash +pip install -r requirements.txt +python visual_calculus.py +``` + +## Future Development + +We have compiled a comprehensive list of 90+ features that can enhance this application into a professional-grade calculus visualization platform. See our planning documents: + +- **[FEATURE_ROADMAP.md](FEATURE_ROADMAP.md)** - Detailed feature descriptions, implementation plans, and technical architecture recommendations +- **[FEATURES_SUMMARY.md](FEATURES_SUMMARY.md)** - Quick reference guide with feature categories and priority rankings + +### Top Priority Features +1. Riemann Sums Visualization +2. Taylor Series Expansion +3. Interactive Parameter Sliders +4. Limits & Asymptote Detection +5. Dark Theme +6. 3D Volume of Revolution +7. Export to PDF/PNG +8. Multi-variable Calculus (Partial Derivatives, 3D Surfaces) + +## Contributing + +Contributions are welcome! Please check our feature roadmap documents to see what's planned and feel free to submit pull requests. + +## License + +Open source - feel free to use and modify. From a5fa75f147092b8759584a6112a6d87b55d63839 Mon Sep 17 00:00:00 2001 From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com> Date: Mon, 26 Jan 2026 12:43:16 +0000 Subject: [PATCH 3/4] Address code review feedback - remove placeholder timestamp Co-authored-by: SharadhNaidu <185215496+SharadhNaidu@users.noreply.github.com> --- FEATURES_SUMMARY.md | 1 - 1 file changed, 1 deletion(-) diff --git a/FEATURES_SUMMARY.md b/FEATURES_SUMMARY.md index 2ecd758..9417194 100644 --- a/FEATURES_SUMMARY.md +++ b/FEATURES_SUMMARY.md @@ -324,6 +324,5 @@ Interested in implementing a feature? --- -**Last Updated**: January 2026 **Status**: Proposal Phase **Maintainer**: Visual Calculus Team From ca2a4742c4ea6bdf76381771fb90c96b212ac48c Mon Sep 17 00:00:00 2001 From: SharadhNaidu Date: Mon, 26 Jan 2026 18:14:31 +0530 Subject: [PATCH 4/4] Delete FEATURES_SUMMARY.md --- FEATURES_SUMMARY.md | 328 -------------------------------------------- 1 file changed, 328 deletions(-) delete mode 100644 FEATURES_SUMMARY.md diff --git a/FEATURES_SUMMARY.md b/FEATURES_SUMMARY.md deleted file mode 100644 index 9417194..0000000 --- a/FEATURES_SUMMARY.md +++ /dev/null @@ -1,328 +0,0 @@ -# Visual Calculus - Feature Enhancement Summary - -## Quick Reference: Proposed Features by Category - -This document provides a condensed overview of all proposed features. See [FEATURE_ROADMAP.md](FEATURE_ROADMAP.md) for detailed descriptions and implementation plans. - ---- - -## 📊 Feature Categories - -### 🔴 Core Calculus Features (17 features) - -#### Integration & Area -- [ ] Definite Integrals Visualizer -- [ ] Indefinite Integrals (Antiderivatives) -- [ ] Riemann Sums (Left, Right, Midpoint, Trapezoidal) -- [ ] Volume of Revolution (Disk/Shell Method) with 3D -- [ ] Arc Length Calculator -- [ ] Numerical Integration (Simpson's, Gaussian Quadrature) - -#### Limits & Continuity -- [ ] Limit Calculator (Left/Right Limits) -- [ ] Asymptote Detection (Vertical, Horizontal, Oblique) -- [ ] Continuity Analysis & Discontinuity Classification - -#### Series & Approximations -- [ ] Taylor Series Expansion -- [ ] Maclaurin Series -- [ ] Series Convergence Visualization -- [ ] Fourier Series Decomposition - -#### Advanced Analysis -- [ ] Monotonicity Analysis (Increasing/Decreasing Intervals) -- [ ] Concavity Analysis (Concave Up/Down Regions) -- [ ] Global Extrema Finder -- [ ] Second Derivative Test Visualization - ---- - -### 🎨 Visualization & UI Enhancements (15 features) - -#### Interactive Controls -- [ ] Parameter Sliders (Real-time Function Adjustment) -- [ ] Interactive Tangent Line Tool (Click to Draw) -- [ ] Zoom & Pan Controls (Mouse Wheel, Drag) -- [ ] Dual-Pane Function Comparison -- [ ] Coordinate Display on Hover - -#### Visual Improvements -- [ ] Color-Coded Regions (Increasing/Decreasing, Concave Up/Down) -- [ ] Dark Theme Toggle -- [ ] Customizable Color Schemes -- [ ] High Contrast Accessibility Mode -- [ ] Better Point Markers with Labels -- [ ] Point Classification (Local Max/Min/Saddle) -- [ ] Vector Field Visualization -- [ ] Heatmap Displays - -#### Themes & Layout -- [ ] Responsive Layout (Screen Size Adaptation) -- [ ] Tabbed Organization for Topics -- [ ] Resizable Panels - ---- - -### 📐 Multi-Variable & 3D Calculus (8 features) - -- [ ] Partial Derivatives (∂f/∂x, ∂f/∂y) -- [ ] 3D Surface Plots for z = f(x,y) -- [ ] Contour Plots (Level Curves) -- [ ] Gradient Vector Fields (∇f) -- [ ] Double Integrals (Volume Under Surface) -- [ ] Constrained Optimization (Lagrange Multipliers) -- [ ] Jacobian & Hessian Matrices -- [ ] Polar & Cylindrical Coordinate Support - ---- - -### 🧮 Numerical Methods & Computation (10 features) - -#### Root Finding -- [ ] Newton-Raphson Method (with iteration visualization) -- [ ] Bisection Method -- [ ] Secant Method - -#### Differential Equations -- [ ] Direction (Slope) Fields for dy/dx = f(x,y) -- [ ] Euler's Method -- [ ] Runge-Kutta Methods (RK2, RK4) -- [ ] Solution Families Visualization - -#### Data & Optimization -- [ ] Curve Fitting (Polynomial Regression) -- [ ] Least Squares Fitting -- [ ] Data Import and Analysis - ---- - -### 🎓 Educational & Learning Features (12 features) - -- [ ] Step-by-Step Solution Display -- [ ] Integration Techniques Breakdown -- [ ] Critical Point Classification Explanation -- [ ] Function Library (Pre-built Examples) -- [ ] LaTeX Reference Guide -- [ ] Example Functions by Category -- [ ] Contextual Help & Tooltips -- [ ] Video Tutorial Links -- [ ] Practice Problems Generator -- [ ] Random Problem Generator -- [ ] Difficulty Level Selection -- [ ] Interactive Calculus Exercises - ---- - -### 💾 Export & Productivity (10 features) - -#### Export Formats -- [ ] High-Resolution PNG Export -- [ ] SVG Vector Graphics Export -- [ ] PDF Report Generation -- [ ] LaTeX Code Export -- [ ] CSV Data Export (Plot Coordinates) -- [ ] Copy to Clipboard - -#### Session Management -- [ ] Save Workspace to JSON -- [ ] Load Previous Sessions -- [ ] Import/Export Functionality -- [ ] Undo/Redo Navigation History - ---- - -### 📚 Function Type Support (6 features) - -- [ ] Parametric Curves (x=f(t), y=g(t)) -- [ ] Polar Coordinates (r=f(θ)) -- [ ] Implicit Functions (F(x,y)=0) -- [ ] Piecewise Functions -- [ ] Complex Functions (Real/Imaginary Parts) -- [ ] Vector-Valued Functions - ---- - -### 🎬 Animation & Interactivity (6 features) - -- [ ] Derivative Definition Animation (h→0) -- [ ] Parameter Animation (Play/Pause Controls) -- [ ] Convergence Animation (Series, Riemann Sums) -- [ ] Revolution Animation (Volume of Solids) -- [ ] Export Animation to GIF/Video -- [ ] Timeline Scrubber for Replays - ---- - -### 🔧 Technical & Performance (8 features) - -- [ ] Modular Code Architecture (Separate Files) -- [ ] Abstract Base Classes for Features -- [ ] Configuration File (Settings, Defaults) -- [ ] Computation Caching -- [ ] Asynchronous Plotting (Non-blocking UI) -- [ ] GPU Acceleration for 3D Plots -- [ ] Error Highlighting in LaTeX Input -- [ ] Keyboard Shortcuts - ---- - -### 🌐 Accessibility & Collaboration (6 features) - -- [ ] Screen Reader Support -- [ ] Keyboard Navigation -- [ ] Larger Font Options -- [ ] Share Session via URL/Code -- [ ] Mobile-Responsive Interface -- [ ] Touch-Friendly Controls - ---- - -## 📈 Implementation Priority Summary - -### 🔴 **Phase 1: Critical (Months 1-2)** -**Total: 8 features** - -1. Riemann Sums Visualization ⭐ -2. Taylor Series Expansion ⭐ -3. Interactive Parameter Sliders ⭐ -4. Limits Calculator & Asymptotes ⭐ -5. Dark Theme Toggle -6. Color-Coded Analysis Regions -7. PNG/PDF Export -8. Function Library (Pre-built Examples) - -**Why**: High educational value, quick wins, foundational for future features - ---- - -### 🟡 **Phase 2: High Value (Months 3-5)** -**Total: 12 features** - -1. Volume of Revolution (3D) ⭐ -2. Partial Derivatives & Surface Plots ⭐ -3. Numerical Methods (Newton-Raphson, Bisection) -4. ODE Solvers & Slope Fields -5. Parametric & Polar Curves -6. Concavity/Monotonicity Shading -7. Interactive Tangent Line Tool -8. Zoom & Pan Controls -9. Step-by-Step Solutions -10. Session Save/Load -11. LaTeX Export -12. Definite/Indefinite Integrals Tab - -**Why**: Expands scope to multi-variable calculus, adds professional features - ---- - -### 🟢 **Phase 3: Polish (Months 6-8)** -**Total: 15+ features** - -1. Code Refactoring (Modular Architecture) 🔧 -2. Advanced Series (Fourier, Sequences) -3. Complex Functions -4. Vector Calculus (Line/Surface Integrals) -5. Constrained Optimization -6. Animation Features -7. Data Fitting & Regression -8. Comprehensive Testing Suite -9. Documentation & User Guide -10. Performance Optimization -11. Accessibility Features -12. Collaboration/Sharing Features -13. Practice Problem Generator -14. Multiple Language Support -15. Plugin System - -**Why**: Long-term sustainability, community building, advanced users - ---- - -## 📊 Statistics - -- **Total Features Proposed**: 92+ -- **Core Calculus Features**: 17 -- **UI/UX Enhancements**: 15 -- **Multi-variable Calculus**: 8 -- **Numerical Methods**: 10 -- **Educational Tools**: 12 -- **Export/Productivity**: 10 -- **Function Types**: 6 -- **Animations**: 6 -- **Technical Improvements**: 8 -- **Accessibility**: 6 - ---- - -## 🎯 Top 10 Most Impactful Features (Quick Wins) - -1. **Riemann Sums Visualization** - Essential for integral understanding -2. **Interactive Parameter Sliders** - Transforms user experience -3. **Taylor Series with Convergence** - Core calculus concept -4. **Limits & Asymptote Detection** - Foundational analysis tool -5. **Dark Theme** - Modern UI expectation, easy to implement -6. **Tangent Line Tool** - Interactive learning enhancement -7. **PDF/PNG Export** - High user value for assignments -8. **Color-Coded Intervals** - Visual clarity for analysis -9. **Function Library** - Better onboarding, quick start -10. **Zoom & Pan** - Essential for detailed exploration - ---- - -## 💡 Innovation Opportunities - -### Unique Features (Not in Most Calculators) -- **3D Volume of Revolution Animation** - Rotate surface in real-time -- **Comparative Analysis Mode** - Side-by-side function comparison -- **AI-Powered Step Suggestions** - Intelligent problem-solving hints -- **Collaborative Sessions** - Share and solve problems together -- **Gamification** - Points, badges for solving problems -- **AR Visualization** - View 3D surfaces in augmented reality -- **Voice Input** - Speak equations naturally - ---- - -## 📝 Notes for Developers - -### Quick Start Development -1. Start with Phase 1 features (highest ROI) -2. Focus on one category at a time -3. Maintain backward compatibility -4. Write tests for mathematical operations -5. Document as you go - -### Code Organization -- Keep UI and logic separate -- Use factory pattern for different plot types -- Implement observer pattern for real-time updates -- Cache expensive SymPy computations - -### User Experience Principles -- **Immediate Feedback**: No lag between input and visualization -- **Discoverability**: Features should be easy to find -- **Error Prevention**: Validate input before processing -- **Consistency**: Similar features should work similarly -- **Accessibility**: Support keyboard, screen readers, high contrast - ---- - -## 🔗 Related Documents - -- [FEATURE_ROADMAP.md](FEATURE_ROADMAP.md) - Detailed feature descriptions and implementation plan -- [README.md](README.md) - Project overview -- [requirements.txt](requirements.txt) - Current dependencies - ---- - -## 📞 Contribution Guidelines - -Interested in implementing a feature? -1. Check if the feature is already in progress -2. Create an issue discussing the feature -3. Submit a pull request with tests -4. Update documentation - ---- - -**Status**: Proposal Phase -**Maintainer**: Visual Calculus Team