src/vector_physics.py

import numpy as np
import matplotlib.pyplot as plt
import streamlit as st
import math
import random

class Vector2D:
    """A 2D vector class for physics calculations"""
    
    def __init__(self, x=0, y=0, magnitude=None, angle=None):
        if magnitude is not None and angle is not None:
            # Create vector from magnitude and angle (in degrees)
            self.x = magnitude * math.cos(math.radians(angle))
            self.y = magnitude * math.sin(math.radians(angle))
        else:
            self.x = x
            self.y = y

    def __repr__(self):
        return f"Vector2D(x={self.x:.2f}, y={self.y:.2f}, mag={self.magnitude:.2f}, angle={self.angle:.1f}°)"
    
    def __rmul__(self, scalar):
        """Allow scalar * vector multiplication"""
        return self.__mul__(scalar)
    
    def cross_product_2d(self, other):
        """2D cross product (returns scalar z-component)"""
        return self.x * other.y - self.y * other.x
    
    def angle_between(self, other):
        """Calculate angle between two vectors in degrees"""
        dot_prod = self.dot_product(other)
        mags = self.magnitude * other.magnitude
        if mags == 0:
            return 0
        cos_angle = dot_prod / mags
        # Clamp to avoid floating point errors
        cos_angle = max(-1, min(1, cos_angle))
        return math.degrees(math.acos(cos_angle))

    @property
    def magnitude(self):
        return math.sqrt(self.x**2 + self.y**2)
    
    @property
    def angle(self):
        return math.degrees(math.atan2(self.y, self.x))
    
    def __add__(self, other):
        return Vector2D(self.x + other.x, self.y + other.y)
    
    def __sub__(self, other):
        return Vector2D(self.x - other.x, self.y - other.y)
    
    def __mul__(self, scalar):
        return Vector2D(self.x * scalar, self.y * scalar)
    
    def dot_product(self, other):
        return self.x * other.x + self.y * other.y
    
    def unit_vector(self):
        mag = self.magnitude
        if mag == 0:
            return Vector2D(0, 0)
        return Vector2D(self.x / mag, self.y / mag)

class UnitConverter:
    """Unit conversion utilities for physics calculations"""
    
    @staticmethod
    def speed_conversions():
        return {
            "m/s": 1.0,
            "km/h": 3.6,
            "mph": 2.237,
            "ft/s": 3.281,
            "knots": 1.944
        }
    
    @staticmethod
    def distance_conversions():
        return {
            "meters": 1.0,
            "kilometers": 0.001,
            "miles": 0.000621,
            "feet": 3.281,
            "yards": 1.094
        }
    
    @staticmethod
    def convert_speed(value, from_unit, to_unit):
        conversions = UnitConverter.speed_conversions()
        # Convert to m/s first, then to target unit
        ms_value = value / conversions[from_unit]
        return ms_value * conversions[to_unit]
    
    @staticmethod
    def convert_distance(value, from_unit, to_unit):
        conversions = UnitConverter.distance_conversions()
        # Convert to meters first, then to target unit
        m_value = value / conversions[from_unit]
        return m_value * conversions[to_unit]

class QuizGenerator:
    """Generate quiz questions for vector concepts"""
    
    def __init__(self):
        self.question_types = [
            "vector_addition",
            "vector_magnitude",
            "vector_angle",
            "boat_crossing",
            "projectile_range"
        ]
    
    def generate_question(self):
        question_type = random.choice(self.question_types)
        
        if question_type == "vector_addition":
            return self._vector_addition_question()
        elif question_type == "vector_magnitude":
            return self._vector_magnitude_question()
        elif question_type == "vector_angle":
            return self._vector_angle_question()
        elif question_type == "boat_crossing":
            return self._boat_crossing_question()
        elif question_type == "projectile_range":
            return self._projectile_range_question()
    
    def _vector_addition_question(self):
        mag_a = random.uniform(3, 8)
        angle_a = random.choice([0, 30, 45, 60, 90, 120, 135, 150, 180])
        mag_b = random.uniform(3, 8)
        angle_b = random.choice([0, 30, 45, 60, 90, 120, 135, 150, 180])
        
        vec_a = Vector2D(magnitude=mag_a, angle=angle_a)
        vec_b = Vector2D(magnitude=mag_b, angle=angle_b)
        result = vec_a + vec_b
        
        return {
            "type": "vector_addition",
            "question": f"Vector A has magnitude {mag_a:.1f} at {angle_a}°, Vector B has magnitude {mag_b:.1f} at {angle_b}°. What is the magnitude of their sum?",
            "answer": result.magnitude,
            "tolerance": 0.5,
            "explanation": f"Vector A + Vector B = ({vec_a.x:.2f}, {vec_a.y:.2f}) + ({vec_b.x:.2f}, {vec_b.y:.2f}) = ({result.x:.2f}, {result.y:.2f})\nMagnitude = √({result.x:.2f}² + {result.y:.2f}²) = {result.magnitude:.2f}"
        }
    
    def _vector_magnitude_question(self):
        x = random.uniform(-10, 10)
        y = random.uniform(-10, 10)
        vec = Vector2D(x, y)
        
        return {
            "type": "vector_magnitude",
            "question": f"A vector has components x = {x:.1f} and y = {y:.1f}. What is its magnitude?",
            "answer": vec.magnitude,
            "tolerance": 0.2,
            "explanation": f"Magnitude = √(x² + y²) = √({x:.1f}² + {y:.1f}²) = √({x**2:.1f} + {y**2:.1f}) = {vec.magnitude:.2f}"
        }
    
    def _vector_angle_question(self):
        x = random.uniform(-10, 10)
        y = random.uniform(-10, 10)
        vec = Vector2D(x, y)
        
        return {
            "type": "vector_angle",
            "question": f"A vector has components x = {x:.1f} and y = {y:.1f}. What is its angle in degrees?",
            "answer": vec.angle,
            "tolerance": 2.0,
            "explanation": f"Angle = arctan(y/x) = arctan({y:.1f}/{x:.1f}) = {vec.angle:.1f}°"
        }
    
    def _boat_crossing_question(self):
        boat_speed = random.uniform(4, 8)
        current_speed = random.uniform(2, 5)
        boat_angle = 90  # Straight across
        current_angle = 180  # Opposite direction
        
        boat_vel = Vector2D(magnitude=boat_speed, angle=boat_angle)
        current_vel = Vector2D(magnitude=current_speed, angle=current_angle)
        result = boat_vel + current_vel
        
        return {
            "type": "boat_crossing",
            "question": f"A boat aims straight across a river at {boat_speed:.1f} m/s. The current flows at {current_speed:.1f} m/s opposite to the boat. What is the boat's actual speed?",
            "answer": result.magnitude,
            "tolerance": 0.3,
            "explanation": f"Resultant velocity = √({boat_speed}² + {current_speed}²) = {result.magnitude:.2f} m/s"
        }
    
    def _projectile_range_question(self):
        speed = random.uniform(15, 25)
        angle = 45  # Optimal angle
        gravity = 9.81
        
        # Range formula: R = v²sin(2θ)/g
        range_m = (speed**2 * math.sin(math.radians(2 * angle))) / gravity
        
        return {
            "type": "projectile_range",
            "question": f"A projectile is launched at {speed:.0f} m/s at 45°. What is its range in meters? (g = 9.81 m/s²)",
            "answer": range_m,
            "tolerance": 2.0,
            "explanation": f"Range = v²sin(2θ)/g = {speed}²×sin(90°)/9.81 = {speed**2}/9.81 = {range_m:.1f} m"
        }

class VectorPhysicsSimulator:
    """Physics simulator for vector problems"""
    
    def __init__(self):
        self.time_step = 0.1
        self.max_time = 20
    
    def boat_crossing_problem(self, boat_speed, boat_angle, current_speed, current_angle):
        """

        Simulate a boat crossing a river with current

        Returns the resultant velocity and trajectory

        """
        boat_velocity = Vector2D(magnitude=boat_speed, angle=boat_angle)
        current_velocity = Vector2D(magnitude=current_speed, angle=current_angle)
        
        # Resultant velocity
        resultant_velocity = boat_velocity + current_velocity
        
        # Calculate angle between intended and actual heading
        heading_difference = boat_velocity.angle_between(resultant_velocity)
        
        # Calculate trajectory points
        time_points = np.arange(0, self.max_time, self.time_step)
        x_points = resultant_velocity.x * time_points
        y_points = resultant_velocity.y * time_points
        
        return {
            'boat_velocity': boat_velocity,
            'current_velocity': current_velocity,
            'resultant_velocity': resultant_velocity,
            'heading_difference': heading_difference,
            'trajectory_x': x_points,
            'trajectory_y': y_points,
            'time_points': time_points
        }
    
    def projectile_motion(self, initial_speed, launch_angle, gravity=9.81):
        """

        Simulate projectile motion with error analysis

        """
        initial_velocity = Vector2D(magnitude=initial_speed, angle=launch_angle)
        
        # Calculate trajectory
        time_flight = 2 * initial_velocity.y / gravity if initial_velocity.y > 0 else 0
        time_points = np.linspace(0, time_flight, 100) if time_flight > 0 else np.array([0])
        
        x_points = initial_velocity.x * time_points
        y_points = initial_velocity.y * time_points - 0.5 * gravity * time_points**2
        
        # Error analysis - show effect of 5% measurement uncertainty
        speed_error = initial_speed * 0.05
        angle_error = 2  # 2 degree uncertainty
        
        # Upper bound
        upper_vel = Vector2D(magnitude=initial_speed + speed_error, angle=launch_angle + angle_error)
        upper_flight = 2 * upper_vel.y / gravity if upper_vel.y > 0 else 0
        upper_time = np.linspace(0, upper_flight, 100) if upper_flight > 0 else np.array([0])
        upper_x = upper_vel.x * upper_time
        upper_y = upper_vel.y * upper_time - 0.5 * gravity * upper_time**2
        
        # Lower bound
        lower_vel = Vector2D(magnitude=max(0.1, initial_speed - speed_error), angle=launch_angle - angle_error)
        lower_flight = 2 * lower_vel.y / gravity if lower_vel.y > 0 else 0
        lower_time = np.linspace(0, lower_flight, 100) if lower_flight > 0 else np.array([0])
        lower_x = lower_vel.x * lower_time
        lower_y = lower_vel.y * lower_time - 0.5 * gravity * lower_time**2
        
        return {
            'initial_velocity': initial_velocity,
            'trajectory_x': x_points,
            'trajectory_y': y_points,
            'time_points': time_points,
            'max_range': max(x_points) if len(x_points) > 0 else 0,
            'max_height': max(y_points) if len(y_points) > 0 else 0,
            'error_upper_x': upper_x,
            'error_upper_y': upper_y,
            'error_lower_x': lower_x,
            'error_lower_y': lower_y,
            'speed_uncertainty': speed_error,
            'angle_uncertainty': angle_error
        }

def plot_vectors(ax, vectors, labels, colors, origin=(0, 0)):
    """Plot vectors on matplotlib axes"""
    ax.clear()
    
    for vector, label, color in zip(vectors, labels, colors):
        ax.arrow(origin[0], origin[1], vector.x, vector.y, 
                head_width=0.5, head_length=0.5, fc=color, ec=color, 
                linewidth=2, label=label)
    
    ax.set_xlim(-10, 15)
    ax.set_ylim(-10, 15)
    ax.grid(True, alpha=0.3)
    ax.set_aspect('equal')
    ax.legend()
    ax.set_xlabel('X (m/s)')
    ax.set_ylabel('Y (m/s)')

def plot_trajectory(ax, x_points, y_points, title="Trajectory", error_bounds=None):
    """Plot trajectory on matplotlib axes with optional error bounds"""
    ax.clear()
    ax.plot(x_points, y_points, 'b-', linewidth=2, label='Trajectory')
    
    if error_bounds:
        ax.plot(error_bounds['upper_x'], error_bounds['upper_y'], 'r--', alpha=0.6, label='Upper bound (+5% speed, +2° angle)')
        ax.plot(error_bounds['lower_x'], error_bounds['lower_y'], 'g--', alpha=0.6, label='Lower bound (-5% speed, -2° angle)')
        ax.fill_between(error_bounds['upper_x'], error_bounds['upper_y'], 
                       error_bounds['lower_y'][:len(error_bounds['upper_y'])], 
                       alpha=0.2, color='yellow', label='Uncertainty range')
    
    ax.scatter(x_points[0], y_points[0], color='green', s=100, label='Start', zorder=5)
    if len(x_points) > 1:
        ax.scatter(x_points[-1], y_points[-1], color='red', s=100, label='End', zorder=5)
    ax.grid(True, alpha=0.3)
    ax.set_xlabel('X Position (m)')
    ax.set_ylabel('Y Position (m)')
    ax.set_title(title)
    ax.legend()