app.py

import streamlit as st
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon, Circle

# Function to calculate the distance between two points
def calculate_distance(x1, y1, x2, y2):
    return np.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

# Function to calculate angles using the Law of Cosines
def calculate_angle(a, b, c):
    try:
        angle = np.degrees(np.acos((b ** 2 + c ** 2 - a ** 2) / (2 * b * c)))
    except ValueError:
        angle = 0  # Handle possible domain error in acos
    return angle

# Function to calculate area using Heron's formula
def calculate_area(a, b, c):
    s = (a + b + c) / 2
    area = np.sqrt(s * (s - a) * (s - b) * (s - c))
    return area

# Function to calculate the perimeter
def calculate_perimeter(a, b, c):
    return a + b + c

# Function to calculate the radius of the inscribed circle
def calculate_radius_inscribed_circle(a, b, c):
    try:
        s = (a + b + c) / 2
        area = calculate_area(a, b, c)
        radius = area / s
    except ZeroDivisionError:
        radius = 0  # Handle case where area or perimeter is zero
    return radius

# Function to calculate the radius of the circumscribed circle
def calculate_radius_circumscribed_circle(a, b, c):
    try:
        area = calculate_area(a, b, c)
        radius = (a * b * c) / (4 * area)
    except ZeroDivisionError:
        radius = 0  # Handle case where area is zero
    return radius

# Function to calculate the centroid coordinates
def calculate_centroid(x1, y1, x2, y2, x3, y3):
    G_x = (x1 + x2 + x3) / 3
    G_y = (y1 + y2 + y3) / 3
    return G_x, G_y

# Function to calculate the incenter coordinates
def calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c):
    try:
        I_x = (a * x1 + b * x2 + c * x3) / (a + b + c)
        I_y = (a * y1 + b * y2 + c * y3) / (a + b + c)
    except ZeroDivisionError:
        I_x, I_y = 0, 0  # Handle division by zero if sides sum to zero
    return I_x, I_y

# Function to calculate the circumcenter coordinates
def calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c):
    try:
        D = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
        U_x = ((x1**2 + y1**2) * (y2 - y3) + (x2**2 + y2**2) * (y3 - y1) + (x3**2 + y3**2) * (y1 - y2)) / D
        U_y = ((x1**2 + y1**2) * (x3 - x2) + (x2**2 + y2**2) * (x1 - x3) + (x3**2 + y3**2) * (x2 - x1)) / D
    except ZeroDivisionError:
        U_x, U_y = 0, 0  # Handle division by zero in circumcenter calculation
    return U_x, U_y

# Function to calculate midpoints of sides
def calculate_midpoints(x1, y1, x2, y2, x3, y3):
    # Midpoint of AB
    M1_x = (x1 + x2) / 2
    M1_y = (y1 + y2) / 2
    # Midpoint of BC
    M2_x = (x2 + x3) / 2
    M2_y = (y2 + y3) / 2
    # Midpoint of CA
    M3_x = (x3 + x1) / 2
    M3_y = (y3 + y1) / 2
    return (M1_x, M1_y), (M2_x, M2_y), (M3_x, M3_y)

# Function to format values close to zero as 0
def format_zero(val):
    if abs(val) < 1e-6:
        return 0.0
    return val

# Function to plot the triangle with all points in different colors and a legend
def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoints, a, b, c):
    fig, ax = plt.subplots(figsize=(8, 6))
    triangle = Polygon([(x1, y1), (x2, y2), (x3, y3)], closed=True, edgecolor='b', facecolor='lightblue')
    ax.add_patch(triangle)
    
    # Define colors for different points
    vertex_color = 'blue'
    midpoint_color = 'green'
    centroid_color = 'orange'
    incenter_color = 'red'
    circumcenter_color = 'purple'
    
    # Plot the triangle vertices
    vertices = [(x1, y1), (x2, y2), (x3, y3)]
    vertex_labels = [f"Vertex A ({x1:.3f}, {y1:.3f})", f"Vertex B ({x2:.3f}, {y2:.3f})", f"Vertex C ({x3:.3f}, {y3:.3f})"]
    for i, (vx, vy) in enumerate(vertices):
        ax.scatter(vx, vy, color=vertex_color, zorder=3)
        
    # Plot key points with their corresponding colors
    key_points = [
        (I_x, I_y, incenter_color),
        (U_x, U_y, circumcenter_color),
        (G_x, G_y, centroid_color)
    ]
    key_points_labels = [f"Incenter ({I_x:.3f}, {I_y:.3f})", f"Circumcenter ({U_x:.3f}, {U_y:.3f})", f"Centroid ({G_x:.3f}, {G_y:.3f})"]
    
    for x, y, color in key_points:
        ax.scatter(x, y, color=color, zorder=4)

    # Plot midpoints of sides
    for i, (mx, my) in enumerate(midpoints):
        ax.scatter(mx, my, color=midpoint_color, zorder=5)
    midpoints_labels = [f"Mid-Point M1 ({(x1 + x2) / 2:.3f}, {(y1 + y2) / 2:.3f})", 
                        f"Mid-Point M2 ({(x2 + x3) / 2:.3f}, {(y2 + y3) / 2:.3f})", 
                        f"Mid-Point M3 ({(x1 + x3) / 2:.3f}, {(y1 + y3) / 2:.3f})"]

    # Draw the inscribed circle (incircle)
    radius_in = calculate_radius_inscribed_circle(a, b, c)
    incircle = Circle((I_x, I_y), radius_in, color=incenter_color, fill=False, linestyle='--', linewidth=2, label="Inscribed Circle")
    ax.add_patch(incircle)
    
    # Draw the circumscribed circle (circumcircle)
    radius_circum = calculate_radius_circumscribed_circle(a, b, c)
    circumcircle = Circle((U_x, U_y), radius_circum, color=circumcenter_color, fill=False, linestyle='--', linewidth=2, label="Circumscribed Circle")
    ax.add_patch(circumcircle)
    
    # Add legend
    handles = [
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=8, label=key_points_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=8, label=key_points_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=centroid_color, markersize=8, label=key_points_labels[2])
    ]
    ax.legend(handles=handles, loc='upper left', fontsize=12)
    
    # Adjust the plot limits and aspect ratio
    padding = 3
    ax.set_xlim([min(x1, x2, x3) - padding, max(x1, x2, x3) + padding])
    ax.set_ylim([min(y1, y2, y3) - padding, max(y1, y2, y3) + padding])
    ax.set_aspect('equal', adjustable='datalim')
    
    ax.set_title('Solved Triangle', fontsize=18)
    ax.set_xlabel('X-axis', fontsize=12)
    ax.set_ylabel('Y-axis', fontsize=12)
    
    plt.grid(True)
    st.pyplot(fig)

# Function to check if the sides form a valid triangle
def is_valid_triangle(a, b, c):
    # Check if the sum of two sides is greater than the third side (Triangle Inequality Theorem)
    return a + b > c and b + c > a and c + a > b

# Main function to interact with the user
def main():
    st.title("Advanced Triangle Solver", anchor='center')

    st.sidebar.header("Enter the coordinates of the three points:")

    # Coordinates input (X1, Y1), (X2, Y2), (X3, Y3)
    x1 = st.sidebar.number_input("X1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y1 = st.sidebar.number_input("Y1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    x2 = st.sidebar.number_input("X2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y2 = st.sidebar.number_input("Y2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    x3 = st.sidebar.number_input("X3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y3 = st.sidebar.number_input("Y3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")

    # Calculate the lengths of the sides
    a = calculate_distance(x2, y2, x3, y3)
    b = calculate_distance(x1, y1, x3, y3)
    c = calculate_distance(x1, y1, x2, y2)

    # Check if the triangle is valid
    if not is_valid_triangle(a, b, c):
        st.error("The given points do not form a valid triangle.")
        return

    # Calculate angles using the law of cosines
    angle_A = calculate_angle(a, b, c)
    angle_B = calculate_angle(b, a, c)
    angle_C = calculate_angle(c, a, b)

    # Calculate area and perimeter
    area = calculate_area(a, b, c)
    perimeter = calculate_perimeter(a, b, c)

    # Calculate the radius of the inscribed and circumscribed circles
    radius_inscribed_circle = calculate_radius_inscribed_circle(a, b, c)
    radius_circumscribed_circle = calculate_radius_circumscribed_circle(a, b, c)

    # Calculate the centroid coordinates
    G_x, G_y = calculate_centroid(x1, y1, x2, y2, x3, y3)

    # Calculate the incenter coordinates
    I_x, I_y = calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c)

    # Calculate the circumcenter coordinates
    U_x, U_y = calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c)

    # Calculate midpoints of sides
    midpoints = calculate_midpoints(x1, y1, x2, y2, x3, y3)

    # Display results
    st.subheader("Calculated Properties:")
    st.write(f"**Side Lengths (a, b, c):** {a:.3f}, {b:.3f}, {c:.3f}")
    st.write(f"**Angles (A, B, C):** {angle_A:.3f}°, {angle_B:.3f}°, {angle_C:.3f}°")
    st.write(f"**Area:** {area:.3f}")
    st.write(f"**Perimeter:** {perimeter:.3f}")
    st.write(f"**Radius of Inscribed Circle:** {radius_inscribed_circle:.3f}")
    st.write(f"**Radius of Circumscribed Circle:** {radius_circumscribed_circle:.3f}")

    plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoints, a, b, c)

if __name__ == "__main__":
    main()