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-4:
        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=(10, 8))
    triangle = Polygon([(x1, y1), (x2, y2), (x3, y3)], closed=True, edgecolor='b', facecolor='lightblue', linewidth=2)
    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:.1f}, {y1:.1f})", f"Vertex B ({x2:.1f}, {y2:.1f})", f"Vertex C ({x3:.1f}, {y3:.1f})"]
    vertex_name = ["A", "B", "C"]
    for i, (vx, vy) in enumerate(vertices):
        ax.scatter(vx, vy, color=vertex_color, zorder=3)
        ax.text(vx+0.01*G_x, vy+0.02*G_y, vertex_name[i], fontsize=10, ha="left", va="bottom", color=vertex_color)
        
    # 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:.1f}, {I_y:.1f})", f"Circumcenter ({U_x:.1f}, {U_y:.1f})", f"Centroid ({G_x:.1f}, {G_y:.1f})"]
    
    for x, y, color in key_points:
        ax.scatter(x, y, color=color, zorder=5)

    # Plot midpoints of sides
    midpoints_labels = [f"Mid-Point M1 ({(x1 + x2) / 2:.1f}, {(y1 + y2) / 2:.1f})", 
                        f"Mid-Point M2 ({(x2 + x3) / 2:.1f}, {(y2 + y3) / 2:.1f})", 
                        f"Mid-Point M3 ({(x1 + x3) / 2:.1f}, {(y1 + y3) / 2:.1f})"]
    midpoint_name = ["M1", "M2", "M3"]
    for i, (mx, my) in enumerate(midpoints):
        ax.scatter(mx, my, color=midpoint_color, zorder=3)
        ax.text(mx+0.01*G_x, my+0.02*G_y, midpoint_name[i], fontsize=10, ha="left", va="bottom", color=midpoint_color)


    # 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=1, 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=1, label="Circumscribed Circle")
    ax.add_patch(circumcircle)


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

    # Calculate the lengths of the sides of the triangle using Euclidean distance
    a = calculate_distance(x2, y2, x3, y3)
    b = calculate_distance(x1, y1, x3, y3)
    c = calculate_distance(x1, y1, x2, y2)
    sides = [f"Side a: {a:.1f}", f"Side b: {b:.1f}", f"Side c: {c:.1f}"]

    # Validate if it's a valid triangle
    if not is_valid_triangle(a, b, c):
        st.error("The entered points do not form a valid triangle.")
        return
        
    # Calculate angles using the Law of Cosines
    A = calculate_angle(a, b, c)
    B = calculate_angle(b, a, c)
    C = calculate_angle(c, a, b)
    vertex_angles = [f"A: {A:.1f}°", f"B: {B:.1f}°", f"C: {C:.1f}°"]

    # Check if angles sum up to 180 degrees
    if abs(A + B + C - 180) > 1e-2:
        st.error("The sum of the angles is not 180 degrees.")
        return
    
    # Add legend
    handles = [
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_labels[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=7, label=midpoints_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=7, label=midpoints_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=7, label=midpoints_labels[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_angles[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_angles[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=7, label=vertex_angles[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=7, label=key_points_labels[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=7, label=key_points_labels[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=centroid_color, markersize=7, label=key_points_labels[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor="blue", markersize=7, label=sides[0]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor="blue", markersize=7, label=sides[1]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor="blue", markersize=7, label=sides[2]),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor="lightblue", markersize=7, label=f"Area: {area:.1f}"),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor="blue", markersize=7, label=f"Perimeter: {perimeter:.1f}"),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=7, label=f"Incircle radius: {radius_in:.1f}"),
        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=7, label=f"Circumcircle radius: {radius_circum:.1f}")
    ]
    ax.legend(handles=handles, loc='upper left', fontsize=8)

    # Adjust the plot limits and aspect ratio
    padding = 5
    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('Triangle Visualization', fontsize=23)
    ax.set_xlabel('X-axis', fontsize=12)
    ax.set_ylabel('Y-axis', fontsize=12)
    
    # Add a light grid
    plt.grid(color='gray', linestyle='--', linewidth=0.5, alpha=0.5)
    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.markdown("""
    <h1 style='text-align: left;'>
        <span style="display: inline-block; transform: scaleX(-1);">◭</span>  Advanced Triangle Solver ◭
    </h1> """, unsafe_allow_html=True)
    
    st.sidebar.header("Enter the cartesian coordinates for the three points of a triangle:")

    # # 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")

    # Coordinates input (X1, Y1), (X2, Y2), (X3, Y3)
    col_x1y1 = st.sidebar.columns([3, 3])  # Wider columns for sliders
    x1 = col_x1y1[0].number_input("X1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y1 = col_x1y1[1].number_input("Y1", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")

    # # Reduced spacing between sections
    # st.sidebar.markdown("<br>", unsafe_allow_html=True)

    col_x2y2 = st.sidebar.columns([3, 3])  # Wider columns for sliders
    x2 = col_x2y2[0].number_input("X2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y2 = col_x2y2[1].number_input("Y2", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")

    # # Reduced spacing between sections
    # st.sidebar.markdown("<br>", unsafe_allow_html=True)

    col_x3y3 = st.sidebar.columns([3, 3])  # Wider columns for sliders
    x3 = col_x3y3[0].number_input("X3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")
    y3 = col_x3y3[1].number_input("Y3", min_value=-100.0, max_value=100.0, step=0.1, format="%.3f")

    # Add extra vertical spacing below the inputs
    st.sidebar.markdown("<br>", unsafe_allow_html=True)

    # Add "Solve Triangle" button centered in a new row
    button_col = st.sidebar.columns([1, 2, 1])  # Center button using column proportions
    if button_col[1].button("Solve Triangle"):
        # Calculate the lengths of the sides of the triangle using Euclidean distance
        a = calculate_distance(x2, y2, x3, y3)
        b = calculate_distance(x1, y1, x3, y3)
        c = calculate_distance(x1, y1, x2, y2)

        # Validate if it's a valid triangle
        if not is_valid_triangle(a, b, c):
            st.error("The entered points do not form a valid triangle.")
            return
        
        # Calculate angles using the Law of Cosines
        A = calculate_angle(a, b, c)
        B = calculate_angle(b, a, c)
        C = calculate_angle(c, a, b)

        # Check if angles sum up to 180 degrees
        if abs(A + B + C - 180) > 1e-2:
            st.error("The sum of the angles is not 180 degrees.")
            return

        # Calculate area, perimeter, and radius of inscribed and circumscribed circles
        area = calculate_area(a, b, c)
        perimeter = calculate_perimeter(a, b, c)
        radius_in = calculate_radius_inscribed_circle(a, b, c)
        radius_circum = calculate_radius_circumscribed_circle(a, b, c)

        # Calculate centroid, incenter, and circumcenter coordinates
        G_x, G_y = calculate_centroid(x1, y1, x2, y2, x3, y3)
        I_x, I_y = calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c)
        U_x, U_y = calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c)

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

        # Display results in columns
        col1, col2 = st.columns(2)
        
        with col1:
            st.subheader("Coordinates of Triangle:")
            st.markdown(f"Vertex A: **({x1:.3f}, {y1:.3f})**")
            st.markdown(f"Vertex B: **({x2:.3f}, {y2:.3f})**")
            st.markdown(f"Vertex C: **({x3:.3f}, {y3:.3f})**")
        
        with col2:
            st.subheader("Mid-Points of Triangle:")
            st.markdown(f"Midpoint of AB: **({midpoints[0][0]:.3f}, {midpoints[0][1]:.3f})**")
            st.markdown(f"Midpoint of BC: **({midpoints[1][0]:.3f}, {midpoints[1][1]:.3f})**")
            st.markdown(f"Midpoint of CA: **({midpoints[2][0]:.3f}, {midpoints[2][1]:.3f})**")

        
        col1, col2 = st.columns(2)
           
        with col1:
            st.subheader("Angles of Triangle:")
            st.markdown(f"Angle A: **{format_zero(A):.3f}°**")
            st.markdown(f"Angle B: **{format_zero(B):.3f}°**")
            st.markdown(f"Angle C: **{format_zero(C):.3f}°**")

        with col2:
            st.subheader("Sides of Triangle:")
            st.markdown(f"Side a: **{format_zero(a):.3f}** units")
            st.markdown(f"Side b: **{format_zero(b):.3f}** units")
            st.markdown(f"Side c: **{format_zero(c):.3f}** units")

        
        col1, col2 = st.columns(2)

        with col1:
            st.subheader("Incenter of Triangle:")
            st.markdown(f"Coordinates: **({format_zero(I_x):.3f}, {format_zero(I_y):.3f})**")
            st.markdown(f"Radius: **{radius_in:.3f}** units")
        
        with col2:
            st.subheader("Circumcenter of Triangle:")
            st.markdown(f"Coordinates: **({format_zero(U_x):.3f}, {format_zero(U_y):.3f})**")
            st.markdown(f"Radius: **{radius_circum:.3f}** units")

        col1, col2, col3 = st.columns([1, 2, 1])  # Create three columns with relative widths
        with col2:  # Center column
            st.subheader("Other Properties:")
            st.markdown(f"Area: **{format_zero(area):.3f}** square units")
            st.markdown(f"Perimeter: **{format_zero(perimeter):.3f}** units")
            st.markdown(f"Centroid: **({format_zero(G_x):.3f}, {format_zero(G_y):.3f})**")

        # Display triangle graph with midpoints and colored points
        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()