# --- Core CSF imports used in this minimal example ---
from csf import (
    Pt, Polygon,integrate_volume,section_statical_moment_partial,section_properties, section_derived_properties,Section, ContinuousSectionField,Visualizer,
    section_full_analysis, section_print_analysis,section_full_analysis_keys
)
# ----------------------------------------------------------------------------------
# 1. DEFINE START SECTION (Z = 0)
# ----------------------------------------------------------------------------------
#   GUIDELINES FOR POLYGON CONSTRUCTION:
# - COUNTER-CLOCKWISE POLYGON
# - VERTICES ORDER: You MUST define vertices in COUNTER-CLOCKWISE (CCW) order.
#   This is MANDATORY for the Shoelace/Green's Theorem algorithm to compute a
#   POSITIVE Area and correct Moments of Inertia. Clockwise order will result
#   in negative area values and mathematically incorrect results.
# - WEIGHT: Use 1.0 for solid parts and 0 to define voids/holes.
# - The start section here is a T-shape composed of two non-overlapping polygons:
#   a "flange" (top horizontal) and a "web" (vertical stem).
# ----------------------------------------------------------------------------------

# Flange Definition: Rectangle from (-1, -0.2) to (1, 0.2)
# Order: Bottom-Left -> Bottom-Right -> Top-Right -> Top-Left (CCW)
poly0_start = Polygon(
    vertices=(Pt(-1, -0.2), Pt(1, -0.2), Pt(1, 0.2), Pt(-1, 0.2)),
    weight=1.0,
    name="flange",
)

# Web Definition: Rectangle from (-0.2, -1.0) to (0.2, 0.2)
# Order: Bottom-Left -> Bottom-Right -> Top-Right -> Top-Left (CCW)
poly1_start = Polygon(
    vertices=(Pt(-0.2, -1.0), Pt(0.2, -1.0), Pt(0.2, -0.2), Pt(-0.2, -0.2)),
    weight=1.0,
    name="web",
)

# ----------------------------------------------------------------------------------
# 2. DEFINE END SECTION (Z = 10)
# ----------------------------------------------------------------------------------
# GEOMETRIC CONSISTENCY:
# - To enable linear interpolation (tapering), the end section must contain the
#   same number of polygons with the same names as the start section.
# - The web depth here increases linearly from 1.0 down to 2.5 (negative Y direction),
#   creating a tapered profile along the longitudinal Z-axis.
# ----------------------------------------------------------------------------------

# Flange remains unchanged for this prismatic top part
poly0_end = Polygon(
    vertices=(Pt(-1, -0.2), Pt(1, -0.2), Pt(1, 0.2), Pt(-1, 0.2)),
    weight=1.0,
    name="flange",
)

# Web becomes deeper: Y-bottom moves from -1.0 to -2.5
# MAINTAIN CCW ORDER: Bottom-Left -> Bottom-Right -> Top-Right -> Top-Left
poly1_end = Polygon(
    vertices=(Pt(-0.2, -2.5), Pt(0.2, -2.5), Pt(0.2, -0.2), Pt(-0.2, -0.2)),
    weight=1.0,
    name="web",
)

# ----------------------------------------------------------------------------------
# 3. CREATE SECTIONS WITH Z-COORDINATES
# ----------------------------------------------------------------------------------
# Sections act as containers for polygons at a specific coordinate along the beam axis.
# All polygons defined at Z=0.0 are grouped into s0, and those at Z=10.0 into s1.
# ----------------------------------------------------------------------------------

# Order matters: poly0_start pairs with poly0_end,
# and poly1_start pairs with poly1_end
# because they appear in the same position in their respective sections.

s0 = Section(polygons=(poly0_start, poly1_start), z=0.0)
s1 = Section(polygons=(poly0_end, poly1_end), z=10.0)

# --------------------------------------------------------
# 4. INITIALIZE CONTINUOUS SECTION FIELD
# --------------------------------------------------------
# A linear interpolator is used to generate intermediate
# sections between Z = 0 and Z = 10.
field = ContinuousSectionField(section0=s0, section1=s1)

# --------------------------------------------------------
# 5. PRIMARY SECTION PROPERTIES (Z = 5.0)
# --------------------------------------------------------
# Properties are computed at mid-span.
sec_mid = field.section(5.0)
props = section_properties(sec_mid)

print("\n" + "="*40)
print("PRIMARY PROPERTIES AT Z=5.0 (Centroidal)")
print("="*40)
print(f"A:   {props['A']:.4f}      # Net Cross-Sectional Area")
print(f"Cx:  {props['Cx']:.4f}     # Horizontal Centroid location (Global X)")
print(f"Cy:  {props['Cy']:.4f}     # Vertical Centroid location (Global Y)")
print(f"Ix:  {props['Ix']:.4f}     # Second Moment of Area about Centroidal X-axis")
print(f"Iy:  {props['Iy']:.4f}     # Second Moment of Area about Centroidal Y-axis")
print(f"Ixy: {props['Ixy']:.4f}    # Product of Inertia (Measure of asymmetry)")

# 2. DERIVED PROPERTIES (Radius of Gyration, Principal Axes)
derived = section_derived_properties(props)
print("\n" + "-"*40)
print("DERIVED GEOMETRIC PROPERTIES")
print("-"*40)
print(f"rx:  {derived['rx']:.4f}     # Radius of Gyration about X (sqrt(Ix/A))")
print(f"ry:  {derived['ry']:.4f}     # Radius of Gyration about Y (sqrt(Iy/A))")
print(f"I1:  {derived['I1']:.4f}     # Maximum Principal Moment of Area")
print(f"I2:  {derived['I2']:.4f}     # Minimum Principal Moment of Area")
print(f"Deg: {derived['theta_deg']:.2f}°   # Principal Axis Rotation Angle")

# --------------------------------------------------------
# 7. STATICAL MOMENT OF AREA (Q)
# --------------------------------------------------------
# Computed at the neutral axis (y = Cy).
# Used in shear stress calculations.
Q_na = section_statical_moment_partial(sec_mid, y_cut=props['Cy'])
print("\n" + "-"*40)
print("SHEAR ANALYSIS PROPERTIES")
print("-"*40)
print(f"Q_na: {Q_na:.4f}    # First Moment of Area above Neutral Axis (for shear stress)")

# 8. VOLUMETRIC PROPERTIES
total_vol = integrate_volume(field,0,10)
print("\n" + "="*40)
print("GLOBAL FIELD PROPERTIES (3D)")
print("="*40)
print(f"Total Volume: {total_vol:.4f} # Total material volume of the ruled solid")

# Technical Explanation for the negative Cy
print("\n" + "-"*50)
print("TECHNICAL NOTE ON COORDINATES:")
print("-"*50)
print("The negative value for 'Cy' is physically correct.")
print("In this model, the flange is centered at y=0, while the web")
print("extends downwards (from y=0.2 to y=-1.0 at Z=0, and y=-2.5 at Z=10).")
print("Since the majority of the T-section's mass is located below the")
print("global X-axis (y=0), the centroid MUST have a negative Y-coordinate.")
print("This indicates the geometric center is below the drawing origin.")
print("-"*50)

# --------------------------------------------------------
# 9. VISUALIZATION
# --------------------------------------------------------
# - 2D section plot at Z = 5.0
# - 3D ruled solid visualization
viz = Visualizer(field)

# Generate 2D plot for the specified slice
viz.plot_section_2d(z=5.0)

# Generate 3D plot of the interpolated solid
# line_percent determines the density of the longitudinal ruled lines
viz.plot_volume_3d(line_percent=100.0, seed=1)

import matplotlib.pyplot as plt
plt.show()