src/sdf_geo/processor.py

"""
Batch Processor Module
Processes geometry problems and generates visualizations.
"""

import torch
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
import json
import re
from pathlib import Path
from typing import Dict, List, Tuple, Optional
from tqdm import tqdm

from .primitives import (
    CircleSDF, EllipseSDF, HyperbolaSDF, ParabolaSDF
)
from .constraints import GeometricConstraints
from .parser import ProblemParser
from .optimizer import GeometryOptimizer
from .renderer import SDFRenderer


class SDFBatchProcessor:
    """
    Process problems using the SDF methodology.
    """
    
    def __init__(self, output_dir: str = 'sdf_output'):
        self.output_dir = Path(output_dir)
        self.output_dir.mkdir(exist_ok=True, parents=True)
        
        self.parser = ProblemParser()
        self.optimizer = GeometryOptimizer()
        
        # Create subdirectories
        for subdir in ['ellipse', 'hyperbola', 'parabola', 'circle']:
            (self.output_dir / subdir).mkdir(exist_ok=True)
    
    def process_problem(self, problem: Dict, idx: int, verbose: bool = False) -> Dict:
        """Process a single problem using SDF methodology."""
        result = {
            'index': idx,
            'success': False,
            'error': None
        }
        
        try:
            fact_expr = problem.get('fact_expressions', '')
            text = problem.get('text', '')
            query_expr = problem.get('query_expressions', '')
            
            # Determine the primary shape to visualize based on query
            # If query is about Expression(G), find what G is
            primary_shape = None
            query_match = re.search(r'Expression\((\w+)\)', query_expr)
            if query_match:
                shape_name = query_match.group(1)
                # Find what type this shape is
                type_match = re.search(rf'{shape_name}:\s*(\w+)', fact_expr)
                if type_match:
                    primary_shape = type_match.group(1).lower()
            
            # Detect main conic names for each type
            main_hyperbola_name = self._detect_main_conic_name(fact_expr, 'hyperbola')
            main_ellipse_name = self._detect_main_conic_name(fact_expr, 'ellipse')
            main_parabola_name = self._detect_main_conic_name(fact_expr, 'parabola')
            main_circle_name = self._detect_main_conic_name(fact_expr, 'circle')
            
            # Try to parse as different conic types, using main conic names
            ellipse_params = self.parser.parse_ellipse(fact_expr)
            hyperbola_params = self.parser.parse_hyperbola(fact_expr, main_hyperbola_name)
            parabola_params = self.parser.parse_parabola(fact_expr)
            circle_params = self.parser.parse_circle(fact_expr)
            
            # Additional constraints
            coords = self.parser.parse_coordinates(fact_expr)
            eccentricity = self.parser.parse_eccentricity(fact_expr)
            asymptote = self.parser.parse_asymptote_slope(fact_expr)
            
            # Special case: moving circle locus (externally tangent to fixed circle, passes through a fixed point)
            moving_circle = self._detect_moving_circle_locus(fact_expr, coords)
            if moving_circle:
                params_hyp = moving_circle
                return self._process_hyperbola(problem, idx, params_hyp, coords, eccentricity=None, asymptote=None, verbose=verbose)
            
            # Process based on primary shape (if determined) or first available
            if primary_shape == 'hyperbola' and hyperbola_params:
                result = self._process_hyperbola(problem, idx, hyperbola_params, coords, eccentricity, asymptote, verbose)
            elif primary_shape == 'ellipse' and ellipse_params:
                result = self._process_ellipse(problem, idx, ellipse_params, coords, eccentricity, verbose)
            elif primary_shape == 'parabola' and parabola_params:
                result = self._process_parabola(problem, idx, parabola_params, coords, verbose)
            elif primary_shape == 'circle' and circle_params:
                result = self._process_circle(problem, idx, circle_params, coords, verbose)
            # Fallback to order of detection, but prioritize hyperbola over ellipse 
            # (many problems have both, with hyperbola as the main subject)
            elif hyperbola_params:
                result = self._process_hyperbola(problem, idx, hyperbola_params, coords, eccentricity, asymptote, verbose)
            elif ellipse_params:
                result = self._process_ellipse(problem, idx, ellipse_params, coords, eccentricity, verbose)
            elif parabola_params:
                result = self._process_parabola(problem, idx, parabola_params, coords, verbose)
            elif circle_params:
                result = self._process_circle(problem, idx, circle_params, coords, verbose)
            else:
                result['error'] = 'Unsupported or unparseable expression'
                return result
            
            # Validation step
            result = self._validate_result(result, problem)
            return result
                
        except Exception as e:
            result['error'] = str(e)
            return result
    
    def _validate_result(self, result: Dict, problem: Dict) -> Dict:
        """
        Rigorous validation following paper-quality standards.
        Validates all explicit geometric constraints from the problem.
        
        Validation includes:
        - Parameter positivity (a, b, p, r > 0)
        - Eccentricity matching (e_calc vs e_target)
        - Asymptote slope matching (b/a vs target slope)
        - Focus position verification (c² = a² ± b²)
        - Point-on-curve verification for constrained points
        - Directrix position verification (parabola)
        """
        if not result.get('success'):
            return result
        
        conic_type = result.get('conic_type')
        fact_expr = result.get('fact_expr', problem.get('fact_expressions', ''))
        coords = result.get('coords', {})
        reasons = []
        
        # Tolerance settings (paper-quality)
        tol_point = 3e-2      # Point on curve tolerance
        tol_param = 0.05      # Parameter matching tolerance (e, slope)
        tol_focus = 0.05      # Focus position tolerance
        
        # Dynamically detect the main conic name from fact_expr
        main_conic = self._detect_main_conic_name(fact_expr, conic_type)
        
        # Get only points that are explicitly on the MAIN conic
        points_on_main = self._points_on_main_conic(fact_expr, coords, main_conic)
        
        # Helper: extract focus coordinates from fact_expr
        def get_focus_coords() -> List[Tuple[float, float]]:
            """Extract focus point coordinates."""
            foci = []
            for name, coord in coords.items():
                # Check if this point is declared as a focus
                if re.search(rf'Focus\s*\(\s*{main_conic}\s*\)\s*=\s*\{{\s*{name}', fact_expr) or \
                   re.search(rf'Focus\s*\(\s*{main_conic}\s*\)\s*=\s*{name}', fact_expr) or \
                   (name in ['F', 'F1', 'F2'] and re.search(rf'Focus\s*\(\s*{main_conic}\s*\)', fact_expr)):
                    foci.append(coord)
            return foci
        
        # Helper: check if point is on curve constraint
        def has_point_constraint(name: str) -> bool:
            return name in points_on_main
        
        if conic_type == 'ellipse':
            params = result.get('params', {})
            if 'a' not in params or 'b' not in params:
                return result  # Skip validation if params incomplete
            a = params['a']
            b = params['b']
            
            # 1. Parameter positivity
            if a <= 0 or b <= 0:
                reasons.append('ellipse_nonpositive_axes')
            
            # 2. Eccentricity verification
            ecc_target = self.parser.parse_eccentricity(fact_expr)
            if ecc_target and 0 < ecc_target < 1:
                a_major, b_minor = max(a, b), min(a, b)
                ecc_calc = np.sqrt(1 - (b_minor / a_major)**2)
                if abs(ecc_calc - ecc_target) > tol_param:
                    reasons.append('ellipse_ecc_mismatch')
            
            # 3. Focus position verification (c² = a² - b² for ellipse)
            foci = get_focus_coords()
            if foci:
                a_major, b_minor = max(a, b), min(a, b)
                c_calc = np.sqrt(max(0, a_major**2 - b_minor**2))
                for fx, fy in foci:
                    # Focus should be at (±c, 0) or (0, ±c) from center
                    c_given = np.sqrt(fx**2 + fy**2)  # Assuming center at origin
                    if abs(c_calc - c_given) > tol_focus:
                        reasons.append('ellipse_focus_mismatch')
                        break
            
            # 4. Point-on-curve verification
            for name, (px, py) in coords.items():
                if has_point_constraint(name):
                    major_axis = params.get('major_axis', 'x')
                    if major_axis == 'x':
                        val = (px**2) / (a**2) + (py**2) / (b**2) - 1
                    else:
                        val = (px**2) / (b**2) + (py**2) / (a**2) - 1
                    if abs(val) > tol_point:
                        reasons.append('ellipse_point_off_curve')
                        break
        
        elif conic_type == 'hyperbola':
            params = result.get('params', {})
            if 'a' not in params or 'b' not in params:
                return result  # Skip validation if params incomplete
            a = params['a']
            b = params['b']
            orientation = params.get('orientation', 'horizontal')
            
            # 1. Parameter positivity
            if a <= 0 or b <= 0:
                reasons.append('hyperbola_nonpositive_axes')
            
            # 2. Asymptote slope verification (b/a for horizontal)
            asym = self.parser.parse_asymptote_slope(fact_expr)
            if asym:
                slope_calc = b / a if orientation == 'horizontal' else a / b
                if abs(slope_calc - asym) > tol_param:
                    reasons.append('hyperbola_asymptote_mismatch')
            
            # 3. Eccentricity verification (e = c/a = sqrt(1 + b²/a²))
            ecc_target = self.parser.parse_eccentricity(fact_expr)
            if ecc_target and ecc_target > 1:
                ecc_calc = np.sqrt(1 + (b / a)**2)
                if abs(ecc_calc - ecc_target) > tol_param:
                    reasons.append('hyperbola_ecc_mismatch')
            
            # 4. Focus position verification (c² = a² + b² for hyperbola)
            foci = get_focus_coords()
            if foci:
                c_calc = np.sqrt(a**2 + b**2)
                for fx, fy in foci:
                    # Focus should be at (±c, 0) or (0, ±c) from center
                    c_given = np.sqrt(fx**2 + fy**2)  # Assuming center at origin
                    if abs(c_calc - c_given) > tol_focus:
                        reasons.append('hyperbola_focus_mismatch')
                        break
            
            # 5. Point-on-curve verification
            for name, (px, py) in coords.items():
                if has_point_constraint(name):
                    if orientation == 'vertical':
                        val = (py**2) / (a**2) - (px**2) / (b**2) - 1
                    else:
                        val = (px**2) / (a**2) - (py**2) / (b**2) - 1
                    if abs(val) > tol_point:
                        reasons.append('hyperbola_point_off_curve')
                        break
        
        elif conic_type == 'parabola':
            params = result.get('params', {})
            p = params.get('p', 0)
            direction = params.get('direction', 'right')
            
            # 1. Parameter positivity
            if p <= 0:
                reasons.append('parabola_nonpositive_p')
            
            # 2. Focus position verification
            # Focus at (p, 0) for y² = 4px (right-opening)
            foci = get_focus_coords()
            if foci:
                for fx, fy in foci:
                    if direction == 'right':
                        focus_expected = (p, 0)
                    elif direction == 'left':
                        focus_expected = (-p, 0)
                    elif direction == 'up':
                        focus_expected = (0, p)
                    else:  # down
                        focus_expected = (0, -p)
                    
                    dist = np.sqrt((fx - focus_expected[0])**2 + (fy - focus_expected[1])**2)
                    if dist > tol_focus:
                        reasons.append('parabola_focus_mismatch')
                        break
            
            # 3. Directrix verification (if specified)
            # Directrix at x = -p for y² = 4px
            directrix_match = re.search(r'Directrix\s*\(\s*\w+\s*\)\s*=\s*\(x\s*=\s*(-?\d+\.?\d*)\)', fact_expr)
            if directrix_match:
                directrix_given = float(directrix_match.group(1))
                if direction == 'right':
                    directrix_expected = -p
                elif direction == 'left':
                    directrix_expected = p
                else:
                    directrix_expected = None  # y-directrix for up/down
                
                if directrix_expected is not None:
                    if abs(directrix_given - directrix_expected) > tol_focus:
                        reasons.append('parabola_directrix_mismatch')
            
            # 4. Point-on-curve verification
            for name, (px, py) in coords.items():
                if has_point_constraint(name):
                    if direction == 'right':
                        val = py**2 - 4 * p * px
                    elif direction == 'left':
                        val = py**2 + 4 * p * px
                    elif direction == 'up':
                        val = px**2 - 4 * p * py
                    else:
                        val = px**2 + 4 * p * py
                    if abs(val) > tol_point:
                        reasons.append('parabola_point_off_curve')
                        break
        
        elif conic_type == 'circle':
            params = result.get('params', {})
            r = params.get('radius', 0)
            cx, cy = params.get('center', (0, 0))
            
            # 1. Parameter positivity
            if r <= 0:
                reasons.append('circle_nonpositive_radius')
            
            # 2. Center verification (if specified)
            center_match = re.search(r'Center\s*\(\s*\w+\s*\)\s*=\s*\(([^,]+),\s*([^)]+)\)', fact_expr)
            if center_match:
                try:
                    cx_given = float(center_match.group(1))
                    cy_given = float(center_match.group(2))
                    if abs(cx - cx_given) > tol_focus or abs(cy - cy_given) > tol_focus:
                        reasons.append('circle_center_mismatch')
                except:
                    pass
            
            # 3. Radius verification (if specified)
            radius_match = re.search(r'Radius\s*\(\s*\w+\s*\)\s*=\s*(\d+\.?\d*)', fact_expr)
            if radius_match:
                r_given = float(radius_match.group(1))
                if abs(r - r_given) > tol_focus:
                    reasons.append('circle_radius_mismatch')
            
            # 4. Point-on-curve verification
            for name, (px, py) in coords.items():
                if has_point_constraint(name):
                    val = (px - cx)**2 + (py - cy)**2 - r**2
                    if abs(val) > tol_point:
                        reasons.append('circle_point_off_curve')
                        break
        
        if reasons:
            result['success'] = False
            result['error'] = 'validation: ' + ';'.join(reasons)
            result['validation_reasons'] = reasons
        return result

    def _point_constraint_names(self, fact_expr: str, coords: Dict, conic_type: str = 'parabola') -> set:
        """
        Collect point names that are explicitly constrained on the main curve.
        Uses _detect_main_conic_name to find the actual conic variable name.
        """
        main_conic = self._detect_main_conic_name(fact_expr, conic_type)
        return self._points_on_main_conic(fact_expr, coords, main_conic)
    
    def _detect_main_conic_name(self, fact_expr: str, conic_type: str) -> str:
        """
        Detect the actual name of the main conic from fact_expr.
        
        Patterns like 'G: Ellipse', 'C: Parabola', 'C: Hyperbola', etc.
        Returns the variable name (e.g., 'G' or 'C').
        """
        # Map conic_type to the type name in fact_expr
        type_map = {
            'ellipse': 'Ellipse',
            'hyperbola': 'Hyperbola',
            'parabola': 'Parabola',
            'circle': 'Circle'
        }
        type_name = type_map.get(conic_type, '')
        
        if type_name:
            # Pattern: variable_name: TypeName (e.g., "G: Ellipse" or "C: Parabola")
            pattern = rf'(\w+)\s*:\s*{type_name}'
            match = re.search(pattern, fact_expr)
            if match:
                return match.group(1)
        
        # Fallback to defaults
        return 'C' if conic_type == 'circle' else 'G'
    
    def _points_on_main_conic(self, fact_expr: str, coords: Dict, conic_name: str = 'G') -> set:
        """
        Collect point names that are EXPLICITLY on the MAIN conic (e.g., G or C).
        
        Includes:
        - PointOnCurve(<name>, G) where G is the main conic
        - Intersection(*, G) = {A, B} where G is the main conic
        
        Excludes:
        - PointOnCurve(<name>, H) where H is a line
        - PointOnCurve(<name>, Asymptote(G)) - on asymptote, not curve
        - PointOnCurve(<name>, Directrix(G)) - on directrix, not curve
        - PointOnCurve(<name>, G1) where G1 is a different curve
        - MidPoint constraints (midpoints of chords are not on the curve)
        """
        names = set()
        
        # Match PointOnCurve(name, G) exactly - second argument must be exactly the conic name
        # Avoid matching things like Asymptote(G), Directrix(G), G1, etc.
        for name in coords.keys():
            # Pattern: PointOnCurve(name, G) - spaces allowed, second arg must be exactly conic_name
            # Use word boundary to avoid matching G1 when looking for G
            pattern = rf'PointOnCurve\(\s*{re.escape(name)}\s*,\s*{re.escape(conic_name)}\s*\)'
            if re.search(pattern, fact_expr):
                names.add(name)
        
        # Match Intersection(*, G) = {A, B} or Intersection(G, *) = {A, B}
        # Only if one of the arguments is exactly the main conic
        inter_pattern = r'Intersection\(\s*([^,)]+)\s*,\s*([^)]+)\s*\)\s*=\s*\{([^}]+)\}'
        for m in re.finditer(inter_pattern, fact_expr):
            arg1 = m.group(1).strip()
            arg2 = m.group(2).strip()
            points_str = m.group(3)
            
            # Check if either argument is exactly the main conic name
            if arg1 == conic_name or arg2 == conic_name:
                for p in points_str.split(','):
                    p = p.strip()
                    if p in coords:
                        names.add(p)
        
        return names

    def _detect_moving_circle_locus(self, fact_expr: str, coords: Dict) -> Optional[Dict]:
        """
        Detect pattern: moving circle through fixed point A, externally tangent to fixed circle C.
        If foci on x-axis, convert to hyperbola params: |PC| - |PA| = R -> 2a = R.
        Returns hyperbola params dict or None.
        """
        if "IsOutTangent" not in fact_expr:
            return None
        # Parse fixed circle C explicitly from its expression (two common orderings)
        patterns = [
            r'Expression\(C\)\s*=\s*\(y\^2\s*\+\s*\(x\s*([+-])\s*(\d+\.?\d*)\)\^2\s*=\s*(\d+\.?\d*)\)',
            r'Expression\(C\)\s*=\s*\(\(x\s*([+-])\s*(\d+\.?\d*)\)\^2\s*\+\s*y\^2\s*=\s*(\d+\.?\d*)\)'
        ]
        cx = cy = R = None
        for pat in patterns:
            m = re.search(pat, fact_expr)
            if m:
                sign = m.group(1)
                val = float(m.group(2))
                cx = -val if sign == '+' else val
                cy = 0.0
                R = np.sqrt(float(m.group(3)))
                break
        if R is None or R <= 0:
            return None
        # pick A if present, else first point
        if 'A' in coords:
            ax, ay = coords['A']
        elif coords:
            ax, ay = next(iter(coords.values()))
        else:
            return None
        # Only handle foci on x-axis for now
        if abs(ay) > 1e-6 or abs(cy) > 1e-6:
            return None
        c = abs(cx - ax) / 2
        if c <= 0:
            return None
        a = R / 2
        if a <= 0 or c <= a:
            return None
        b_sq = c * c - a * a
        b = np.sqrt(b_sq)
        return {'a': a, 'b': b}
    
    def _process_ellipse(self, problem: Dict, idx: int, params: Dict,
                        coords: Dict, eccentricity: Optional[float], verbose: bool) -> Dict:
        """Process ellipse problem with SDF optimization."""
        
        fact_expr = problem.get('fact_expressions', '')
        point_names = self._point_constraint_names(fact_expr, coords, 'ellipse')
        # Create SDF with initial parameters
        center = torch.tensor([0.0, 0.0])
        # Ensure params has 'a' and 'b' keys
        if 'a' not in params or 'b' not in params:
            return {
                'index': idx,
                'success': False,
                'error': f"Ellipse params missing 'a' or 'b': {list(params.keys())}"
            }
        a = torch.tensor([params['a']])
        b = torch.tensor([params['b']])
        
        sdf = EllipseSDF(center, a, b)
        
        # Check if we have explicit numeric coefficients (not symbolic)
        has_explicit_coeffs = not params.get('symbolic', False) and not params.get('from_constraints', False)
        
        # Only apply optimization if we don't have explicit coefficients
        # or if constraints are compatible
        should_optimize = False
        constraints = []
        weights = []
        
        if not has_explicit_coeffs:
            # If we have eccentricity constraint for ellipse (must be < 1)
            if eccentricity and eccentricity < 1:
                constraints.append(lambda: GeometricConstraints.eccentricity_ellipse(
                    sdf.a, sdf.b, eccentricity
                ))
                weights.append(10.0)
                should_optimize = True
            
            # Collect positions for crowd penalty
            all_positions = [sdf.center]
            
            # Point on curve constraints
            for name, (px, py) in coords.items():
                if name in point_names and name not in ['F1', 'F2', 'F', 'O']:
                    point = torch.tensor([px, py])
                    constraints.append(lambda p=point: GeometricConstraints.point_on_curve(sdf, p))
                    weights.append(5.0)
                    should_optimize = True
                    all_positions.append(point)
            
            # Crowd regularization (Paper Section 3.3, Equation 2)
            # Prevents geometric elements from collapsing
            if len(all_positions) > 1:
                constraints.append(lambda pos=all_positions: GeometricConstraints.crowd_penalty(pos, min_dist=0.5))
                weights.append(3.0)  # λ_crowd = 3.0 (paper default)
            
            # Positive constraints
            constraints.append(lambda: GeometricConstraints.positive_constraint(sdf.a))
            constraints.append(lambda: GeometricConstraints.positive_constraint(sdf.b))
            weights.extend([1.0, 1.0])
        
        # Optimize only if needed and constraints are valid
        if should_optimize and len(constraints) > 2:
            opt_result = self.optimizer.optimize(sdf, constraints, weights, verbose)
            
            # Check if optimization produced valid result
            with torch.no_grad():
                a_opt = abs(sdf.a.item())
                b_opt = abs(sdf.b.item())
            
            # If optimization produced degenerate result, revert to original params
            if b_opt < 0.1 or a_opt < 0.1:
                sdf.a.data = torch.tensor([params['a']])
                sdf.b.data = torch.tensor([params['b']])
                opt_result = {'final_loss': 0.0, 'converged': True, 'note': 'reverted to explicit params'}
        else:
            opt_result = {'final_loss': 0.0, 'converged': True, 'note': 'using explicit params'}
        
        # Extract final parameters
        with torch.no_grad():
            a_final = abs(sdf.a.item())
            b_final = abs(sdf.b.item())
        
        # Determine major axis based on original coefficients
        major_axis = params.get('major_axis', 'x')
        
        # Visualize
        output_path = self.output_dir / 'ellipse' / f'problem_{idx:04d}.png'
        self._visualize_ellipse(sdf, problem, params, output_path, major_axis)
        
        return {
            'index': idx,
            'success': True,
            'conic_type': 'ellipse',
            'error': None,
            'params': {
                'a': a_final,
                'b': b_final,
                'major_axis': major_axis,
                'x_coef': params['x_coef'],
                'y_coef': params['y_coef']
            },
            'optimization': opt_result,
            'output_path': str(output_path),
            'answer': problem.get('answer_expressions', ''),
            'fact_expr': fact_expr,
            'coords': coords
        }
    
    def _process_hyperbola(self, problem: Dict, idx: int, params: Dict,
                          coords: Dict, eccentricity: Optional[float],
                          asymptote: Optional[float], verbose: bool) -> Dict:
        """Process hyperbola problem with SDF optimization."""
        
        fact_expr = problem.get('fact_expressions', '')
        point_names = self._point_constraint_names(fact_expr, coords, 'hyperbola')
        
        # Check if foci come from an ellipse (Focus(G) = Focus(H) where H is Ellipse)
        c_from_ellipse = None
        if 'Focus(G) = Focus(H)' in fact_expr or 'Focus(H) = Focus(G)' in fact_expr:
            # Find the ellipse expression
            ellipse_match = re.search(r'Expression\(\w+\)\s*=\s*\(x\^2/(\d+)\s*\+\s*y\^2/(\d+)\s*=\s*1\)', fact_expr)
            if ellipse_match:
                x_coef = float(ellipse_match.group(1))
                y_coef = float(ellipse_match.group(2))
                a_ell = np.sqrt(max(x_coef, y_coef))
                b_ell = np.sqrt(min(x_coef, y_coef))
                c_from_ellipse = np.sqrt(a_ell**2 - b_ell**2)
        
        # If we have eccentricity and c from ellipse, calculate a and b directly
        if eccentricity and eccentricity > 1 and c_from_ellipse:
            # For hyperbola: e = c/a, so a = c/e
            a_val = c_from_ellipse / eccentricity
            # c² = a² + b², so b² = c² - a²
            b_squared = c_from_ellipse**2 - a_val**2
            if b_squared > 0:
                b_val = np.sqrt(b_squared)
                params['a'] = a_val
                params['b'] = b_val
                params['a_squared'] = a_val**2
                params['b_squared'] = b_squared
        
        center = torch.tensor([0.0, 0.0])
        # Ensure params has 'a' and 'b' keys
        if 'a' not in params or 'b' not in params:
            return {
                'index': idx,
                'success': False,
                'error': f"Hyperbola params missing 'a' or 'b': {list(params.keys())}"
            }
        a = torch.tensor([params['a']])
        b = torch.tensor([params['b']])
        
        sdf = HyperbolaSDF(center, a, b)
        
        # Check if we already have explicit params from the above calculation
        has_explicit_params = c_from_ellipse is not None and eccentricity and eccentricity > 1
        
        constraints = []
        weights = []
        
        if not has_explicit_params:
            # Collect positions for crowd penalty
            all_positions = [sdf.center]
            
            # Eccentricity constraint
            if eccentricity and eccentricity > 1:
                constraints.append(lambda: GeometricConstraints.eccentricity_hyperbola(
                    sdf.a, sdf.b, eccentricity
                ))
                weights.append(10.0)
            
            # Asymptote slope constraint
            if asymptote:
                constraints.append(lambda: GeometricConstraints.asymptote_slope(
                    sdf.a, sdf.b, asymptote
                ))
                weights.append(10.0)
            
            # Focus constraint from coordinates
            focus_coords = [(n, c) for n, c in coords.items() if 'F' in n]
            if len(focus_coords) >= 2:
                f1 = focus_coords[0][1]
                f2 = focus_coords[1][1]
                c_target = abs(f1[0] - f2[0]) / 2 if f1[1] == f2[1] == 0 else None
                if c_target:
                    constraints.append(lambda ct=c_target: GeometricConstraints.focus_constraint_hyperbola(
                        sdf.a, sdf.b, ct
                    ))
                    weights.append(10.0)
            
            # Add extra points to crowd penalty
            for name, (px, py) in coords.items():
                if name in point_names and name not in ['F1', 'F2', 'F', 'O']:
                    all_positions.append(torch.tensor([px, py]))
            
            # Crowd regularization (Paper Section 3.3, Equation 2)
            if len(all_positions) > 1:
                constraints.append(lambda pos=all_positions: GeometricConstraints.crowd_penalty(pos, min_dist=0.5))
                weights.append(3.0)  # λ_crowd = 3.0
            
            # Positive constraints
            constraints.append(lambda: GeometricConstraints.positive_constraint(sdf.a))
            constraints.append(lambda: GeometricConstraints.positive_constraint(sdf.b))
            weights.extend([1.0, 1.0])
        
        if len(constraints) > 2:
            opt_result = self.optimizer.optimize(sdf, constraints, weights, verbose)
        else:
            opt_result = {'final_loss': 0.0, 'converged': True, 'note': 'using explicit params'}
        
        with torch.no_grad():
            a_final = abs(sdf.a.item())
            b_final = abs(sdf.b.item())
        
        output_path = self.output_dir / 'hyperbola' / f'problem_{idx:04d}.png'
        self._visualize_hyperbola(sdf, problem, params, output_path)
        
        return {
            'index': idx,
            'success': True,
            'conic_type': 'hyperbola',
            'error': None,
            'params': {
                'a': a_final,
                'b': b_final,
                'orientation': params.get('orientation', 'horizontal')
            },
            'optimization': opt_result,
            'output_path': str(output_path),
            'answer': problem.get('answer_expressions', ''),
            'fact_expr': fact_expr,
            'coords': coords
        }
    
    def _process_parabola(self, problem: Dict, idx: int, params: Dict,
                         coords: Dict, verbose: bool) -> Dict:
        """Process parabola problem with SDF optimization."""
        
        fact_expr = problem.get('fact_expressions', '')
        point_names = self._point_constraint_names(fact_expr, coords, 'parabola')
        vertex = torch.tensor([0.0, 0.0])
        p = torch.tensor([params['p']])
        direction = params.get('direction', 'right')
        
        sdf = ParabolaSDF(vertex, p, direction)
        # Keep vertex fixed at origin to avoid unintended translation during optimization
        sdf.vertex.requires_grad_(False)
        
        # 如果题目给出了显式的抛物线方程（非符号/约束推导），直接使用，不做优化
        has_explicit_params = not params.get('symbolic', False) and not params.get('from_constraints', False)
        
        if has_explicit_params:
            opt_result = {'final_loss': 0.0, 'converged': True, 'note': 'using explicit params'}
        else:
            # Collect positions for crowd penalty
            all_positions = [sdf.vertex]
            
            constraints = [
                lambda: GeometricConstraints.positive_constraint(sdf.p)
            ]
            weights = [1.0]
            
            # Point on curve constraints
            for name, (px, py) in coords.items():
                if name in point_names and name not in ['F', 'O']:
                    point = torch.tensor([px, py])
                    constraints.append(lambda pt=point: GeometricConstraints.point_on_curve(sdf, pt))
                    weights.append(5.0)
                    all_positions.append(point)
            
            # Crowd regularization (Paper Section 3.3, Equation 2)
            if len(all_positions) > 1:
                constraints.append(lambda pos=all_positions: GeometricConstraints.crowd_penalty(pos, min_dist=0.5))
                weights.append(3.0)  # λ_crowd = 3.0
            
            if len(constraints) > 1:
                opt_result = self.optimizer.optimize(sdf, constraints, weights, verbose)
            else:
                opt_result = {'final_loss': 0.0, 'converged': True}
        
        with torch.no_grad():
            p_final = abs(sdf.p.item())
        
        output_path = self.output_dir / 'parabola' / f'problem_{idx:04d}.png'
        self._visualize_parabola(sdf, problem, params, output_path)
        
        return {
            'index': idx,
            'success': True,
            'conic_type': 'parabola',
            'error': None,
            'params': {'p': p_final, 'direction': direction},
            'optimization': opt_result,
            'output_path': str(output_path),
            'answer': problem.get('answer_expressions', ''),
            'fact_expr': fact_expr,
            'coords': coords
        }
    
    def _process_circle(self, problem: Dict, idx: int, params: Dict,
                        coords: Dict, verbose: bool) -> Dict:
        """Process circle problem with SDF."""
        
        fact_expr = problem.get('fact_expressions', '')
        point_names = self._point_constraint_names(fact_expr, coords, 'circle')
        # Get center and radius
        if params.get('from_diameter'):
            # Compute circle from diameter endpoints
            # Pattern: IsDiameter(LineSegmentOf(A, B), C) where C is the circle
            fact_expr = problem.get('fact_expressions', '')
            coords = self.parser.parse_coordinates(fact_expr)
            
            # Find the two points that form the diameter
            diameter_match = re.search(r'IsDiameter\(LineSegmentOf\((\w+),\s*(\w+)\)', fact_expr)
            if diameter_match:
                pt1_name = diameter_match.group(1)
                pt2_name = diameter_match.group(2)
                if pt1_name in coords and pt2_name in coords:
                    x1, y1 = coords[pt1_name]
                    x2, y2 = coords[pt2_name]
                    # Center = midpoint, radius = half of distance
                    params['center'] = ((x1 + x2) / 2, (y1 + y2) / 2)
                    params['radius'] = np.sqrt((x2 - x1)**2 + (y2 - y1)**2) / 2
                else:
                    result = {
                        'index': idx,
                        'success': False,
                        'error': 'Circle from diameter: missing point coordinates'
                    }
                    return result
            else:
                result = {
                    'index': idx,
                    'success': False,
                    'error': 'Circle from diameter: cannot parse diameter pattern'
                }
                return result
        
        center = torch.tensor(list(params.get('center', (0.0, 0.0))))
        radius = torch.tensor([params.get('radius', 1.0)])
        
        sdf = CircleSDF(center, radius)
        
        # No optimization needed for explicit circles
        opt_result = {'final_loss': 0.0, 'converged': True}
        
        with torch.no_grad():
            cx = sdf.center[0].item()
            cy = sdf.center[1].item()
            r = abs(sdf.radius.item())
        
        output_path = self.output_dir / 'circle' / f'problem_{idx:04d}.png'
        self._visualize_circle(sdf, problem, params, output_path)
        
        return {
            'index': idx,
            'success': True,
            'conic_type': 'circle',
            'error': None,
            'params': {'center': (cx, cy), 'radius': r},
            'optimization': opt_result,
            'output_path': str(output_path),
            'answer': problem.get('answer_expressions', ''),
            'fact_expr': fact_expr,
            'coords': {k:v for k,v in coords.items() if k in point_names}
        }
    
    def _visualize_circle(self, sdf: CircleSDF, problem: Dict, params: Dict,
                         output_path: Path):
        """Visualize circle using SDF zero-level set."""
        
        with torch.no_grad():
            cx = sdf.center[0].item()
            cy = sdf.center[1].item()
            r = abs(sdf.radius.item())
        
        # Set up plot range
        margin = r + 2
        xlim = (cx - margin, cx + margin)
        ylim = (cy - margin, cy + margin)
        
        # Create renderer
        renderer = SDFRenderer(resolution=400, xlim=xlim, ylim=ylim)
        
        # Create figure with info panel
        fig, (ax, ax_info) = plt.subplots(2, 1, figsize=(10, 12),
                                          gridspec_kw={'height_ratios': [0.6, 0.4]})
        
        # Render SDF field and zero-level set
        renderer.render_sdf_field(sdf, ax, show_field=True, field_alpha=0.15)
        
        # Mark center
        ax.plot(cx, cy, 'ro', markersize=10, label='Center')
        ax.annotate('C', (cx, cy), textcoords="offset points", xytext=(10, 10), fontsize=12)
        
        # Draw radius line
        ax.plot([cx, cx + r], [cy, cy], 'g--', linewidth=2, label=f'r = {r:.2f}')
        
        # Plot any additional points from constraints
        for name, (px, py) in params.get('coords', {}).items():
            ax.plot(px, py, 'go', markersize=8)
            ax.annotate(name, (px, py), textcoords="offset points", xytext=(5, 5), fontsize=10)
        
        ax.set_xlabel('x')
        ax.set_ylabel('y')
        ax.set_title('Circle - SDF Zero-Level Set')
        ax.legend(loc='upper right')
        ax.set_aspect('equal')
        ax.grid(True, alpha=0.3)
        
        # Info panel
        ax_info.axis('off')
        
        text = problem.get('text', '')
        wrapped_text = self._wrap_text(text, width=60)
        
        info_text = f"""PROBLEM
{'─' * 50}
{wrapped_text}

EQUATION (SDF Zero-Level Set)
{'─' * 50}
(x - {cx:.2f})² + (y - {cy:.2f})² = {r**2:.2f}

SDF PARAMETERS
{'─' * 50}
center: ({cx:.4f}, {cy:.4f})
radius: {r:.4f}

EXPECTED ANSWER: {problem.get('answer_expressions', 'N/A')}
QUERY: {problem.get('query_expressions', 'N/A')}"""
        
        ax_info.text(0, 1, info_text, transform=ax_info.transAxes,
                    fontsize=10, verticalalignment='top', fontfamily='monospace',
                    wrap=True)
        
        plt.tight_layout()
        output_path.parent.mkdir(parents=True, exist_ok=True)
        plt.savefig(output_path, dpi=150, bbox_inches='tight', facecolor='white')
        plt.close()
    
    def _wrap_text(self, text: str, width: int = 50) -> str:
        """Wrap text to specified width."""
        words = text.split()
        lines = []
        current_line = []
        current_len = 0
        
        for word in words:
            if current_len + len(word) + 1 <= width:
                current_line.append(word)
                current_len += len(word) + 1
            else:
                if current_line:
                    lines.append(' '.join(current_line))
                current_line = [word]
                current_len = len(word)
        
        if current_line:
            lines.append(' '.join(current_line))
        
        return '\n'.join(lines)
    
    def _visualize_ellipse(self, sdf: EllipseSDF, problem: Dict, params: Dict,
                          output_path: Path, major_axis: str):
        """Visualize ellipse using SDF zero-level set, including related shapes."""
        
        with torch.no_grad():
            a = abs(sdf.a.item())
            b = abs(sdf.b.item())
        
        # Ensure minimum b value for visualization
        b_viz = max(b, 0.1)
        
        fact_expr = problem.get('fact_expressions', '')
        
        # Check if there's also a hyperbola in the problem
        hyperbola_params = self.parser.parse_hyperbola(fact_expr)
        has_hyperbola = hyperbola_params is not None and 'a' in hyperbola_params and 'b' in hyperbola_params
        
        # Determine plot limits - ensure all curves visible
        if has_hyperbola:
            a_hyp = hyperbola_params['a']
            b_hyp = hyperbola_params['b']
            max_dim = max(a, b_viz, a_hyp, b_hyp) * 1.8 + 1
        else:
            max_dim = max(a, b_viz) * 1.3
        
        # Use vertical layout: plot on top, info below
        fig = plt.figure(figsize=(10, 14), dpi=120)
        
        # Main plot takes up top 60%
        ax_main = fig.add_axes([0.1, 0.4, 0.8, 0.55])
        
        # Create renderer with appropriate limits
        renderer = SDFRenderer(
            resolution=500,
            xlim=(-max_dim, max_dim),
            ylim=(-max_dim, max_dim)
        )
        
        # Render SDF field and zero-level set
        renderer.render_sdf_field(sdf, ax_main, show_field=True)
        
        # If there's a hyperbola, also draw it
        if has_hyperbola:
            center = torch.tensor([0.0, 0.0])
            a_hyp_t = torch.tensor([hyperbola_params['a']])
            b_hyp_t = torch.tensor([hyperbola_params['b']])
            hyp_sdf = HyperbolaSDF(center, a_hyp_t, b_hyp_t)
            
            # Draw hyperbola zero-level set in a different color
            with torch.no_grad():
                grid_flat = renderer.grid.reshape(-1, 2)
                hyp_distances = hyp_sdf(grid_flat).reshape(renderer.resolution, renderer.resolution)
                hyp_distances_np = hyp_distances.cpu().numpy()
            
            ax_main.contour(renderer.xx.numpy(), renderer.yy.numpy(), hyp_distances_np,
                           levels=[0], colors=['#E74C3C'], linewidths=2.5, linestyles='-')
            
            # Asymptotes for hyperbola
            slope_hyp = hyperbola_params['b'] / hyperbola_params['a']
            x_asym = np.linspace(-max_dim, max_dim, 100)
            ax_main.plot(x_asym, slope_hyp * x_asym, '--', color='#C73E1D', linewidth=1.5, alpha=0.5)
            ax_main.plot(x_asym, -slope_hyp * x_asym, '--', color='#C73E1D', linewidth=1.5, alpha=0.5)
            
            # Add to legend
            ellipse_line = Line2D([0], [0], color='#2E86AB', linewidth=2.5, 
                                  label=f'Ellipse (x²/{params["x_coef"]:.0f} + y²/{params["y_coef"]:.0f} = 1)')
            hyperbola_line = Line2D([0], [0], color='#E74C3C', linewidth=2.5, 
                                    label=f'Hyperbola (x²/{hyperbola_params["a"]:.2f}² - y²/{hyperbola_params["b"]:.2f}² = 1)')
        
        # Calculate and plot foci
        c = np.sqrt(abs(a**2 - b**2)) if a > b else np.sqrt(abs(b**2 - a**2))
        if major_axis == 'x':
            ax_main.plot([c, -c], [0, 0], 'ro', markersize=12, 
                        label='Shared Foci' if has_hyperbola else 'Foci', zorder=5)
            ax_main.annotate('$F_1$', (-c, 0), xytext=(-c-0.4, 0.4), fontsize=14, fontweight='bold')
            ax_main.annotate('$F_2$', (c, 0), xytext=(c+0.2, 0.4), fontsize=14, fontweight='bold')
        else:
            ax_main.plot([0, 0], [c, -c], 'ro', markersize=12, 
                        label='Shared Foci' if has_hyperbola else 'Foci', zorder=5)
            ax_main.annotate('$F_1$', (0, -c), xytext=(0.3, -c-0.4), fontsize=14, fontweight='bold')
            ax_main.annotate('$F_2$', (0, c), xytext=(0.3, c+0.2), fontsize=14, fontweight='bold')
        
        # Plot additional points
        coords = self.parser.parse_coordinates(problem.get('fact_expressions', ''))
        for name, (px, py) in coords.items():
            if name not in ['F1', 'F2', 'F', 'O']:
                ax_main.plot(px, py, 'go', markersize=10, zorder=6)
                ax_main.annotate(f'${name}$', (px, py), xytext=(px+0.3, py+0.3), fontsize=13, fontweight='bold')
        
        # Styling
        ax_main.axhline(y=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.axvline(x=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.grid(True, alpha=0.3, linestyle='--')
        ax_main.set_xlim(-max_dim, max_dim)
        ax_main.set_ylim(-max_dim, max_dim)
        ax_main.set_xlabel('x', fontsize=14)
        ax_main.set_ylabel('y', fontsize=14)
        
        if has_hyperbola:
            ax_main.set_title('Ellipse & Hyperbola - SDF Zero-Level Sets', fontsize=16, fontweight='bold', pad=10)
            handles, labels = ax_main.get_legend_handles_labels()
            handles.extend([ellipse_line, hyperbola_line])
            ax_main.legend(handles=handles, loc='upper right', fontsize=10)
        else:
            ax_main.set_title('Ellipse - SDF Zero-Level Set', fontsize=16, fontweight='bold', pad=10)
            ax_main.legend(loc='upper right', fontsize=11)
        
        ax_main.set_aspect('equal')
        ax_main.tick_params(labelsize=11)
        
        # Info panel at bottom
        ax_info = fig.add_axes([0.05, 0.02, 0.9, 0.35])
        ax_info.axis('off')
        
        x_coef = params['x_coef']
        y_coef = params['y_coef']
        
        # Wrap problem text
        problem_text = self._wrap_text(problem.get('text', ''), width=70)
        
        if has_hyperbola:
            equations_text = f"""Ellipse: x²/{np.sqrt(x_coef):.2f}² + y²/{np.sqrt(y_coef):.2f}² = 1  (Blue)
Hyperbola: x²/{hyperbola_params['a']:.2f}² - y²/{hyperbola_params['b']:.2f}² = 1  (Red)"""
        else:
            equations_text = f"x²/{np.sqrt(x_coef):.2f}² + y²/{np.sqrt(y_coef):.2f}² = 1"
        
        info_text = f"""PROBLEM
{'─'*70}
{problem_text}

EQUATIONS (SDF Zero-Level Sets)
{'─'*70}
{equations_text}

SDF PARAMETERS (Ellipse)
{'─'*70}
a (semi-major): {a:.4f}    b (semi-minor): {b:.4f}    c (focal dist): {c:.4f}
eccentricity: {c/max(a,b):.4f}    major_axis: {major_axis}

EXPECTED ANSWER: {problem.get('answer_expressions', '')}
QUERY: {problem.get('query_expressions', '')}
"""
        
        ax_info.text(0.0, 1.0, info_text, transform=ax_info.transAxes,
                    fontsize=10, verticalalignment='top', family='monospace',
                    bbox=dict(boxstyle='round,pad=0.5', facecolor='#E8F4F8', alpha=0.9, edgecolor='#CCCCCC'))
        
        plt.savefig(output_path, bbox_inches='tight', dpi=120, facecolor='white')
        plt.close(fig)
    
    def _visualize_hyperbola(self, sdf: HyperbolaSDF, problem: Dict, params: Dict,
                            output_path: Path):
        """Visualize hyperbola using SDF zero-level set, including related shapes."""
        
        with torch.no_grad():
            a = abs(sdf.a.item())
            b = abs(sdf.b.item())
        
        fact_expr = problem.get('fact_expressions', '')
        
        # Check if there are other shapes in the problem
        ellipse_params = self.parser.parse_ellipse(fact_expr)
        line_params = self.parser.parse_line(fact_expr)
        has_ellipse = ellipse_params is not None and 'a' in ellipse_params and 'b' in ellipse_params
        has_line = line_params is not None and (line_params.get('a') is not None or line_params.get('slope') is not None)
        
        # If line has slope but no explicit equation, try to construct it
        if has_line and line_params.get('slope') is not None and line_params.get('a') is None:
            # Check if line passes through a focus
            slope = line_params['slope']
            # Find focus coordinates
            if 'LeftFocus' in fact_expr or 'RightFocus' in fact_expr:
                # Line passes through focus
                c_hyp = np.sqrt(a**2 + b**2)
                if 'LeftFocus' in fact_expr:
                    focus_x = -c_hyp
                else:
                    focus_x = c_hyp
                # Line: y - 0 = slope * (x - focus_x) => slope*x - y - slope*focus_x = 0
                line_params['a'] = slope
                line_params['b'] = -1.0
                line_params['c'] = -slope * focus_x
                line_params['equation'] = f'y = {slope:.2f}(x - {focus_x:.2f})'
        
        # Determine plot limits
        if has_ellipse:
            a_ell = ellipse_params['a']
            b_ell = ellipse_params['b']
            max_dim = max(a, b, a_ell, b_ell) * 1.5 + 1
        else:
            max_dim = max(a, b) * 2.5 + 2
        
        # Use vertical layout
        fig = plt.figure(figsize=(10, 14), dpi=120)
        ax_main = fig.add_axes([0.1, 0.4, 0.8, 0.55])
        
        renderer = SDFRenderer(
            resolution=500,
            xlim=(-max_dim, max_dim),
            ylim=(-max_dim, max_dim)
        )
        
        # Render hyperbola SDF field
        renderer.render_sdf_field(sdf, ax_main, show_field=True)
        
        # If there's an ellipse, also draw it
        if has_ellipse:
            center = torch.tensor([0.0, 0.0])
            a_ell_t = torch.tensor([ellipse_params['a']])
            b_ell_t = torch.tensor([ellipse_params['b']])
            ellipse_sdf = EllipseSDF(center, a_ell_t, b_ell_t)
            
            # Draw ellipse zero-level set in a different color
            with torch.no_grad():
                grid_flat = renderer.grid.reshape(-1, 2)
                ell_distances = ellipse_sdf(grid_flat).reshape(renderer.resolution, renderer.resolution)
                ell_distances_np = ell_distances.cpu().numpy()
            
            ax_main.contour(renderer.xx.numpy(), renderer.yy.numpy(), ell_distances_np,
                           levels=[0], colors=['#27AE60'], linewidths=2.5, linestyles='-')
            
            # Add ellipse to legend
            ellipse_line = Line2D([0], [0], color='#27AE60', linewidth=2.5, label=f'Ellipse (x²/{ellipse_params["x_coef"]:.0f} + y²/{ellipse_params["y_coef"]:.0f} = 1)')
            hyperbola_line = Line2D([0], [0], color='#2E86AB', linewidth=2.5, label=f'Hyperbola (x²/{a:.2f}² - y²/{b:.2f}² = 1)')
        
        # Draw line if present (only if we have complete line equation)
        if has_line and line_params.get('a') is not None and line_params.get('b') is not None:
            line_a = line_params['a']
            line_b = line_params['b']
            line_c = line_params.get('c', 0)
            
            # Line: ax + by + c = 0 => y = (-ax - c) / b or x = (-by - c) / a
            x_line = np.linspace(-max_dim, max_dim, 100)
            if abs(line_b) > 1e-6:
                y_line = (-line_a * x_line - line_c) / line_b
                ax_main.plot(x_line, y_line, '-', color='#9B59B6', linewidth=2.5, 
                            label=f'Line ({line_params["equation"]} = 0)', zorder=4)
            else:
                # Vertical line
                x_val = -line_c / line_a if abs(line_a) > 1e-6 else 0
                ax_main.axvline(x=x_val, color='#9B59B6', linewidth=2.5,
                               label=f'Line (x = {x_val:.2f})', zorder=4)
        
        # Foci (shared between hyperbola and ellipse if Focus(G) = Focus(H))
        c = np.sqrt(a**2 + b**2)
        ax_main.plot([c, -c], [0, 0], 'ro', markersize=12, label='Shared Foci' if has_ellipse else 'Foci', zorder=5)
        ax_main.annotate('$F_1$', (-c, 0), xytext=(-c-0.4, 0.6), fontsize=14, fontweight='bold')
        ax_main.annotate('$F_2$', (c, 0), xytext=(c+0.2, 0.6), fontsize=14, fontweight='bold')
        
        # Asymptotes
        slope = b / a
        x_asym = np.linspace(-max_dim, max_dim, 100)
        ax_main.plot(x_asym, slope * x_asym, '--', color='#C73E1D', linewidth=2, 
                    alpha=0.7, label='Asymptotes')
        ax_main.plot(x_asym, -slope * x_asym, '--', color='#C73E1D', linewidth=2, alpha=0.7)
        
        # Plot additional points
        coords = self.parser.parse_coordinates(problem.get('fact_expressions', ''))
        for name, (px, py) in coords.items():
            if name not in ['F1', 'F2', 'F', 'O']:
                ax_main.plot(px, py, 'go', markersize=10, zorder=6)
                ax_main.annotate(f'${name}$', (px, py), xytext=(px+0.3, py+0.3), fontsize=13, fontweight='bold')
        
        ax_main.axhline(y=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.axvline(x=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.grid(True, alpha=0.3, linestyle='--')
        ax_main.set_xlim(-max_dim, max_dim)
        ax_main.set_ylim(-max_dim, max_dim)
        ax_main.set_xlabel('x', fontsize=14)
        ax_main.set_ylabel('y', fontsize=14)
        
        # Set title based on what shapes are present
        title_parts = ['Hyperbola']
        if has_ellipse:
            title_parts.append('Ellipse')
        if has_line:
            title_parts.append('Line')
        
        if len(title_parts) > 1:
            ax_main.set_title(' & '.join(title_parts) + ' - SDF Zero-Level Sets', fontsize=16, fontweight='bold', pad=10)
            handles, labels = ax_main.get_legend_handles_labels()
            if has_ellipse:
                handles.extend([ellipse_line, hyperbola_line])
            ax_main.legend(handles=handles, loc='upper right', fontsize=10)
        else:
            ax_main.set_title('Hyperbola - SDF Zero-Level Set', fontsize=16, fontweight='bold', pad=10)
            ax_main.legend(loc='upper right', fontsize=11)
        
        ax_main.set_aspect('equal')
        ax_main.tick_params(labelsize=11)
        
        # Info panel at bottom
        ax_info = fig.add_axes([0.05, 0.02, 0.9, 0.35])
        ax_info.axis('off')
        
        problem_text = self._wrap_text(problem.get('text', ''), width=70)
        
        equations_parts = [f"Hyperbola: x²/{a:.2f}² - y²/{b:.2f}² = 1  (Blue)"]
        if has_ellipse:
            equations_parts.append(f"Ellipse: x²/{ellipse_params['x_coef']:.0f} + y²/{ellipse_params['y_coef']:.0f} = 1  (Green)")
        if has_line:
            equations_parts.append(f"Line: {line_params.get('equation', 'slope defined')} = 0  (Purple)")
        
        equations_text = '\n'.join(equations_parts)
        
        info_text = f"""PROBLEM
{'─'*70}
{problem_text}

EQUATIONS (SDF Zero-Level Sets)
{'─'*70}
{equations_text}

SDF PARAMETERS (Hyperbola)
{'─'*70}
a: {a:.4f}    b: {b:.4f}    c: {c:.4f}
eccentricity: {c/a:.4f}    asymptote slope: ±{slope:.4f}

EXPECTED ANSWER: {problem.get('answer_expressions', '')}
QUERY: {problem.get('query_expressions', '')}
"""
        
        ax_info.text(0.0, 1.0, info_text, transform=ax_info.transAxes,
                    fontsize=10, verticalalignment='top', family='monospace',
                    bbox=dict(boxstyle='round,pad=0.5', facecolor='#E8F4F8', alpha=0.9, edgecolor='#CCCCCC'))
        
        plt.savefig(output_path, bbox_inches='tight', dpi=120, facecolor='white')
        plt.close(fig)
    
    def _visualize_parabola(self, sdf: ParabolaSDF, problem: Dict, params: Dict,
                           output_path: Path):
        """Visualize parabola using SDF zero-level set."""
        
        with torch.no_grad():
            p = abs(sdf.p.item())
        
        direction = params.get('direction', 'right')
        
        # Adjust limits based on direction and p value
        extent = max(p * 8, 6)
        if direction == 'right':
            xlim = (-p * 2, extent)
            ylim = (-extent * 0.8, extent * 0.8)
        elif direction == 'left':
            xlim = (-extent, p * 2)
            ylim = (-extent * 0.8, extent * 0.8)
        else:  # up
            xlim = (-extent * 0.8, extent * 0.8)
            ylim = (-p * 2, extent)
        
        # Use vertical layout
        fig = plt.figure(figsize=(10, 14), dpi=120)
        ax_main = fig.add_axes([0.1, 0.4, 0.8, 0.55])
        
        # Increase resolution slightly to sharpen zero-level near the vertex
        renderer = SDFRenderer(resolution=600, xlim=xlim, ylim=ylim)
        renderer.render_sdf_field(sdf, ax_main, show_field=True)
        
        # Focus and directrix
        if direction == 'right':
            focus = (p, 0)
            ax_main.plot(p, 0, 'ro', markersize=12, label='Focus', zorder=5)
            ax_main.annotate('$F$', (p, 0), xytext=(p+0.4, 0.4), fontsize=14, fontweight='bold')
            ax_main.axvline(x=-p, color='#2ECC71', linestyle='--', linewidth=2, 
                           alpha=0.8, label='Directrix')
            equation = f"y² = {4*p:.2f}x"
        elif direction == 'left':
            focus = (-p, 0)
            ax_main.plot(-p, 0, 'ro', markersize=12, label='Focus', zorder=5)
            ax_main.annotate('$F$', (-p, 0), xytext=(-p-0.6, 0.4), fontsize=14, fontweight='bold')
            ax_main.axvline(x=p, color='#2ECC71', linestyle='--', linewidth=2,
                           alpha=0.8, label='Directrix')
            equation = f"y² = -{4*p:.2f}x"
        else:  # up
            focus = (0, p)
            ax_main.plot(0, p, 'ro', markersize=12, label='Focus', zorder=5)
            ax_main.annotate('$F$', (0, p), xytext=(0.4, p+0.4), fontsize=14, fontweight='bold')
            ax_main.axhline(y=-p, color='#2ECC71', linestyle='--', linewidth=2,
                           alpha=0.8, label='Directrix')
            equation = f"x² = {4*p:.2f}y"
        
        # Plot additional points with staggered labels to reduce overlaps
        coords = self.parser.parse_coordinates(problem.get('fact_expressions', ''))
        for idx, (name, (px, py)) in enumerate(coords.items()):
            if name not in ['F', 'O']:
                ax_main.plot(px, py, 'go', markersize=10, zorder=6)
                offset_y = 0.3 + 0.25 * idx
                ax_main.annotate(f'${name}$', (px, py), xytext=(px + 0.3, py + offset_y),
                                 fontsize=13, fontweight='bold')
        
        ax_main.axhline(y=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.axvline(x=0, color='black', linewidth=0.8, alpha=0.6)
        ax_main.grid(True, alpha=0.3, linestyle='--')
        ax_main.set_xlim(xlim)
        ax_main.set_ylim(ylim)
        ax_main.set_xlabel('x', fontsize=14)
        ax_main.set_ylabel('y', fontsize=14)
        ax_main.set_title('Parabola - SDF Zero-Level Set', fontsize=16, fontweight='bold', pad=10)
        ax_main.set_aspect('equal')
        ax_main.legend(loc='upper right', fontsize=11)
        ax_main.tick_params(labelsize=11)
        
        # Info panel at bottom
        ax_info = fig.add_axes([0.05, 0.02, 0.9, 0.35])
        ax_info.axis('off')
        
        problem_text = self._wrap_text(problem.get('text', ''), width=70)
        
        info_text = f"""PROBLEM
{'─'*70}
{problem_text}

EQUATION (SDF Zero-Level Set)
{'─'*70}
{equation}

SDF PARAMETERS
{'─'*70}
p (focal param): {p:.4f}    focus: {focus}
directrix: {'x = ' + f'{-p:.2f}' if direction in ['right', 'left'] else 'y = ' + f'{-p:.2f}'}
direction: {direction}

EXPECTED ANSWER: {problem.get('answer_expressions', '')}
QUERY: {problem.get('query_expressions', '')}
"""
        
        ax_info.text(0.0, 1.0, info_text, transform=ax_info.transAxes,
                    fontsize=10, verticalalignment='top', family='monospace',
                    bbox=dict(boxstyle='round,pad=0.5', facecolor='#E8F4F8', alpha=0.9, edgecolor='#CCCCCC'))
        
        plt.savefig(output_path, bbox_inches='tight', dpi=120, facecolor='white')
        plt.close(fig)
    
    def process_batch(self, problems_input, max_problems: int = None,
                     verbose: bool = False) -> List[Dict]:
        """Process a batch of problems.
        
        Args:
            problems_input: Either a list of problem dicts or a path to JSON file
            max_problems: Maximum number of problems to process
            verbose: Whether to print verbose output
        """
        # Handle both list and file path inputs
        if isinstance(problems_input, str):
            with open(problems_input, 'r', encoding='utf-8') as f:
                problems = json.load(f)
        else:
            problems = problems_input
            
        if max_problems:
            problems = problems[:max_problems]
        
        results = []
        stats = {'total': len(problems), 'success': 0, 'failed': 0}
        type_stats = {'ellipse': 0, 'hyperbola': 0, 'parabola': 0, 'circle': 0}
        reason_counts: Dict[str, int] = {}
        
        print(f"\n{'='*60}")
        print(f"SDF-Based Processing: {len(problems)} problems")
        print(f"{'='*60}\n")
        
        for idx, problem in enumerate(tqdm(problems, desc="Processing")):
            result = self.process_problem(problem, idx, verbose)
            results.append(result)
            
            if result['success']:
                stats['success'] += 1
                ctype = result.get('conic_type')
                if ctype in type_stats:
                    type_stats[ctype] += 1
            else:
                stats['failed'] += 1
                for reason in result.get('validation_reasons', []):
                    reason_counts[reason] = reason_counts.get(reason, 0) + 1
        
        # Save summary
        summary = {
            'stats': stats,
            'type_stats': type_stats,
            'reason_counts': reason_counts,
            'results': results
        }
        with open(self.output_dir / 'summary.json', 'w') as f:
            json.dump(summary, f, indent=2, default=str)
        
        print(f"\n{'='*60}")
        print("PROCESSING COMPLETE")
        print(f"{'='*60}")
        print(f"Success: {stats['success']} / {stats['total']} ({100*stats['success']/stats['total']:.1f}%)")
        print(f"By type: {type_stats}")
        print(f"Output: {self.output_dir}")
        
        return results