Coordinate Systems

def coord_cartesian(xlim=None, ylim=None, expand=True):
    """
    Standard Cartesian coordinate system (default).
    
    Linear mapping between data coordinates and plot coordinates with
    optional zoom functionality that doesn't affect statistical computations.
    
    Parameters:
    - xlim: tuple, x-axis limits for zooming (min, max)
    - ylim: tuple, y-axis limits for zooming (min, max)  
    - expand: bool, whether to expand limits to include data
    
    Note: This coordinate system preserves distances and angles.
    """

def coord_flip(xlim=None, ylim=None, expand=True):
    """
    Flipped coordinate system (swap x and y axes).
    
    Exchanges the x and y coordinates, effectively rotating the plot 90 degrees.
    Useful for horizontal bar charts, box plots, and making long labels readable.
    
    Parameters:
    - xlim: tuple, limits for original x-axis (becomes y-axis after flip)
    - ylim: tuple, limits for original y-axis (becomes x-axis after flip)
    - expand: bool, whether to expand limits
    
    Note: After flipping, 'x' aesthetics control vertical position and 
    'y' aesthetics control horizontal position.
    """

def coord_fixed(ratio=1, xlim=None, ylim=None, expand=True):
    """
    Fixed aspect ratio coordinate system.
    
    Maintains a fixed relationship between units on the x and y axes,
    ensuring specific aspect ratios are preserved.
    
    Parameters:
    - ratio: float, aspect ratio (y/x). ratio=1 makes axes equal,
             ratio=2 makes y-axis twice as long as x-axis
    - xlim: tuple, x-axis limits
    - ylim: tuple, y-axis limits
    - expand: bool, whether to expand limits
    
    Usage: Essential for maps, scatter plots where distances matter,
    and any visualization where proportional relationships are important.
    """

def coord_equal(xlim=None, ylim=None, expand=True, ratio=1):
    """
    Equal scale coordinate system (alias for coord_fixed with ratio=1).
    
    Ensures that one unit on the x-axis is the same length as one unit
    on the y-axis. Identical to coord_fixed(ratio=1).
    
    Parameters:
    - xlim: tuple, x-axis limits
    - ylim: tuple, y-axis limits
    - expand: bool, whether to expand limits
    - ratio: float, aspect ratio (kept for compatibility, default=1)
    """

def coord_trans(x=None, y=None, xlim=None, ylim=None, expand=True):
    """
    Transformed coordinate system.
    
    Applies transformations to the coordinate axes, allowing for
    non-linear mappings of data to plot space.
    
    Parameters:
    - x: str or transformer, transformation for x-axis
         ('identity', 'log10', 'sqrt', 'reverse', etc.)
    - y: str or transformer, transformation for y-axis
    - xlim: tuple, x-axis limits (in transformed space)
    - ylim: tuple, y-axis limits (in transformed space)
    - expand: bool, whether to expand limits
    
    Common transformations:
    - 'log10': logarithmic transformation
    - 'sqrt': square root transformation  
    - 'reverse': reverse the axis direction
    - 'identity': no transformation (default)
    """

# Default coordinate system (usually not specified explicitly)
ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    coord_cartesian()

# Zoom in on specific region without affecting statistics
ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    geom_smooth(method='lm') + \
    coord_cartesian(xlim=(2, 8), ylim=(0, 10))

# Horizontal bar chart
ggplot(data, aes(x='category', y='value')) + \
    geom_col() + \
    coord_flip()

# Horizontal box plots  
ggplot(data, aes(x='group', y='measurement')) + \
    geom_boxplot() + \
    coord_flip()

# Better label readability
ggplot(data, aes(x='long_category_names', y='count')) + \
    geom_col() + \
    coord_flip() + \
    theme(axis_text_y=element_text(hjust=1))

# Equal axes for scatter plots where distance matters
ggplot(data, aes(x='width', y='height')) + \
    geom_point() + \
    coord_equal()

# Geographic data (approximate equal projection)
ggplot(map_data, aes(x='longitude', y='latitude')) + \
    geom_polygon(aes(group='group'), fill='lightblue', color='black') + \
    coord_fixed(ratio=1.3)  # Adjust for latitude distortion

# Custom aspect ratio
ggplot(data, aes(x='time', y='price')) + \
    geom_line() + \
    coord_fixed(ratio=0.5)  # Make x-axis twice as long as y-axis

# Log-scale coordinates
ggplot(data, aes(x='dose', y='response')) + \
    geom_point() + \
    geom_smooth() + \
    coord_trans(x='log10', y='log10')

# Square root transformation for count data
ggplot(data, aes(x='x', y='count')) + \
    geom_point() + \
    coord_trans(y='sqrt')

# Reverse one axis
ggplot(data, aes(x='year', y='rank')) + \
    geom_line() + \
    coord_trans(y='reverse')  # Lower ranks (1, 2, 3) at top

# Flipped coordinates with free scales in facets
ggplot(data, aes(x='category', y='value')) + \
    geom_col() + \
    facet_wrap('group', scales='free_y') + \
    coord_flip() + \
    theme(axis_text_x=element_text(angle=0))

# Fixed aspect ratio with custom scales
ggplot(spatial_data, aes(x='x', y='y', color='elevation')) + \
    geom_point() + \
    scale_color_gradient(low='blue', high='red') + \
    coord_equal() + \
    theme_void()

# Transformed coordinates with statistical layers
ggplot(data, aes(x='income', y='health_outcome')) + \
    geom_point(alpha=0.6) + \
    geom_smooth(method='lm', se=True) + \
    coord_trans(x='log10') + \
    scale_x_continuous(breaks=[1000, 10000, 100000], 
                      labels=['1K', '10K', '100K'])

# Correlation matrix with equal axes
correlation_data = data.corr().reset_index().melt(id_vars='index')
ggplot(correlation_data, aes(x='index', y='variable', fill='value')) + \
    geom_tile() + \
    scale_fill_gradient2(low='blue', high='red', mid='white') + \
    coord_equal() + \
    theme(axis_text_x=element_text(angle=45))

# Time series with custom aspect ratio for trend visibility
ggplot(time_data, aes(x='date', y='value')) + \
    geom_line() + \
    coord_fixed(ratio=30)  # Emphasize changes over time

# Rank plots with reversed y-axis
ggplot(ranking_data, aes(x='year', y='rank', color='country')) + \
    geom_line(size=1) + \
    geom_point(size=2) + \
    coord_trans(y='reverse') + \
    scale_y_continuous(breaks=range(1, 11))

# World map with appropriate projection approximation
ggplot(world_data, aes(x='long', y='lat')) + \
    geom_polygon(aes(group='group'), fill='lightgray', color='white') + \
    coord_fixed(ratio=1.3) + \
    theme_void()

# Regional map with equal coordinates
ggplot(region_data, aes(x='longitude', y='latitude')) + \
    geom_point(aes(size='population', color='category')) + \
    coord_equal() + \
    theme_minimal()

# Dose-response curves with log transformation
ggplot(dose_data, aes(x='dose', y='response', color='treatment')) + \
    geom_point() + \
    geom_smooth(method='lm', se=False) + \
    coord_trans(x='log10') + \
    scale_x_continuous(trans='log10', 
                      breaks=[0.1, 1, 10, 100],
                      labels=['0.1', '1', '10', '100'])

# Growth curves with log y-axis
ggplot(growth_data, aes(x='time', y='size', color='condition')) + \
    geom_line() + \
    coord_trans(y='log10') + \
    labs(y='Size (log scale)')

# Combining zoom with transformations
ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    coord_trans(x='sqrt', xlim=(1, 25), ylim=(0, 100))

# Multiple coordinate adjustments for complex layouts
ggplot(data, aes(x='category', y='value')) + \
    geom_boxplot() + \
    facet_wrap('treatment') + \
    coord_flip() + \
    theme(strip_text_x=element_text(angle=0))

# Scale transformation (affects statistics)
ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    geom_smooth(method='lm') + \
    scale_x_log10()  # Statistics computed on log-transformed data

# Coordinate transformation (affects display only)
ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    geom_smooth(method='lm') + \
    coord_trans(x='log10')  # Statistics computed on original data, display transformed

# Fixed aspect ratios may require plot size adjustments
plot = ggplot(data, aes(x='x', y='y')) + \
    geom_point() + \
    coord_equal()

# Save with appropriate dimensions
plot.save('equal_aspect.png', width=8, height=8)  # Square for equal aspect

# Cartesian zoom (doesn't affect data range for statistics)
coord_cartesian(xlim=(0, 10))

# Scale limits (removes data outside range before statistics)  
scale_x_continuous(limits=(0, 10))

# Coordinate transformation limits (applied after transformation)
coord_trans(x='log10', xlim=(0, 2))  # Limits on log10-transformed values