Parliamentarch

Utility math functions for the generation of arch-styled parliamentary arches.

Base math and layout

The idea is to lay a certain number of seats in the form of a hemicycle. The shape we're after can be mathematically described as follows:

• Take two concentric circles where the outer one's radius is twice the inner's
• Consider the area between the two, which is called an annulus.
• Cut the annulus in half, following a diameter of the larger circle.

The result is the hemicycle. Now, to place the seats so that they make the form of the hemicycle:

• The hemicycle fits in a 2:1 rectangle, which we will consider in a "landscape" orientation, and with the cut diameter being on the bottom (the top left and top right corners of the rectangle are empty).
• The seats will placed in rows, such that:
  • The rows are semicircular arcs, concentric to the inner and outer arcs.
  • The difference between the radii of two consecutive rows is a constant called the "row thickness" (radii is the plural of radius).
  • The seat are circles (or disks) of equal radius. That radius divided by half of the row thickness makes the "seat radius factor".
  • The center of a seat is on the arc of that seat's row.
  • In any given row, the distance between two neighboring seats is a constant.
  • The innermost row's arc is the inner arc of the annulus.
  • The radius of the outermost row's arc is equal to the radius of the outer arc minus half of the row thickness, such that no seat may overlap the outer arc.
  • The vertical distance between the center of the bottom-most seats of each row, which are the first and last seat of each row, is equal to half of the row thickness, such that no seat may overlap the inner arc.
  • When only one seat is placed in a row, the previous rule does not apply and the seat is placed at the horizontal center of the diagram.

As a result, there is a maximum number of seats that can be placed on a given number of rows. For numbers of seats inferior to that value, there exists several strategies to distribute the seats among the rows.

It should be noted that all of the above applies for the classical case of a 180°-spanning hemicycle. If you specify a smaller angle, the initial annulus is to be cut using two radii of the larger circle. For seat placements, what applied to the bottom of the rectangle now applies to the two cut radii.

Tweakable rules

As hinted above, there are several parameters that can be tweaked to change the layout of the hemicycle. Among them:

• The span angle of the hemicycle can be set to a value lower than 180° (higher values are not supported). However, values so low as to prevent some row from containing even one seat are not supported, will yield incorrect results, and may raise errors in future versions.
• The number of rows can be set higher than the minimum required to hold the provided number of seats.
• The seat radius factor can be changed between 0 and 1, with the seats touching their lateral neighbors when the factor is 1.
• As long as the number of seats is not the maximum number the number of rows can hold, different strategies can be chosen to distribute the seats.

Main module content

These are found in the parliamentarch module.

SeatData

This class is defined and explained in the SVG submodule below, but it is exposed as part of the main module.

write_svg_from_attribution(file, attrib, *, seat_radius_factor: float = 1., **kwargs)

This function writes an SVG file representing a hemicycle. The parameters are as follows:

• file: str|io.TextIOBase: a file-like object open in text mode, or the path to the file to write on. If a path is provided, the file will be written to in UTF-8 encoding, and it will be created if it doesn't exist or overwritten if it does.
• attrib: dict[SeatData, int]: a mapping from a SeatData object applying to a number of seats in the resulting hemicycle, to the number of seats each object applies to. Typically, each SeatData object corresponds to a group or party. The ordering of the keys matter, and the elements will be arranged from left to right in the hemicycle.
• seat_radius_factor: float: the ratio of the seats radius over the row thickness. Defaults to 1, which makes seats touch their neighbors.
• **kwargs: all optional keyword parameters taken by parliamentarch.geometry.get_seats_centers or by parliamentarch.svg.write_svg can be passed to this function.

get_svg_from_attribution(attrib, **kwargs) -> str

Instead of writing it to a file, this function returns the SVG content as a string. The parameters are otherwise the same.

Command-line interface

See py -m parliamentarch -h for the accepted parameters.

Geometry submodule contents

These are found in the parliamentarch.geometry submodule.

get_nrows_from_nseats(nseats: int, span_angle: float = 180.) -> int

Returns the minimum number of rows required to hold the given number of seats, in a diagram with the given span angle.

get_rows_from_nrows(nrows: int, span_angle: float = 180.) -> list[int]

From a given number of rows (and span angle), returns a list of each row's maximum seat capacity, starting from inner to outer. The list is increasing and its length is the number of rows.

get_row_thickness(nrows: int) -> float

From a given number of rows, returns the thickness of the row, i.e the difference between the radii of successive rows. This can help converting a seat radius factor (as passed to write_svg_from_attribution) to a seat radius as taken by write_svg.

FillingStrategy

This is an enumeration of the different implemented strategies to fill the seats among the rows. The strategies are:

• FillingStrategy.DEFAULT: The seats are distributed proportionally to the maximum number of seats each row can hold. The result is that the lateral distance between neighboring seats is close between the rows.
• FillingStrategy.EMPTY_INNER: This selects as few outermost rows as necessary to hold the given seats, then distributes the seats proportionally among them. Depending on the number of seats and of rows, this either leaves empty inner rows, or is equivalent to the DEFAULT strategy. This is equivalent to the legacy "dense rows" option, in that not counting the potential empty rows, the distance between neighboring seats is the smallest possible, and is close between the rows.
• FillingStrategy.OUTER_PRIORITY: This fills the rows to their maximum capacity, starting with the outermost rows going in. The result is that given a number of rows, adding one seat makes a change in only one row.

get_seats_centers(nseats: int, *, min_nrows: int = 0, span_angle: float = 180., filling_strategy: FillingStrategy = FillingStrategy.DEFAULT) -> list[tuple[float, float]]

This is the main function. Other than self-explanatory parameters similar to the functions above:

• min_nrows: The minimum number of rows to use. Only taken into account if the required number of rows to hold the given number of seats is less than that. Defaults to 0, which means using the minimum number of rows possible.

The function returns a dict representing the ensemble of seats. The keys are (x, y), the cartesian coordinates of the center of the seat. The coordinates start from the bottom-left corner of the rectangle, with the x axis pointing right and the y axis pointing up. The radius of the outermost circle (equal to the height and half the width of the rectangle) is 1, so x goes from 0 to 2 and y goes from 0 to 1.

The value of each entry is the angle, in radians, calculated from the right-outermost point of the annulus arc, to the center of the arcs, to the center of the seat.

Calling sorted(di, key=di.get, reverse=True) will return a list of the seats arranged from left to right.

SVG submodule content

These are found in the parliamentarch.svg submodule.

SeatData(data, color, border_size=0, border_color="#000")

A class representing how to display a given seat or set of seats.

• data: str: metadata about the group of seats, which will end up in the SVG file. Typically the name of the party or of the member.
• color: Color: the color with which to fill the seat circles. This may take any number of formats: a "#RGB", "#RRGGBB", "#RGBA" or "#RRGGBBAA" string, a RBG tuple[int, int, int], or a RGBA tuple[int, int, int, int] with ints between 0 and 255. CSS color names are also supported.
• border_size: float: the size of the border around the seat circle. (to be documented at greater length)
• border_color: Color: the color of the border.

write_svg(file, seat_centers, seat_actual_radius, *, canvas_size=175, margins=5., write_number_of_seats=True, font_size_factor=...)

This function writes an SVG file representing a hemicycle. The parameters are as follows:

• file: str|io.TextIOBase: a file-like object open in text mode, or the path to the file to write on. If a path is provided, the file will be written to in UTF-8 encoding, and it will be created if it doesn't exist or overwritten if it does.
• seat_centers: dict[tuple[float, float], SeatData]: a mapping from the (x, y) coordinates of each seat's center to a SeatData object.
• seat_actual_radius: float: the seat radius, in the same unit as the coordinates returned by get_seat_centers, i.e as a fraction of canvas_size.
• canvas_size: float: the height of the 2:1 rectangle in which the hemicycle will be drawn.
• margins: float|tuple[float, float]|tuple[float, float, float, float]: the margins around that rectangle. If four values are given, they are the left, top, right, and bottom margins, in that order. If two values are given, they are the horizontal and vertical margins, in that order. If one value is given, it is used for all four margins.
• write_number_of_seats: bool: whether to write the total number of seats at the bottom center of the diagram - in the well of the House.
• font_size_factor: float: a factor you should tweak to change the font size of the number of seats. The default value is around 0.2. Keeping this constant will keep the font size in scale when changing the canvas size.

write_grouped_svg(file, seat_centers_by_group, *args, **kwargs)

This takes the relationship between seats and SeatData a different way, which is way more optimized both in SVG file size and in time. The other parameters are the same.

• seat_centers_by_group: dict[SeatData, list[tuple[float, float]]]: a mapping from the SeatData of a group of seats to a list of (x, y) seat center coordinates as output by get_seats_centers.

These two functions have equivalents which return the content of the SVG file a string. They take the same parameters except for the file, and are named get_svg and get_grouped_svg.

dispatch_seats(group_seats, seats) -> dict[SeatData, list[S]]

A function helps make the transition from parliamentarch.get_seats_centers's output to the way write_grouped_svg expects it:

• group_seats: dict[SeatData, int]: a mapping from the SeatData of a group of seats to the number of seats in that group. Key ordering matters.
• seats: Iterable[S]: an iterable of seats in whatever format, but intended to be (x, y) tuples. Its length must be the sum of the values of group_seats. Its ordering matters.

Typically the groups are ordered from left to right, and the seats are ordered from left to right. sorted(di, key=di.get, reverse=True) helps with that.

SeatData and dispatch_seats may be moved to another module in the future.

Todos and future features

• Have the main functions support a sequence of SeatData objects using dict.fromkeys(seq, 1)
• Allow SeatData to take some <a> element properties (like href), and if so use <a> instead of <g>
• Allow SeatData to contain more creative SVG content like gradients
  • Maybe give it a .wrap method that wraps the circles in a g or a, and make it subclassable ?
  • Maybe just give a style method ?
• Add tests
• Add the option to force all rows to contain an even number of seats
• Add a simpler way to input parameters in CLI
  • Maybe by allowing the use of the standard input to pass JSON content ?