Remove consecutive points in linear path string if they have zero length or direction does not change

Problem statement:

A path M2 2h2h3v1v3h-2v-1l-1-1l-2-2 could be simplified to M2 2h5v4h-2v-1l-3-3.

If you compare these paths, the same shape as above can be represented with less points, thus saving precious bytes: Technically, the last step could be replaced with a z, but this goes beyond the scope of this optimisation.

In a nutshell:

Add each path to the output stack
Compare the direction of the last two entries, e.g. by calculating atan2 of l-1-1 and l-2-2
If the direction matches, compare the paths
Also remove zero-length segments, e.g. l-1-1h0l-2-2 to l-3-3

Example Python code:

This example code parses a path of Saxony, Germany which contains segments such as: l -1 -1 -2 -2 which could be simplified to l -3 -3 or h3 0 2 which could be simplified to h5 as well as combinations of these. It analyses the segments and combines them. It converts all h and v segments into l and only supports relative coordinates with the exception of mMzZ, which are just passed through. Thus it also doesn't support curves, sorry! Optimising the output back into h and v shorthands, changing precision etc. could be done with the already existing optimisation steps of SVGOMG.

import re
import math

def parse_path(path):
    # Regular expression to match SVG path commands and their parameters
    path_re = re.compile(r'([mlhvz])|(-?\d*\.?\d+(?:e[-+]?\d+)?)', re.IGNORECASE)
    tokens = path_re.findall(path)
    commands = []
    current_command = None

    for token in tokens:
        if token[0]:
            if current_command:
                commands.append(current_command)
            current_command = [token[0]]
        else:
            current_command.append(float(token[1]))

    if current_command:
        commands.append(current_command)

    return commands

def expand_chained_commands(commands):
    expanded_commands = []
    for command in commands:
        if command[0] in 'hv':
            for i in range(1, len(command)):
                if command[0] == 'h':
                    expanded_commands.append(['l', command[i], 0])
                else:
                    expanded_commands.append(['l', 0, command[i]])
        elif command[0] == 'l':
            for i in range(1, len(command), 2):
                expanded_commands.append(['l', command[i], command[i+1]])
        else:
            expanded_commands.append(command)
    return expanded_commands

def combine_segments(commands):
    combined_commands = []
    stack = []

    def direction(x, y):
        return math.atan2(y, x)

    for command in commands:
        if command[0] == 'l':
            if command[1] == 0 and command[2] == 0:
                continue

            if stack and stack[-1][0] == 'l':
                last_command = stack.pop()
                if direction(last_command[1], last_command[2]) == direction(command[1], command[2]):
                    command = ['l', last_command[1] + command[1], last_command[2] + command[2]]
                else:
                    stack.append(last_command)
            stack.append(command)
        else:
            if stack:
                combined_commands.extend(stack)
                stack = []
            combined_commands.append(command)

    if stack:
        combined_commands.extend(stack)

    return combined_commands

def format_path(commands):
    path_str = ''
    for command in commands:
        path_str += command[0]
        for param in command[1:]:
            path_str += '%.2f ' % param
    return path_str.strip()

def optimize_path(path):
    commands = parse_path(path)
    expanded_commands = expand_chained_commands(commands)
    combined_commands = combine_segments(expanded_commands)
    return format_path(combined_commands)

# Example usage
path = "M621 618h0v-1l-2-1h-2 0l-3-2h-1v-3h0v-1h0l-2-1-1-2h0v-1h-3l-1-1h1v-1h1l1-1h0v-1h0l1-1h0v-2h0l-1-1h0-1v-1h1v-1l1-1 2-2 1-1h0v-1h2l1 1h0v1h2v-1l2-3h2v1h1l1-1h1v-1l1-1v-2l1-2v-1h6l2-2 1-1h0l1-3h0-2 0-1 0v-1h0l-1-1v-1h0l1-1h0l-1-1h0-1 0-1 0v-1l1-1v-1h2v-1l1-1h0v-1h-2v-2l5-2h1l1-2h5l1-2 2-2 2-1h1v-1h7v1h0l1-1 1-1h0l1-1h0v-1l-1-3-2-3-2-1h-1l-1-1-1-1-1-2-2-3h0l-1-4-11-3h-8v-1h0l-1-1v-1h0v-1l-1-1-1-1v-3l-1-1h-1v-1h0l1-1h0v-1h0v-5l-2-2v-3h0v-1h0v-1h0l1-2h1l1-1h0v-1h0v-4h-1v-6h0l-1-1h0v-2h0l1-1h1v-1h0v-1h1v-7l2-1v-1h0l1-1h0v-1h1v1h1l3 1v-1l4-1 5-1h1v-1h0v-2l1-1h0l6 1h1l7-1h0v1h1l1-1 1-1v-1l1-1 1-1 3 1 2 1 1-1 4-3 1-1h2l1 1 1 1h1l1 1h1l1 2 1-1h3l1 2h2l2 3 1 1h1l1-1h0v1h1l1 1h0v2h0v1h0l1 1 1 1v1h1v4h0l-1 1h0v1h0v6h0l-1 1h0-1v1h1v1h0v1h0l1-1h1l1-1h1l1 2h2l6-3h1l1-1h2l3 1 1 1 1 1 1 1h1l1 2 1 1 1-1h1l4 2h11l7-1h8l1-2 4-6 1-3v-1h0l1-1 2-4 1-1 3-2 5-1 3 1 3 1 2 1h3l10-5 3-1h3l2 1 3 2h3v1l2 2 5 1 1 1 2 1 3 1 2 1 1 1 2 2v11h0l1 2v1l1 2 2 2 1 2v4h0l-1 3-1 3-1 3v5h0l-1 1v4l-1 1-3 9-4 8-2 3-1 2v2l-1 3-1 1v1h-1l-1 1h-2l-2-1-3-2-1-1h-3v-3l2-3v-3h-1l-4 2-1-1v-1l1-2 1-1v-3l-1-1-1-1-1-1-2-1h-1v-1l-1-1h0-1 0-3 0l-1 1h-3v-1l-1-1h0l-3-1h-2l-1 1-1 1-1 4-1 1h1l2 1h2l-1 1v1l2 2 3 1 2 1-1 3h0l-2 2-6-1-2 1h0-1l-2 2v1h0l-9 4-1 1-2 1h-1l-3-1-1 1h-1l-1 1v1h-3 0l-1 1v3h0v1h0-1 0l-2 1v1h-7l-2 1h-8 0-1l-3 1-2 1h-1l1 2v2h0l-1 1h0l-1 1v1h0v1h0-1l-1 2h-1l-1 1-1 1-2-1v-1l-1-2h0-1 0-1 0v1h-1l-1 1h0l-1 1h0l-1 2v1h-3l-1-1h-1 0l-3 6-1 2v1l-2 1-3-1-2 1h-2 0-2 0-2v7h0-1 0v1h0v1h0-1 0l-1 1h-1 0-2l-7-4h-1 0-1v1h-4l-1 1h0l-1 1-1 1v1h0-1l-1 1-4-1h-5l-3 1-1 1-1 1h0l-1 1v1h0v1h0v1h0-1 0l-1 1h0l-2 1h0-1v1l-2 3v1h-1v1h-1l-1 1v2h0l-1 2-1 1v3l1 1v1h0l-1 1h-1l-1-1-1-3v-2h-1v-1l-1-1h0v-1h0l1-1h0l-1-1h0-3l-1-1v-3l-1-1-1-1h-4z"
print optimize_path(path)

svg / svgo