# Complex paths in generativepy

By Martin McBride, 2022-01-05
Tags: generativepy tutorial complex path hole self intersection
Categories: generativepy generativepy tutorial

This tutorial shows how to complex paths in generativepy. It follows on from the composite path tutorial.

A complex path is a single path that either:

• Encloses more than one area.
• Contains more than one subpath.
• Or both.

The main difference between a complex path and multiple simple paths is that the complex path is treated as one path when it is filled. This means that, depending on the fill rule selected, various parts of the shape will be filled or unfilled.

## Complex polygons

A complex polygon can enclose more than one area, if it is self-intersecting. A well known example is a star-polygon:

from generativepy.drawing import make_image, setup, EVEN_ODD
from generativepy.color import Color
from generativepy.geometry import Polygon
import math

def draw(ctx, pixel_width, pixel_height, frame_no, frame_count):
setup(ctx, pixel_width, pixel_width, background=Color(0.8))

black = Color(0)
red = Color('red')

Polygon(ctx).of_points([(150, 50),
(100, 250),
(250, 150),
(50, 150),
(200, 250),
]).fill(red).stroke(black, 5)

Polygon(ctx).of_points([(450, 50),
(400, 250),
(550, 150),
(350, 150),
(500, 250),
]).fill(red, fill_rule=EVEN_ODD).stroke(black, 5)

make_image("complex-polygon.png", draw, 700, 300)


This code is available on github in tutorial/shapes/complex-polygon.py.

Here is the resulting image:

The code simply draws two polygons, each with 5 points. Due to the order the points are defined in the of_points list, the shape is drawn as a star shape rather than a simple convex pentagon.

In the first case we use the WINDING fill rule (the default) which causes the whole shape to be filled.

In the second case we specify the EVEN_ODD fill rule, which causes the central region of the star shape to be unfilled.

## Multiple subpaths

This code draws two rectangles, however it creates them as two separate subpaths within the same path:

from generativepy.drawing import make_image, setup, EVEN_ODD
from generativepy.color import Color
from generativepy.geometry import Line, Rectangle

def draw(ctx, pixel_width, pixel_height, frame_no, frame_count):
setup(ctx, pixel_width, pixel_width, background=Color(0.8))

black = Color(0)

Rectangle(ctx).of_corner_size((100, 100), 250, 150).as_sub_path()\
.fill(Color('red'), fill_rule=EVEN_ODD)\
.stroke(Color('blue'), 5)

make_image("complex-subpaths.png", draw, 500, 400)


This code is available on github in tutorial/shapes/complex-subpaths.py.

Here is the resulting image:

We create the first Rectangle object, but instead of filling or stroking it, we use add() to add it to the current path (similar to creating a composite path).

For the second Rectangle, we call as_sub_path() to add the item as a subpath within the existing path.

When we fill and stroke the item, both rectangles will be drawn because they are both part of the path. Due to the EVEN_ODD fill rule, the inner rectangle is unfilled.