# Ellipse

Martin McBride, 2020-08-26
Tags geometry ellipse arc sector segment
Categories generativepy generative art

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The Ellipse class draws ellipses, arcs, sectors and segments.

An ellipse is similar to a circle, but it has two radii, one in the x direction and one in the y direction.

There is also a ellipse function that just creates a ellipse as a new path.

## Ellipse class methods

The Ellipse class inherits add, fill, stroke, fill_stroke, path, clip and other methods from Shape.

It has an additional method:

• of_center_radius
• as_arc
• as_sector
• as_segment

### of_center_radius

Creates a ellipse based on the centre point and the two radii.

of_center_radius(center, radius_x, radius_y)

Parameter Type Description
center (number, number) A tuple of two numbers, giving the (x, y) position of the centre of the ellipse.
radius_x number A number, giving the x radius of the ellipse.
radius_y number A number, giving the y radius of the ellipse.

### as_arc

Modifies a ellipse, to show only an arc. An arc is part of the circumference of the ellipse.

as_arc(start_angle, end_angle)

Parameter Type Description
start_angle number A number, giving the start angle of the arc
end_angle number A number, giving the end angle of the arc

This is used as a modifier with of_center_radius, to draw just an arc. To draw an arc use:

Ellipse(ctx).of_center_radius((0, 0), 1).as_arc(0, 1).stroke(Color('black'), 0.1)


Angles are measured in radians. Angle zero lies along the positive x-axis, and the angle increases in the clockwise direction - note that this is opposite to the normal mathematical convention, where angle increases in the counterclockwise direction. The difference is due to the fact that y increases as you move down the image in generativepy.

If you are using a flipped coordinate system (see the setup function in the drawing module), the angle increases in the counterclockwise direction.

Since an arc is a line, you should normally use the stroke method to draw it. If you attempt to fill the arc, it will fill it as if it was a segment.

### as_segment

Modifies a ellipse, to show only a segment. An segment is the part of the ellipse that is cut off by a chord.

as_segment(start_angle, end_angle)


This function works in a similar way to the as_arc function, but it includes the area of the segment. You can fill or stroke the area, see the example below.

### as_sector

Modifies a ellipse, to show only a sector. An sector is a "pizza slice", like you would use in a pie chart,.

as_sector(start_angle, end_angle)


This function works in a similar way to the as_arc function, but it includes the area of the sector. You can fill or stroke the area, see the example below.

## ellipse function

Adds a ellipse as a new path, without the need to create a Ellipse object in code.

ellipse(ctx, center, radius)

Parameter Type Description
ctx Context The Pycairo Context to draw to
center (number, number) A tuple of two numbers, giving the (x, y) position of the centre of the ellipse.
radius_x number A number, giving the x radius of the ellipse.
radius_y number A number, giving the y radius of the ellipse.

The ellipse function doesn't allow you to create arcs, segments or sectors.

## Example

Here is some example code that draws ellipses using the class and the utility function. The full code can be found on github.

from generativepy.drawing import make_image, setup
from generativepy.color import Color
from generativepy.geometry import Ellipse, ellipse

'''
Create ellipses using the geometry module.
'''

def draw(ctx, width, height, frame_no, frame_count):
setup(ctx, width, height, width=5, background=Color(0.8))

# The ellipse function is a convenience function that adds a ellipse as a new the path.
# You can fill or stroke it as you wish.
ellipse(ctx, (1, 1), 0.7, 1.1)
ctx.set_source_rgba(*Color(1, 0, 0))
ctx.fill()

# Ellipse objects can be filled, stroked, filled and stroked.
Ellipse(ctx).of_center_radius((2.5, 1), 0.7, 0.3).fill_stroke(Color(0, 0, 1), Color(0), 0.05)
Ellipse(ctx).of_center_radius((4, 1), 0.7, 0.3).as_arc(0, 1).stroke(Color(0, 0.5, 0), 0.05)

Ellipse(ctx).of_center_radius((1, 2.5), 0.7, 0.3).as_sector(1, 3).stroke(Color('orange'), 0.05)
Ellipse(ctx).of_center_radius((2.5, 2.5), 0.7, 0.3).as_sector(2, 4.5).fill(Color('cadetblue'))
Ellipse(ctx).of_center_radius((4, 2.5), 0.7, 0.3).as_sector(2.5, 6).fill_stroke(Color('yellow'), Color('magenta'), 0.05)

Ellipse(ctx).of_center_radius((1, 4), 0.7, 0.3).as_segment(1, 3).stroke(Color('orange'), 0.05)
Ellipse(ctx).of_center_radius((2.5, 4), 0.7, 0.3).as_segment(2, 4.5).fill(Color('cadetblue'))
Ellipse(ctx).of_center_radius((4, 4), 0.7, 0.3).as_segment(2.5, 6).fill_stroke(Color('yellow'), Color('magenta'), 0.05)

make_image("/tmp/geometry-ellipses.png", draw, 500, 500)


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