2. Cairofunctions.py

The cairofunctions.py file contains all the objects and functions used for graphing. A table of objects is given below.

Objects

Object	Description
Point	These are used like vectors. Used to describe coordinates, locations, unit vectors, etc.
Transform	These are 2 Dimensional linear transformations. When multiplied with a point, they output the transformed point.
Context	This contains most of the code that draws to the cairo context.
Coordinate Grid	This objects contains the Coordinate Grid. To plot, you need to define a coordinate grid.

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Point

These are used like vectors. Used to describe coordinates, locations, unit vectors, etc.

To make a point object, use the following syntax.

import graphing.cairofunctions as cairofunctions

point = cairofunctions.Point(x, y) # x and y are floats, that represent the X-Coordinate and Y-Coordinate Respectively.

Points have 2 fields. Given in the table below.

Field	Description
x	Gives the x coordinate of the point object.
y	Gives the y coordinate of the point object.

The behavior of point objects with operators is given in the table below.

Operator	Return Type	Function
Point + Point	Point	This adds the corresponding X and Y coordinates of the points.
Point * Scalar	Point	This scales the X and Y coordinates by a scalar.
Point - Point	Point	This subtracts the corresponding X and Y coordinates of the points.
Point / Scalar	Point	This scales the X and Y coordinates down by a scalar.

The methods that the point object has is given in the table below.

Method	Return Type	Function
mod	float	Returns the Euclidean Length of the Point.
norm	Point	Returns the unit vector in the direction of the Point.

Transform

When multiplied with a point, the Transform object returns the transformed Point.

To make a Transform object, use the following syntax.

import graphing.cairofunctions as cairofunctions

# The unit vectors of the transformed coordinate system
i = cairofunctions.Point(x1, y1)
j = cairofunctions.Point(x2, y2)

transform = cairofunctions.Transform(i, j)

The Transform object has the following fields.

Field	Description
i	X Axis Unit Vector
j	Y Axis Unit Vector

The Transform object can be multiplied with a Point object. See the Example below.

import graphing.cairofunctions as cairofunctions

i = cairofunctions.Point(0,1)
j = cairofunctions.Point(-1,0)

rot90 = cairofunctions.Transform(i, j) # Linear Transformation corresponding to a pi/2 radians rotation.

point = cairofunctions.Point(2,3)

point_rotated = rot90 * point # Applies Linear Transformation to point.

print(f"Original Point = {point.x, point.y}\n"
    f"Transformed Point = {point_rotated.x, point_rotated.y}"
)
"""
Sample Output:

Original Point = (2, 3)
Transformed Point = (-3, 2)
"""