Creating Conic Sections and Mathematical Curves using Python Turtle

We have created a Python package 'turtle_conics'.Using this package, we can draw different curves like Ellipse ,Parabola, Hyperbola in Python Turtle in any orientation as you like. We can also draw many beautiful Mathematical Curves using Python Turtle.

Feel free to contribute with a pull request if you want to add any Curve, also check out the Source code for the Package in my Github Repository

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FEATURES

-Simple function to create any of the above mentioned curves by importing functions from all_curves module specifying the arguments. -Can be used inside Looping structures to create different patterns.

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WHAT'S NEW

• Added Epitrochoid Curves in the new update
• Added Hypocycloid Curves in the update(0.2.1)
• Added Butterfly curve in the update(0.1.3)
• Added Heart curve in the update (0.1.1)
• Added Cardioid curve in the update (0.1.0)

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How To Import The Package ?

*NOTE:- While Importing the Package, the name of the package is 'turtle_conics' and not 'turtle-conics'.

• For importing all functions inside the package:-

import turtle

from turtle_conics.all_curves import *

#Now make a function call for any of the curves

turtle.done()

• For importing a single function inside package:

import turtle

from turtle_conics.all_curves import (func)

#Now make a function call for any of the curves

turtle.done()

HISTORY

0.0.1 (2020-05-22)

• First release on PyPI

0.0.2(2020-05-24)

• Added Rectangular Hyperbola

0.1.0(2020-05-27)

• Added Cardioid curve

0.1.1(2020-06-05)

• Added Heart curve

0.1.2(2020-06-05)

• Made few changes in the package

0.1.3(2020-06-15)

• Added Butterfly curve

0.2.0(2020-06-29)

• Added Leminiscate curve

0.2.1(2020-07-20)

• Added Hypocycloid Curves

0.2.2(2020-08-07)

• Added Epitrochoid Curves

Package Description

The 'turtle_conics' package consists of module 'all_curves' with 8 functions to draw Ellipse, Parabola, Hyperbola, Cardioid, Heart curve,Butterfly curve, Leminiscate, Hypocycloid and Epitrochoid.

Latest Curves

--Epitrochoid These are set of curves formed when a point attached to Outer Circle(with radius 'b') rolls around the outside of another fixed Circle(with radius 'a').

We can draw different types of Epitrochoids:- - We can draw different types of limacon(i.e when a=b) - We can draw different types of Hypocycloids(i.e when b=ht)

def epitrochoid(a, b, ht, no_of_loops=None, h=None, k=None)

• a:-It is the radius of the Inner circle.

• b:- It is the radius of Outer circle which is rolling outside the Inner circle to generate these set of curves.

• ht:- It is the distance of the pt(whose locus is this curve) from centre of Outer Circle.

• no_of_loops(Optional):- This parameter is for the no of loops. NOTE:- This parameter is useful when the ratio 'a/b' is a fraction and we can adjust the no of loops accordingly.

• h,k:-(Optional) For drawing an epitrochoid with centre of Inner circle at (h,k).By default both are zero.Using this parameter we can draw these curves at any position in the Turtle Window. NOTE:- When the ratio of radius of Outer Circle to radius of Inner Circle (i.e a/b) is fractional, then the curve may or may not be closed entirely hence we can adjust the value for no of loops.

--Hypocycloid

These are a set of curves formed when a Circle rolls inside another fixed Circle.

We can draw different types of Hypocycloids:- - Curves having integer value of 'n'(Curves like Astroid,Deltoid etc) - Curves having Fractional/Rational value of 'n' Here 'n' is ratio of radii of Outer circle with Inner circle(a/b).

def hypocycloid(a, b, no_of_loops=None, h=None, k=None)

• a:-It is the radius of the Outer circle.

• b:- It is the radius of Inner circle which is rolling inside the Outer circle to generate these set of curves.

• no_of_loops(Optional):- This parameter is for the no of loops required to complete any curve.NOTE:- If while using this function, any curve is incomplete then by adjusting the value to this parameter we can complete that curve.

• h,k:-(Optional) For drawing any hypocycloid with centre of Outer circle at (h,k).By default both are zero.Using this parameter we can draw these curves at any position in the Turtle Window. NOTE:- In this Function we have defined the no of loops required for drawing curves with value of 'a/b' as fractional only upto the ratio '1/10'(i.e 1/2, 1/3,1/4 and so on upto 1/10).Hence if we provide different radii resulting in ratios that were not defined in this function, then the no of loops is set to a default value of '100'.Hence we can adjust the no of loops accordingly to complete any curve..

--LEMINISCATE

We can draw 2 types of leminiscate:- - Along X axis(Horizontally) - Along Y axis(Vertically)

def leminiscate(a, orientation, angle=None, angle_unit=None, h=None, k=None)

• a:-It defines the size of the leminiscate.
• orientation:-Takes argument as 'x' or 'y' for drawing leminiscate along X axis or Y axis.
• angle(Optional) By providing the angle we can draw arcs of leminiscate of that specific angle. By default angle is set to 360 degrees.
• angle_unit(Optional) The argument for angle can be in degrees or radians. By default it is set to 'd'.
• h,k:-(Optional) For drawing leminiscate with starting point at (h.k).By default both are zero. NOTE:- For angle_units specify argument as 'd' or 'r'.

--THE BUTTERFLY CURVE

def butterfly(a, b, n=None,h= None, k= None)

• a:-It defines the Horizontal size of the butterfly.
• b:-It defines the Vertical size of the butterfly.
• n:-(Optional) It is the Number of Turns to draw a Butterfly. By Default it is set to 602 turns.
• h,k:-(Optional) For drawing a butterfly whose starting point is (h,k). By default both are zero. NOTE:- To make a Perfect Butterfly you can set the values of 'a' and 'b' as equal.

--HEART CURVE

We can draw 4 types of hearts:- -Axis along X-axis #Heart along +ve X axis #Heart along -ve X axis

-Axis along Y-axis #Heart along +ve Y axis #Heart along -ve Y axis

def heart(a, b, orientation, h=None, k=None, angle=None, angle_unit=None)

• a:-It defines the Horizontal size of the heart.
• b:-It defines the Vertical size of the heart.
• orientation:-Takes argument as 'x' or 'y' for drawing heart along X axis or Y axis.
• h,k:-(Optional) For drawing heart whose starting point is (h,k). By default both are zero.
• angle(Optional) By providing the angle we can draw arcs of the heart upto that specific angle. By default angle is set to 360 degrees.
• angle_unit(Optional) The argument for angle can be in degrees or radians. By default it is set to 'd'. NOTE:- For angle_units specify argument as 'd' or 'r'. For drawing Heart along Negative Axes pass Negative value for 'b'.

--CARDIOID

We can draw 4 types of cardioid:- -Axis along X-axis #Cardioid along +ve X axis #Cardioid along -ve X axis

-Axis along Y-axis #Cardioid along +ve Y axis #Cardioid along -ve Y axis

def cardioid(a, orientation, h=None, k=None, angle=None, angle_unit=None)

• a:-It defines the size of the cardioid.
• orientation:-Takes argument as 'x' or 'y' for drawing cardioid along X axis or Y axis.
• h,k:-(Optional) For drawing cardioid whose starting point is (h,k). By default both are zero.
• angle(Optional) By providing the angle we can draw arcs of the cardioid upto that specific angle. By default angle is set to 360 degrees.
• angle_unit(Optional) The argument for angle can be in degrees or radians. By default it is set to 'd'. NOTE:- For angle_units specify argument as 'd' or 'r'. For drawing Cardioid along Negative Axes pass Negative value for 'a'.

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--ELLIPSE

We can draw 2 types of ellipse:- - Major axis along X axis (a>b) - Major axis along Y axis (b>a)

def ellipse(a, b, h= None, k= None, angle= None, angle_unit= None)

• a:-It is the half-length of major axis of ellipse if (a>b) else half-length of minor axis when(b>a).
• b:-It is the half-length of major axis of ellipse if (b>a) else half-length of minor axis when (a>b).
• h,k:-(Optional) For drawing ellipses with center (h,k).By default both are zero.
• angle(Optional) By providing the angle we can draw elliptical arcs upto that specific angle. By default angle is set to 360 degrees.
• angle_unit(Optional) The argument for angle can be in degrees or radians. By default it is set to 'd'. NOTE:- For angle_units specify argument as 'd' or 'r'.

--Parabola

We can draw 4 types of parabola:- -Parabola along +ve X axis -Parabola along -ve X axis -Parabola along +ve Y axis -Parabola along -ve Y axis

def parabola(a, t, orientation, h=None, k=None)

• a:- It is the distance from the origin to the focus of parabola.
• t:- It is a parameter of a parabola.Used to define the curvature of parabola.Value of t should be greater than zero.
• orientation:-Takes argument as 'x' or 'y' for drawing parabola along X axis or Y axis.
• h,k:-(Optional) For drawing parabola with vertex at (h,k).By default both are zero.
• NOTE:- For drawing Parabola along Negative Axes pass Negative value for 'a'.

--Hyperbola

We can draw 2 types of Hyperbola:- -Transverse axis ie hyperbola along X axis(a>b) -Transverse axis ie hyperbola along Y axis(b>a)

def hyperbola(a, b, h=None, k=None)

• a :-It represents the distance from the vertex to the center of hyperbola when (a>b) else it represents the distance perpendicular to the transverse axis from the vertex to the asymptote line when (b>a).
• b:-It represents the distance from the vertex to the center of hyperbola when (b>a) else it represents the distance perpendicular to the transverse axis from the vertex to the asymptote line when (a>b).
• h,k:-(Optional) For drawing hyperbola with center (h,k).By default both are zero.
• We can also make a Rectangular Hyperbola by giving equal values to 'a' and 'b'.
• NOTE:-For drawing Hyperbola along X axis enter values for 'a' and 'b' such that (a>b) else for drawing hyperbola along Y axis put (b>a) .