Learning to draw a circle

Question

Im trying practice deep learning while drawing a circle by using neural network techniques (neuralnet package in R), My inputs are vectors (x,y,r) where x,y = coordinates in a 2d plane, and r = radius.

My equation for the model looks like this, Im using one hidden node:

circle_model <- neuralnet(formula = radius ~ x + y, data = circle_train)

for predicting the values I am using predicted_radius <- model_results$net.result

The problem is that this model only predicts the radius (one variable output) of a given point and what I want is two varaible output from model with any given center point and radius.

Thanks

Answer 1

Neural networks are used to learn and approximate mathematical functions. If we consider the standard equation of a circle,

x^2 + y^2 = a^2 # a is the radius

You can't represent this equation as a function. You may refer to the mathematical definition of a function. Yes, you can train a model which learns several images of circles and then generates an image of a circle.