Interactive Math Functions

Simon was reading about math functions on Wikipedia and came up with an idea to create an interactive math functions editor in JavaScript that would visualize (i.e. show the graphs for) all the functions. Simon was especially excited about cosecant, secant and cotangent (csc, sec and cot for short), which were new to him:

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Simon partially programmed the interactive math functions editor, but it remained unfinished:

 

 

 

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Simon’s Codea Tutorials and the Arc-Tangent

A set of awesome Codea tutorials that Simon recorded for those who are just starting to program in Codea. Simon ported examples from Processing (java) into Codea (Lua):

In the second tutorial (in two parts), Simon explains how to write a physics simulation program in Codea using forces like gravity, friction and spring force. Anyone watching will get to use some trigonometry and see what arc-tangent is for! The original code in Java comes from Keith Peters (Processing).

Here are some notes from when Simon was explaining the arc-tangent to me the other day:

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Solar System in Processing Coding Challenge

Simon returned to the Solar System in Processing Coding Challenge by Daniel Shiffman – something he tried before and got stuck. He has now successfully completed both the 2D and the 3D parts:

 

 

 

 

 

Simon’s changes to Daniel Shiffman’s Spherical Geometry Coding Challenge

Simon talks about his changes to Daniel Shiffman’s Spherical Geometry Coding Challenge: He has rewritten the code in an object oriented manner. Later he also turned the sphere into an ellipsoid using three radii.

Object oriented (Simon’s idea):

Adding colour (Daniel’s feature):

Turning the sphere into ellipsoid (Simon’s idea):

Simon would also like to try this with a cylinder:

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Simon wanted to share his code in a readme in GitHub but he didn’t manage to create one within the specific (Sphere Geometry) project. Here is a screenshot of him sharing the code in Slack chat (for Coding Train fans):

Spherical Geometry sharing in Slack 29 Jun 2017

Perlin Noise Combined with Sine Wave Translation into Processing

Simon translated Daniel Shiffman’s Graphing 1D Perlin Noise tutorial into Processing (Java). The project involved combining perlin noise and sine wave:

 

He also attempted to translate Perlin Noise Flow Field into Processing:

 

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Polar to Cartesian converter (Simon’s own code)

Simon built a Polar to Cartesian converter (Simon’s own code). You can enter the radius in pixels and the angle in degrees, click “convert” and you get the coordinates in x and y and a circle appears n that spot.

You are welcome to play with Simon’s converter online in CodePen at: https://codepen.io/simontiger/pen/MmdodP

Simon is also planning to make a similar converter for Spherical to Cartesian (where you would enter radius, latitude and longitude and convert those into x,y,z).

 

 

Here Simon explains the formulas to convert between Polar and Cartesian coordinates:

 

Steering Behaviors: flow field, dot product, scalar projection

Simon’s big project the last couple of days was about making a steering behaviors database, complete with a navigation menu (in Cloud9):

Steering Behaviors Navigation Menu 24 Mei 2017

He managed to finish the first two examples – “Seek and Flee” and “Pursuit and Evasion” – and worked on the Flow Field Following and Path Following.

As recommended by Daniel Shiffman, Simon largely relied on the paper called Steering Behaviors For Autonomous Characters (written by Craig W. Reynolds from Sony). As Simon told me, he tried to guess the code to make the static drawings in the paper come to life. For instance, for the “Seek and Flee” example, Simon animated this drawing:

Craig W. Reynolds Steering Behaviors Seek and Flee 25 Mei 2017

 

 

 

Simon also made a “Seek” example in the language called Lua (from the Codea app):

 

The second example was about Pursuit and Evasion:

Craig W. Reynolds Steering Behaviors Pursuit and Evasion 25 Mei 2017

 

 

Simon also explained to me how Flow Field Following worked:

 

Another steering behavior he scrutinized was Path Following. For Path Following, he first had to learn what the “dot product” was. In math, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

The way Simon learns is usually by studying (deconstructing) and memorizing the formulas (even if he doesn’t fully understand them in the beginning). After he comes back to the formula later on he seems to have grasped the meaning of it.  I often observe him actually apply different formulas in real life. When it comes to the “dot product”, Simon is in the beginning of the learning curve:

 

 

 

The formula for scalar projection is:

s=|{\mathbf  {a}}|\cos \theta ={\mathbf  {a}}\cdot {\mathbf  {{\hat  b}}},

or the way Simon put it:

 

Pinball Dilemma. Simon’s own code.

Simon heard the word “pinball” and looked it up on Google (never played it himself). He then decided to write a pinball program in Processing (Java), but soon encountered a mathematical dilemma: the flippers at the bottom of the canvas (their role is to protect the ball from falling) didn’t stop rotating the way Simon wanted. This slowly unfolded into a real drama.

Here Simon explains the problem:

As his math tutor came to give Simon his regular math lesson, Simon turned to him for help and they thought to have solved the problem by applying cosine and setting it to 1. But after the teacher left Simon realized that the angular velocity of the flipper was too high for the cosine to reach 1, which would mean the flipper wouldn’t stop. Unless approximate values could be programmed, which Simon said he doubted. Simon was crying hard. We just sat there hugging after we recorded this:

Then Simon tried writing an approximate function.

I’m not sure he will come back to this unfinished project. It is all part of his learning experience and learning to apply math/ physics though.

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Approximate cosine:

Pinball cos solution 22 Mei 2017

Approximate Function and 1D distance function:

Pinball. Approximate Function and 1D distance function 22 Mei 2017