[Feature]: Add support for plotting inequalities in parametric and implicit relations

[atulya-srivastava]

So, what is it about?

Issue Description

The codebase's current implementation does not support plotting inequalities. Inputting an inequality into the input field produces an incorrect result or fails to plot, which must be corrected

• Should support parametric and implicit relations.

Proposed Solution

• To plot the inequalities correctly by -- covering and showing the area that the inequality covers.

Code of Conduct

• I agree to follow this project's Code of Conduct

[atulya-srivastava]

@nsh07, Please assign this issue to me.

[nsh07]

How are you going to implement this?

[atulya-srivastava]

Approach:
I will first create a function that will look for strings of inequalities (<,>=..), which if found will return its position along with the identification of the operator
then I will split the string into LHS and RHS and create an LHS - RHS expression with the exprtk setup
Then according to type of the operator parsed I will scan the grid at each point, checking if (expression.value < or > or <= or >= 0) , then I will plot the result in semi transparent color using draw_list->AddRectFilled() to cover the area.
If i encounter >= or <= then I will run the previous implicit and parametric logic to plot the boundaries as well

[ArashPartow]

I will first create a function that will look for strings of inequalities (<,>=..), which if found will return its position along with the identification of the operator
then I will split the string into LHS and RHS and create an LHS - RHS expression with the exprtk setup

That all seems needlessly over complicated.

Assume the following expression: "x^2 + y^2 < 3". A point should only be drawn/plotted IFF the result of that expression is true for some pair of x and y values. otherwise no point should be drawn.

Rough sketch of solution:

using T               = double; // long double/float/mpfr etc...
using symbol_table_t  = exprtk::symbol_table<T>
using expression_t    = exprtk::expression<T>
using parser_t        = exprtk::parser<T>

const std::string function = "x^2 + y^2 < 3";

T x;
T y;

symbol_table_t symbol_table;
symbol_table.add_variable("x",x);
symbol_table.add_variable("y",y);
symbol_table.add_constants();

expression_t expression;
expression.register_symbol_table(symbol_table);

parser_t parser;

if (!parser.compile(function,expression))
{
   // log error etc.
   return ...
}

for (x = view_min_x; x <= view_max_x; x += scaled_x_increment)
{
    for (y = view_min_y; y <= view_max_y; y += scaled_y_increment)
    {
       if (expression.value() == T(1))
       {
          plot_point(x,y);
       }
    }
}

For:

1. x^2 + y^2 < 3 you should get a filled circle
2. x^2 + y^2 == 3 you should get an outline of a circle
3. x^2 + y^2 > 3 you should get an empty circle with the outter area all filled in, aka opposite of [1]
4. (x-3)^2 + y^2 < 3 you should get a filled circle shifted to the right by 3 units

Examples:

1. Filled Circle
2. Unfilled Circle
3. Circle Contour

---

Why does this work? Expressions in equality or inequality form result in a boolean value as their return value.

[nsh07]

Wow! I really didn't expect @ArashPartow himself to show up on this repo. Thank you so much for making ExprTk! And thanks for the feedback as well.

If you don't mind answering, how'd you find this repo? I'm genuinely curious 😅

[ArashPartow]

If you don't mind answering, how'd you find this repo?

@nsh07 IFTTT does the trick.