EquationParser

Type an equation. See a 3D shape.

EquationParser takes a math string like ((x^2+y^2)^0.5 - 15)^2 + z^2 < 15 and renders the implicit 3D surface it describes — no mesh, no model, just an inequality over x, y, z evaluated at every point in space.

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What it does

You write an equation as a C string. The parser evaluates it at every point on a 3D grid. Wherever the condition holds, that point is part of the surface. The result gets rendered as a 3D shape.

char *str = "((x^2+y^2)^0.5 - 15)^2 + z^2 < 15";  // donut

char *str = "x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 11.8 < 0";  // tanglecube

char *str = "min(min(x^2+y^2, y^2+z^2), x^2+z^2) < 1";  // three intersecting cylinders

Any implicit surface you can express as an inequality over x, y, z — just type it.

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Equation syntax

Category	What to write
Variables	x y z
Arithmetic	+ - * / ^
Grouping	( )
Comparison	< > = <= >=
Logic	& |
Functions	abs(v) min(a, b) max(a, b)
Numbers	3 1.5 0.75 etc.

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How it works

1. Tokenizer — scans the string character by character into typed tokens: numbers, variables, operators, functions.

2. Shunting-yard — reorders tokens into Reverse Polish Notation, respecting operator precedence, parentheses, and unary operators.

3. RPN evaluator — walks the token queue, substitutes x/y/z from the current point, and applies operators via a number stack. Returns a single value.

4. Visualization — iterates over a 3D voxel grid, calls the evaluator at each point, and renders wherever the inequality holds.

Parse once, evaluate millions of points.

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API

// Parse a string into a reusable RPN queue
tokenQueue q = init("(x^2 + y^2 + z^2)^0.5 < 1");

// Evaluate at any (x, y, z) point — non-destructive, call repeatedly
point p = {0.5, 0.5, 0.0};
double result = evalPolish(&q, p);

free_queue(&q);

Functions

Function	Description
tokenQueue init(char* str)	Parse equation string → RPN queue
double evalPolish(tokenQueue* queue, point p)	Evaluate queue at point p
int parseRule(char* rule, token** res)	Tokenize string, return token count
void convertToPolish(...)	Convert token array to RPN

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Project structure

EquationParser/
├── include/        # Headers — parser.h, types, operator table
└── src/            # Sources — parser, stack, queue, operators

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Building

Plain C, no external dependencies:

gcc -o parser src/*.c -Iinclude -lm