Passing formulas to OpenSCAD modules/functions

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This page is mainly for reference. Most users will want this simpler solution which parses strings containing OpenSCAD formulas: http://www.thingiverse.com/thing:2295309 One of the features that OpenSCAD is lacking is the ability to pass functions to modules or to functions. This is a quick-and-dirty proof-of-concept solution to the not uncommon problem of wanting to pass a mathematical formula to a module or function: an eval() function that evaluates expressions in a simple LISP-inspired language that supports all of the OpenSCAD mathematical operators. The evaluation is moderately fast: about 10,000 evaluations of the sample formula below per second on my laptop. The downside is that it's pretty inconvenient to write expressions in this language. Call the function with: eval(expression, variables). Here, variables is a table of variable values, where each line of the table has the name of the variable followed by its value, e.g., [["x", 12.3], ["y", 7]]. An expression is one the following: 1. a string naming a variable and expressing the value of that variable 2. a vector of the form ["'", value] expressing the given literal value (e.g., ["'", [12,3]] expresses the vector [12,3]) 3. for convenience, a number expressing itself (e.g., 12.3) 4. a vector of the form [operator argument1 argument2 ...] For instance, the OpenSCAD formula 3*(x*pow(y,3)-pow(x,3)*y) is expressed with ["*", 3, [ "-", ["*", "x", ["^", "y", 3]], ["*", ["^", "x", 3], "y"] ]]. The operators supported…