**HyperFun: Operators and Expressions**

There are two types of expressions permissible in the language: 'functional' expression and 'logical' expression.

**Functional expression**- numerical constants,
- external numerical parameters 'a[i]',
- coordinate variables 'x[i]',
- local variables (including elements of arrays),
- arithmetic operators,
- special geometric operators,
- standard mathematical functions,
- F-rep library functions,
- geometric objects defined before.
**Arithmetic operators****Special geometric operators**- Set-theoretic union '|' used in infix form as binary operator,

e.g.,`sphere1 | sphere2`; - Set-theoretic intersection '&'used in infix form as binary operator,

e.g.,`sphere1 & sphere2`; - Set-theoretic subtraction (difference) '\'used in infix form as binary
operator,

e.g.,`sphere1 \ sphere2`; - Set-theoretic negation '~' used in prefix form as unary operator,

e.g.,`~sphere`; - Set-theoretic Cartesian product '@' used in infix form as binary operator,

e.g.,`disk @ segment`. **Standard mathematical functions**-
**F-rep library****functions** - Sphere:
`hfSphere`; - Ellipsoid:
`hfEllipsoid`; - Torus with x, y, z axes:
`hfTorusX`,`hfTorusY`,`hfTorusZ`; - Cylinder with x, y, z axes:
`hfCylX`,`hfCylY`,`hfCylZ`; - Block:
`hfBlock`; - Blobby object:
`hfBlobby`; - Metaball object:
`hfMetaball`; - Soft object:
`hfSoft`; - Scaling tranformation:
`hfScale3D`; - Shift (translation):
`hfShift3D`; - Rotation around x, y, z axes:
`hfRotate3DX`,`hfRotate3DY`,`hfRotate3DZ`; - Blending union:
`hfBlendUni`; - Blending intersection:
`hfBlendInt`; - Twisting around x, y, z axes:
`hfTwistX`,`hfTwistY`,`hfTwistZ`; - Stretch:
`hfStretch3D`; - Tapering along x, y, z axes:
`hfTaperX`,`hfTaperY`,`hfTaperZ`.

The functional expression is a conventional numerical expression built with using:

There are usual arithmetic operators, all of them always result in a floating point (double) number:

An extendible F-rep library contains functions representing geometric
primitives and transformations. Each function has its own set of arguments,
all of which are functional expressions. The result is a real number.

Examples of library functions:

There can be references in the functional expression to
geometric objects
defined in the same program or saved in the special library.
The form of a corresponding call stems from a syntax of object's head.

Example:

`
Sphere(xx,aa)
`

**Logical expression**

The logical expression is built of functional expressions as its arguments, with using relational and boolean operators. The functional expression value '0' is treated as boolean 'false'; other values are treated as 'true' in the logical expressions.

There are the following relational operators:

'<', '>', '<=', '>=', '=', '/='.

There are two infix boolean operators ('and', 'or') and one being used in prefix form ('not').

Examples:

i < 4;

(x[1] = a[1] and (2 <= xx[3] < 5.5))

In both kinds of expressions, parentheses can be used by a traditional manner and are recommended for usage to make expressions structure more clear. The rules of precedence in the expressions are also traditional. Note only that the special geometric operators have lower precedence (and accordingly are executed later) than the arithmetic operators.