Expressions

Anywhere PiQ asks for a number or a position — a point, a variable, a tool option, a line in the Interactive panel — you can type an expression instead. Points and variables defined by expressions keep them: change a variable or move a point and everything defined from it follows. Names and functions can be typed in any case.

Example drawing

The examples on these pages are worked out in a millimetre drawing with:

Name	Is
`L`, `W`	500 and 300
P0, P1, P2	[0,0], [500,0] and [500,300]: `P1` is `RIGHT(P0,L)`, `P2` is `UP(P1,W)`
P6	[60,80]
`@5`	A line segment from [0,0] to [100,0]
`@6`	A circle round [50,10], radius 20
`@7`	A line segment from [100,0] to P6

Values and names

The values an expression is made of, and the names it refers to.

Expression	What it gives
Numbers	A number: whole, decimal, a fraction, or feet and inches.
Strings	Text in double quotes.
TRUE and FALSE	The two true-or-false values.
Names	A variable, by its name, or a point, by its number.
.NAME	A property of a value by name: an element's point, a fillet's centre …
NAME(…)	A function of your own, defined with FUNCTION, worked out with the arguments given.

Operators

Working with values: arithmetic, comparing, and combining TRUE and FALSE.

Expression	What it gives
( )	Works out what is inside first.
- and !	Minus a number or a position; the opposite of TRUE or FALSE.
+ - * / %	Adding, subtracting, multiplying and dividing numbers and positions; remainders.
< <= > >=	Whether one number is less than, or more than, another.
== != ~=	Whether two values are equal, not equal, or as near as makes no difference.
&& \|\| ^	Combines TRUE and FALSE values.

Choosing

A value chosen by a test.

Expression	What it gives
? :	One value or another, depending on a test.
SWITCH	A value looked up in a dictionary or a list, with one for when it isn't there.
	Lists and dictionaries: several values as one, and one of them by `[index]` or `[key]`.
CONCAT, SUBRANGE, INDEXOF, CONTAINS	Lists (and strings) joined, part of one, where a value is in one, and whether it is.

Numbers

Functions of numbers.

Expression	What it gives
ABS	The size of a number, without its sign.
SIGN	Whether a number is negative, zero or positive.
SQR	A number squared: times itself.
SQRT	The square root of a number.
CBRT	The cube root of a number.
EXP	e (2.71828…) to the power of a number.
LOG	The natural logarithm of a number (to base e).
LOG10	The logarithm of a number to base 10.
TRUNC	A number with its fraction cut off, towards 0.
ROUND	A number rounded to the nearest whole number.
NEARESTFRAC	A number rounded to the nearest fraction of an inch (halves, quarters … to a largest denominator).
FLOOR	The whole number at or below a number.
CEIL	The whole number at or above a number.
DOUBLE	A value as a decimal number.
INT	A number as a whole number.
TOMM	Inches in millimetres.
TOIN	Millimetres in inches.
MIN	The smaller of two numbers.
MAX	The larger of two numbers.
POW	A number raised to a power.

Angles and trigonometry

The trigonometry functions work in radians; POLAR, ROTATE and the tools take degrees. DTOR and RTOD convert.

Expression	What it gives
DTOR	Degrees in radians.
RTOD	Radians in degrees.
SIN	The sine of an angle in radians.
COS	The cosine of an angle in radians.
TAN	The tangent of an angle in radians.
ASIN	The angle (in radians) whose sine is a number.
ACOS	The angle (in radians) whose cosine is a number.
ATAN	The angle (in radians) whose tangent is a number.
SINH	The hyperbolic sine of a number.
COSH	The hyperbolic cosine of a number.
TANH	The hyperbolic tangent of a number.
ASINH	The inverse hyperbolic sine of a number.
ACOSH	The inverse hyperbolic cosine of a number.
ATANH	The inverse hyperbolic tangent of a number.
ATAN2	The angle of a direction, from its Y and X, all the way round.
ANGLE	The angle of a direction (a step such as `P2-P1`).

Points and directions

Positions, and points defined from other points.

Expression	What it gives
[x,y]	A position made from an X and a Y.
.X and .Y	The X or the Y of a position.
NORMALIZE	A direction made 1 long.
DISTANCE	How far apart two positions are.
DOT	The dot product of two directions: how far one goes along the other.
CROSS	The cross product of two directions: which way one turns to the other.
LEFT, RIGHT, UP, DOWN	A point straight across or up or down from another.
POLAR	A point at an angle and distance from another.
POLARDISTANCEX	How far along an angled line from one point you go to be level with another (the same X).
POLARDISTANCEY	How far along an angled line from one point you go to be level with another (the same Y).
ALONG	A point a distance from one position towards another.
ALONGFROMEND	A point a distance from the second position back towards the first.
TRIANGULATE	The point a distance from each of two points.
RAYCROSSING	Where lines at an angle through two points cross.
LINECIRCLE	Where a line through two points crosses a circle.
BENDALLOWANCE	Sheet metal: the length of a bend along its neutral line.
BENDDEDUCTION	Sheet metal: what to take off the outside sizes for a bend.
KFACTOR	Sheet metal: a material's K-factor at a bend's R / T, from its K-factor table.
Sheet fields	What a drawing holds, for a border's title block: HOSTNOTE, DRAWINGTITLE, SHEETNO, SHEETSCALE, TODAY …

Blending and limits

Values between others, and values kept within limits.

Expression	What it gives
LERP	A value part of the way from one to another.
LERPFROMEND	A value part of the way from the second back to the first.
INVERSELERP	How far a value is from one to another, as a part of the way.
REMAP	A value moved from one range to another.
CLAMP	A value kept within limits.
SMOOTHSTEP	A smooth step from 0 to 1 as a number goes from 0 to 1.
SMOOTHERSTEP	An even smoother step from 0 to 1 as a number goes from 0 to 1.

Transformations

Transformations, for moving, turning and scaling positions: a position times a transformation is the position moved.

Expression	What it gives
TRANSLATE	A transformation that moves positions by a step.
ROTATE	A transformation that turns positions about a centre.
SCALE	A transformation that scales positions about a centre.
SKEW	A transformation that slants positions.
MATRIX	A transformation given by its six numbers (nine: a perspective).
IDENTITY	The transformation that changes nothing.
MIRROR	A transformation that mirrors positions across the line through two points.
INVERSE	The transformation that undoes another.
HOMOGRAPHY	The perspective transformation taking four or more positions to as many others.

Points on elements

An element is written by its id, @5, and an expression can work out a position on it, so a point defined this way follows the element when it changes. The Split, Intersect, Fillet and Chamfer tools and the object snaps define their points like this rather than fixing them in space.

Expression	What it gives
@n	An element, by its id.
ONELEMENT	The point a fraction of the way along an element.
ALONGELEMENT	The point a distance along an element.
FROMEND	Measures a position along an element back from its end.
CROSSING	Where two elements cross.
LENGTHOF	How long an element is, along it.
AREAOF	The area a closed element encloses.
PERIMETEROF	The length round a closed element.
CENTEROF	The centre of a circle, arc or ellipse.
QUADRANT	A quadrant point of a circle, arc or ellipse.
FOOT	The foot of a perpendicular from a point to an element.
TANGENT	Where a line from a point touches a circle or arc.
FILLET	The fillet arc that rounds the corner between two elements.
CHAMFERDISTANCES	The chamfer cutting the corner between two elements, a distance back along each.
CHAMFEREQUAL	The chamfer cutting the corner between two elements, the same distance back along both.
CHAMFERDISTANCEANGLE	The chamfer cutting the corner between two elements, a distance back along the first and leaving it at an angle.

Laying out work on elements

The vinyl-cutting and flooring tools lay their work out on the elements of a design or a room with these, in points and blocks, so it follows the elements when they change. Elements are given by id (@5) or in lists ({@5,@6}).

Expression	What it gives
EXTENTMIN	The lower left corner of the box round elements.
EXTENTMAX	The upper right corner of the box round elements.
WEEDLINES	Weed lines across a box, stopping at a design.
CONTOUR	The outline round elements' shapes, a distance out.
CLIPTO	The parts of elements inside a box, moved.
ROLLDROPS	A roll's drops across a floor.
ROLLSEAMS	The seams between them.
ROLLPLAN	The drops as cut from the roll, with their trims.
ROLLLENGTH	The length of roll the drops need.
FLOORAREA	The area of a floor's outlines joined.

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