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CJ Quines edited this page Feb 25, 2021 · 3 revisions

Structure

There are three kinds of TSQX commands:

  • Special commands
  • Point declarations
  • Drawing commands

End-of-line comments begin with #.

Pairs and paths

A pair is a sequence of two real numbers, representing a point, written in the code as (x, y), where x and y are the x- and y-coordinates of the point respectively. Pairwise operations can be done on pairs, so the midpoint of segment AB would be (A+B)/2 and we can double the coordinates of P by writing 2*P.

A path is any sequence of lines or curves. The segment joining two points A and B is written as A--B. Segments can be chained, as in A--B--C, which contains segments AB and BC, or A--B--C--cycle which contains segments AB, BC, CA.

Point declaration

name [direction] [:|.|;|d?l?]= expression

Declares the point with the label name as the pair expression.

  • name. Point name.
  • direction. Optional string for label direction, e.g. NE for north-east of the point, 150 for dir(150), or 2S3E for 2*S + 3*E.
  • [:|.|;|d?l?]=. Controls whether the point is dotted or labeled. d makes the point dotted and l makes it labeled. The other symbols are aliases; the default ones are
No dot Has dot
No label := .= or d=
Has label ;= or l= = or ld=
  • expression. An expression that returns a point.

Drawing commands

expression [/ [fillpens /] outlinepens]

Draws the expression expression.

  • expression. An expression that returns a point.
  • fillpens. Pens that determine the fill, e.g. 0.2 lightblue becomes opacity(0.2)+lightblue.
  • outlinepens. Pens that determine the opacity, e.g. dotted black becomes dotted+black.

Expressions

Expressions in TSQX are written as in a Lisp. So for example, circumcircle A (foot B C D) E produces circumcircle(A, foot(B, C, D), E). It's also possible to use comma-separated syntax, and to use space-separated syntax within it, e.g. circumcircle(A, (foot B C D), E) also works.

For convenience, although TSQX supports all Asymptote functions, here are the functions you're likely to use most often.

Functions that return pairs:

  • dir A returns the point on the unit circle A degrees from 0.
  • midpoint P returns the midpoint of path P.
  • intersect P Q returns the intersection of paths P and Q, if it exists.
  • IP P Q returns the first intersection of paths P and Q using cse5. With three arguments, IP P Q R returns the Rth intersection of paths P and Q.
  • OP P Q returns the second intersection of paths P and Q using cse5.
  • extension A B C D returns the intersection of the lines AB and CD.
  • `foot A B C`` returns the foot of the perpendicular from A to line BC.
  • circumcenter A B C returns the circumcenter of triangle ABC.
  • orthocenter A B C returns the orthocenter of triangle ABC.
  • incenter A B C returns the incenter of triangle ABC.
  • centroid A B C returns the centroid of triangle ABC.
  • bisectorpoint A B returns a point on the perpendicular bisector of segment AB a unit distance from AB. With three arguments, bisectorpoint A B C returns a point on the angle bisector of angle ABC a unit distance from B.
  • tangent A B C returns the Cth tangent from A to circle B.

Functions that return paths:

  • incircle A B C returns the incircle of triangle ABC.
  • circumcircle A B C returns the circumcircle of triangle ABC.
  • CP A B returns the circle with center A passing through B.
  • CR A B returns the circle with center A and radius B.
  • Line A B returns the line joining A and B.
  • arc A B C D returns the arc, centered at A through B, from C degrees to D degrees.

Functions for drawing:

  • anglemark A B C draws an angle mark at angle ABC. With four arguments, anglemark A B C D draws an angle mark of size D at angle ABC.
  • rightanglemark A B C draws a right angle mark at angle ABC. With four arguments, rightanglemark A B C D draws a right angle mark of size D at angle ABC.
  • pathticks A B draws B tick marks on path A.

Special commands

For now the only special commands are:

  • ~triangle A B C. Assign to ABC points of an acute triangle, A = dir 110, B = dir 210, C = dir 330.
  • ~regular A B C .... Assigns to ABC... points of a regular polygon.

Arguments

Command line arguments:

  • --pre, -p adds an Asymptote preamble. The preamble includes importing olympiad and cse5, both of which are important for lots of TSQX functions.
  • --size, -s if provided, sets the image size in the preamble. Default size is 8cm.
  • --soft-label, -sl regular = does not dot points, only labels them.
  • fname if provided, reads from the designated file rather than stdin.
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