Language Reference

Complete listing of valid Tilde syntax. Entries marked (not yet implemented) parse without error but have no effect.

General

• let is optional before any declaration — let segment ab and segment ab are identical
• Statements are separated by newlines or semicolons (;)
• # starts a line comment

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Settings

Must appear before any geometry declarations.

set unit cm           # cm | mm | m | in | inches | unit
set unit degrees      # degrees | radians
set grid on           # on | off
set winding clockwise # clockwise | counterclockwise

If set unit is omitted, the active unit is inferred from the first length that carries a unit suffix. If no suffixed length exists, lengths are abstract numbers.

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Declarations

Point

point a               # free vertex — solver places it
point a = (1, 2)      # fixed at (1, 2)

Line

line l                # defaults to y = x
line l = (m, k)       # y = mx + k
line l = (a, b, c)    # ax + by + c = 0

Segment

A segment name is either a 2-character all-distinct lowercase name (decompose mode) or any other name (subscript mode).

segment ab            # decompose: vertices a and b
segment ab = 5        # decompose: vertices a and b, length 5
segment ab with <constraints>

segment s             # subscript: vertices s_1 and s_2
segment hello         # subscript: vertices hello_1 and hello_2

Triangle

A triangle name is either a 3-character all-distinct lowercase name (decompose mode) or any other name (subscript mode).

triangle abc          # decompose: vertices a, b, c — sides ab, bc, ca
triangle abc with <constraints>

triangle t            # subscript: vertices t_1, t_2, t_3 — sides t_12, t_23, t_31
triangle hey          # subscript: all chars same length but repeated → subscript

Naming modes

Decompose mode — the name is split into individual vertex characters:

• Segment: exactly 2 characters, all lowercase, all distinct
• Triangle: exactly 3 characters, all lowercase, all distinct

Any name that does not meet the criteria for decompose mode uses subscript mode, where the name becomes a label and vertices are name_1, name_2, etc.

Repeated characters (e.g. triangle aba) force subscript mode.

Other shapes (not yet implemented)

square abcd
rectangle abcd
polygon 5 abcde

These parse but register nothing in the solver.

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Constraints

Constraints can appear in two places:

• Standalone — as their own statement
• Inline — after with in a declaration, joined by and

triangle abc with ab = 3 and bc = 4 and ca = 5

Length

ab = 5
ab = 5cm             # with unit suffix
ABC_12 = 5           # subscript segment

Angle

angle abc = 60       # angle at b, measured from a to c
angle abc = 60deg    # with unit suffix
angle ABC_2 = 90     # subscript angle at vertex 2

Position

a = (1, 2)           # place vertex a at (1, 2)

If a is already placed at the same position, this is a no-op. If a is placed at a different position, it throws a constraint error.

On-line

a on l               # vertex a lies on named line l
a on line l          # same, with optional keyword
point a on l         # same, with optional keyword
point a on line l    # same

A vertex may be constrained to multiple lines:

a on l
a on m               # a is placed at the intersection of l and m

On-segment

a on ab              # vertex a lies on segment ab
a on segment ab      # same, with optional keyword
point a on ab        # same
point a on segment ab

Equal lengths (not yet implemented)

ab = cd

Parallel / perpendicular (not yet implemented)

ab parallel cd
ab perpendicular cd

Point coincidence (not yet implemented)

a = b

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Pick

Collapses an ambiguous vertex (two discrete solutions) to a specific one.

pick a 1             # use solution 1
pick a 2             # use solution 2
pick ABC_1 1         # subscript vertex

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Units

Length

Suffix	Meaning
cm	centimetres
mm	millimetres
m	metres
in or inches	inches
unit	abstract unit

Angle

Suffix	Meaning
deg or degrees	degrees
rad or radians	radians

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Subscript references

Shapes in subscript mode expose their components via subscripts.

t_1            # vertex 1 of shape t
t_1_2          # segment between vertices 1 and 2 of shape t
angle t_2      # angle at vertex 2 of shape t

Works for any label, any case:

ABC_1          # vertex 1 of shape ABC
ABC_1_2        # segment between vertices 1 and 2
angle ABC_2    # angle at vertex 2

The double-underscore delimiter (_1_2) is required for segment refs so the parser can distinguish vertex 12 from edge 1→2.

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What is not valid

• set after any geometry declaration
• Redefining a name that is already declared (e.g. two let point a statements)
• A vertex constrained to two parallel lines
• A vertex constrained to three or more lines with no common point