# Geometry

Geometry viewer and editor for Android and desktop (macOS, Linux, Windows)

# Tutorial

## Basic syntax

Geometry uses code-like definitions.

Points are represented as complex numbers. The center of screen is 0 and short side is 200, so the same code would look the same on all devices.

Lets draw triangle:

A = 20+60i
B = 60-40i
C = -60-40i
t = triangle(A, B, C)

## Styles

Lets make our triangle orange, fill it, and make border dashed

A = 20+60i
B = 60-40i
C = -60-40i
[orange] [fill] [dash] t = triangle(A, B, C)

## Constructors

In the reality, function triangle expects triangle (and returns it), not three points.

But the following rules work:

• when function expects triangle you can put three points to it
• when function expects segment you can put two point to it
• when function expects line you can put segment or two points to it
• when function expects circle you can put two points (center and some point on circle) to it
• when function expects polygon you can put arbitrary many points to it
• Complex and Point in functions signatures are synonyms

## Movable points

Lets allow moving of our points in the view mode:

A = #(20+60i)
B = #(60-40i)
C = #(-60-40i)
[orange] [fill] t = triangle(A, B, C)

## Moving by traectory

Lets choose arbitrary point on BC and try to move it:

A = #(20+60i)
B = #(60-40i)
C = #(-60-40i)
[orange] [fill] t = triangle(A, B, C)

D = project(#(-40i), B, C)

## Technical details of points moving

When you define X = ... #(...) ... X will be evaluated as if there is no # and the anchor for # will be created where X is. You will be able to move this anchor and expression in parens will be replaced by position of anchor.

So, the code like X = #(0) + 50 will work contrintuitive.

## Animation (dynamic objects)

Your code can use time to animate the drawing. Lets, for example, animate point D from moving by traectory chapter:

A = #(20+60i)
B = #(60-40i)
C = #(-60-40i)
[orange] [fill] t = triangle(A, B, C)

D = choose(segment(B, C), time()/500)

The choose function chooses a point on given object (segment or circle): it smoothly moves with second parameter increasing and reaches initial value when second parameter reaches integer

## Ambiguity

Some geometric constructions is ambiguous: they have many results. For example, line and circle intersects in two points.

Such functions have 3 variations:

• returning first (in some not obvious sense) result
• returning second result
• returning other result

To use last way, you must provide one of results. For example, lets intersect line with circle:

O = 0
c = circle(O, 60)
A = cproject(#(45+40i), c)
l = line(A, O)

B = cintersect(A, l, c)

# Installing

Currently, only Windows and Android versions are builded. You can download it here:

For Linux and macOS you can build app from source

View Github