Sage-Code Laboratory
index<--

Bee Graphic

Most languages have graphic system implemented by using functions. Wehat if we define new data types and keywords to make dynamic 2D technical drawings. This could be more expressive and have a maintenable aspect as code.

Degree

Bee support radians using (π) prefix. Instead of (2 · π) you can write ( 2π )

With Comb Dot: ° 30°_30′_30″

symbol same value in degree
0 0°0′0″
π/4 45°
π/2 90°
π 180°
360°

Minutes and Seconds:

Bee is using Unicode symbols prime (′) for minutes and (″) for seconds of arc:

make α:= 180°   ∈ ∠;
make β:= 0°0′0″ ∈ ∠;
pass if α ≈ π;  //α ≠ π

Notes:

Graphic types

Type Name Signature Description
V Canvas {o ∈ ⊡, w,h ∈ Z, m ∈ [Y]} Canvas (with points and shapes)
Y Layer {c ∈ B, v ∈ L, m ∈ [H]} Layer with c = color, m = set of shapes
H Shape {o ∈ ⊡, s ∈ ⌂, α ∈ ∠ } Shape, with origin and rotation
G Tag {o ∈ ⊡, t ∈ S, α, β ∈ ∠} Graphic label with rotation

legend

w = width
h = height
s = shape
m = members
d = distance
v = visible 

Drawing Elements

Each graphic element is a composite data type.

Type Name Description
Angle (0 .. 2π) or (0°..360°)
Cartesian {x, y ∈ Q}
Polar {r ∈ P, α ∈ ∠ }
Vector {o, p ∈ ⊡}
Relative {o ∈ ⊡, r ∈ P, α ∈ ∠ }
Circle {o ∈ ⊡, r ∈ P}
Arc {o ∈ ⊡, r ∈ P, α,β ∈ ∠ }
Square {o ∈ ⊡, b ∈ P}
Triangle {o ∈ ⊡, b ∈ P, α,β,ɣ ∈ ∠}
Diamond {o ∈ ⊡, α,β ∈ ∠}
Regular {o ∈ ⊡, r, n ∈ P}
Polygon {o ∈ ⊡, c ∈ [⊡]}
Fill { ▤, ▥, ▦, ▧, ▨, ▩ }

Note:

Drawing keywords

Keyword Description
draw put shape on layer
wipe remove drown shapes
show show canvas
hide hide canvas

Latitude Longitude

Any location on Earth is described by two numbers: its latitude and its longitude. If a pilot or a ship captain wants to specify position on a map, these are the "coordinates" they would use.

Latitude and longitude are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols ( "°", "′", "″" ) For example: 35° 43′ 9″ means an angle of 35 degrees, 43 minutes and 9 seconds. A degree contains 60 minutes of arc and a minute contains 60 seconds of arc and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

Bee language has limited support for measurement units. Calculations often represent angles by small letters of the Greek alphabet, and that way latitude will be represented by λ (lambda, Greek L), and longitude by φ (phi, Greek F). Here is how they are defined.

Precision

Earth coordinates can be represented using default Q numbers on 32 bit.

.digits angle (g°)equivalent
2 0.01° 1.1132 km
3 0.001° 111.32 m
4 0.0001° 11.132 m
5 0.00001° 1.1132 m (default precision)

Data Types

type Δ: (0..+100000000) <: Q; //twice equatorial
type Λ: (-180°..+180° ) <: Q; //longitude angle (degree)
type Φ: (-90°..+90°   ) <: Q; //latitude angle (degree)

Map data types are represented by Unicode symbols:

** map simple point: λ = Latitude, φ = Longitude, i = index
  type • : {i ∈ N, λ ∈ Λ, φ ∈ Φ} <: Object;
  
** network node:  λ = Latitude, φ = Longitude, ε = Elevation
  type ◉ : {id ∈ N, λ ∈ Λ, φ ∈ Φ, ε ∈ P} <: Object;             
 
** network link
  type ↯ : {id ∈ N, start_node ∈ ◉, end_node ∈ ◉, shape ∈ [•]} <: Object;
  
** place of interest
  type ◈ : {id ∈ N, point ∈ •, label ∈ S} <: Object;
** map area 
  type ■ : {id ∈ N, origin ∈ •, shape ∈ [•], category ∈ S} <: Object;
** area of interest
  type ▣ : {id ∈ N, point ∈ •, shape ∈ [•], label ∈ S} <: Object;
  
** map data model
  type ♁ : {origin ∈ •, extent ∈ •, scale ∈ Q 
             nodes ∈ [◉], links ∈ [↯], 
             area ∈ [■], pint ∈ [◈], aint ∈  [▣] } <: Object;

legend

Space objects

Type Description
Galactic Galactic space
Solar Solar space
Star A celestial body similar to the Sun with position relative to our Sun
Planet Planed similar to Earth with: mass, radius, year duration, day duration
Moon Natural celestial body bound to a planet by gravity
Satellite Artificial celestial body bound to a planet or moon by gravity
Craft Space-craft capable to travel in space, not bounded to a planet

Planets

Type Name
Sun
Mercury
Venus
Earth
Marth
Jupiter
Saturn
Uraus
Neptun
Pluto

Read next: System Library