<content> Plot function </content>

b49a9302-14af-4017-a65d-0142640dbd8c 366 4 5 false false false 0 0 decimal

Bresenham Algorithm

q# t# f# If q# t# f# if 11 line :

x IsArray x rows 0 ≥ 0 try 11 line :

X# Y# Π K pBres x1 x2 px ox tx ax y1 y2 py oy ty ay 26 mat Π eval : x Tx px ox - x2 x1 - / x x1 - (* T# : y Ty py oy - y2 y1 - / y y1 - (* T# : 12 mat u T# u trunc vectorize eval 11 line : co 0 Tx : ro 0 Ty : 13 mat M 0 : k K 4 K length range el K 3 el - eval : 12 mat 0 ax < M ro co px ax * - ox 113 mat max co px ax * + abs px ox - 12 mat min range T# el K 1 el : if 0 ay < M ro py ay * - oy 113 mat max ro py ay * + abs py oy - 12 mat min range T# co el K 2 el : if X Y 12 mat X# 1 el IsArray X# X# 11 mat If Y# 1 el IsArray Y# Y# 11 mat If 12 mat eval : k length Y length < k k 0.75 k * T# stack eval : while m 1 Y length range x X m X length 12 mat min el Tx : y Y m el Ty : 12 mat n 1 y length 1 - (range dx dy 12 mat x n 1 + el x n el - abs y n 1 + el y n el - abs 12 mat eval : ε 0.5 dx dy > dx dy - If * eval : x n el x n 1 + el ≠ (y n el y n 1 + el ≠ (| y n el oy py oy - ty - ltlt (x n el ox px ox - tx - ltlt (& M y n el y n el ty + 1 - (range x n el x n el tx + 1 - (range el k m el : if ε dx - > x n el x n el x n el x n 1 + el < 11 - If + eval : ε ε dy - : 12 mat ε dy < y n el y n el y n el y n 1 + el < 11 - If + eval : ε ε dx + : 12 mat if 21 line while 31 line for 21 line for M M px py * el 0 : reverse K 3 el + eval : A M 256 / T# : 12 mat A 256 / T# A 256 mod vectorize M 256 mod vectorize 13 mat 111 line :

Can introduce some colorize function:

x y m n k Π pBres k m el :

C a rgb A C 3 el C 2 el C 1 el 255 a * 14 mat : k Clear 12 mat d 0255 A k el trunc 12 mat min 12 mat max 162 k 1 - (*^* k 14 sum : d 232^2 d * 232^1 - ≥ (* - eval 31 line :

r g b a rgb r g b 13 mat a rgb 11 line :

C rgb C 0 rgb 11 line :

X Y Π pBres X Y Π 12812812813 mat 12812812813 mat 25525525513 mat 012825513 mat 255128013 mat 025512813 mat 25512825513 mat 12825525513 mat 25525512813 mat 00013 mat 101 mat rgb vectorize pBres 11 line :

x-axis color
y-axis color
background color

trace colors

Default Foreground,
Background and axis colors

<content> Examples </content>

Define the plot range, the size of the plot window and the offstet in pixeles, the
thikness of the plot trace and the percent for axes:

Box 2 - 52006130 % * 3 - 610012115 % * 26 mat :

x.min x.max px ox tx ax y.min y.max py oy ty ay 26 mat Box :

N 100 :

Functions to plot:

X x.min x.max x.min x.max x.min - N 1 - / + range :

Y X 5 X * cos * vectorize X 2^2 - vectorize X X - 41 mat :

img X Y Box pBres : IMG image:{img} 00 0.01 py * 0.01 px * 41 mat black dot 151 mat 11 mat : 21 line

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 img IMG 1 1 mat

Parametric equations

B 3.5 - 3.5 3002130 % * 3 - 32002160 % * 26 mat :

N 200 :

T 02 π * (2 π * N 1 - / range :

X 3 T cos * vectorize 0.5 T * 3 T * cos * vectorize 2 T sin * vectorize 31 mat :

Y 2 T sin * vectorize 0.5 T * 3 T * sin * vectorize 2.5 4 T * sin * vectorize 31 mat :

img X Y B pBres : IMG image:{img} 00 0.01 B 23 el * 0.01 B 13 el * 41 mat gray lines 151 mat 11 mat : 21 line

IMG 1 1 mat

Array of plots

m 2 : n 3 : 21 mat

B 2 - 10400010 % * 2 - 6200010 % * 26 mat :

N 100 :

T 02 π * (2 π * N 1 - / range :

r c f 1.4 c 5 + (T * sin * vectorize 4 c 1 - (* + 1.8 r T * sin * vectorize 4 r 1 - (* + 12 mat :

X 0 : Y 0 : 21 mat

r 1 m range c 1 n range X r m c 1 - (* + el Y r m c 1 - (* + el 12 mat r c f eval : for for

img X Y B pBres : IMG image:{img} 00 0.01 B 23 el * 0.01 B 13 el * 41 mat gray lines 151 mat 11 mat : 21 line

IMG 1 1 mat

Polygons

X 26246216 mat 121114 mat 7997715 mat 13 mat :

B 1 - 1020004100 % * 1 - 2010002100 % * 26 mat :

Y 141421821416 mat 661614 mat 6611615 mat 13 mat :

img X Y B pBres : IMG image:{img} 001241 mat transparent 151 mat 11 mat : 21 line

IMG 1 1 mat

Alvaro

4 appVersion 1.73.9126.0