Essays/Clockwise Angles
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Angle B is clockwise to angle A (A cw B) if the counter-clockwise arc which spans from A to B is reflex (greater than 180 degrees).
Clockwise relation is independent of angle representation and invariant to shift of angles around the circle.
Rows have the same angle A and spanning angle B across columns. The uncolored angle in each graphic position quantifies the clockwise angle.
Blue is 1 = A cw B
Red is _1 = A cw B
Gray is 0 = A cw B
Note: the diagonals parallel to main (i-j = const) represent arcs of the same size.
The following script generates the illustration above. [{{#file: ""}} Download script: ]
require 'gl2 trig ~system/examples/phrases/phrc7.ijs' coinsert 'jgl2' vec2=: +.@r. cw=: *@cross1&vec2"0 F=: 0 : 0 pc f;pn "Clockwise Angles"; xywh 6 6 200 200;cc g isigraph rightmove bottommove; pas 6 6;pcenter; rem form end; ) f_run=: 3 : 0 wd F wd 'pshow;' ) f_close=: 3 : 0 wd'pclose' ) arc=: 4 : 0 'X Y R'=. x 'A Z'=. y x0=. X-R [ y0=. Y-R xa=. X+R*cos A [ ya=.Y-R*sin A [ xz=.X+R*cos Z [ yz=.Y-R*sin Z glpie x0,y0,(2*R),(2*R),xa,ya,xz,yz gllines xa,ya,X,Y,xz,yz ) f_g_paint=: 3 : 0 glclear'' for_i. i.20 do. for_j. i.20 do. select. cw/ az=. 1r4p1*i,j case. 1 do. glpen 1 0 [ glrgb 180 90 90 glbrush [ glrgb 255 160 160 case. _1 do. glpen 1 0 [ glrgb 100 100 160 glbrush [ glrgb 160 160 255 case. do. glpen 1 0 [ glrgb 120 120 120 glbrush [ glrgb 200 200 200 end. ((10+20*j,i),9) arc az end. end. glpaint'' ) f_run''
Contributed by Oleg Kobchenko