% % Copyright (c) 2011, 2012, Sebastian Schubert % % This Font Software is licensed under the SIL Open Font License, % Version 1.1. This license is in the accompanying file OFL.txt, and % is also available with a FAQ at: http://scripts.sil.org/OFL % design_size := 10; font_size design_size * pt#; if known ps_output: font_version := "2.000"; font_comment := "Copyright (c) 2012, Sebastian Schubert. This Font Software is licensed under the SIL Open Font License, Version 1.1."; fi u# := 0.57pt#; cap_height# := 6.74pt#; %7.37pt#; asc_height# := 7.10pt#; % 8.56pt#; desc_depth# := 1.98pt#; % 2.94pt#; x_height# := 4.84pt#; math_axis# := 2.75pt#; if weight_index = 0: % Light line_thickness# := 0.40pt#; letter_line_thickness# := 0.40pt#; dot_size# := line_thickness#; elseif weight_index = 1: % Regular line_thickness# := 0.68pt#; letter_line_thickness# := 0.73pt#; dot_size# := line_thickness#; elseif weight_index = 2: % Semibold line_thickness# := 0.93pt#; letter_line_thickness# := 1.01pt#; dot_size# := 0.85pt#; else: % Bold line_thickness# := 1.14pt#; letter_line_thickness# := 1.25pt#; dot_size# := 1.0pt#; fi; side_bearing# := 1.u#; small_op_size# := 8u#; % radius of small operators med_op_size# := 12.5u#; % radius of medium operators plus_size# := 9u#; large_op_size# := 18u#; % radius of large operators order_width# := 8u#; % width of equal sign turnstile_width# := 11u#; % width of turnstile symbols equal_spread# := .7math_axis#; % distance between the lines of the equal sign greater_spread# := 10/4equal_spread#; % distance between the ends of the greater sign arrow_horiz_len# := 12.5u#; % length of horizontal arrows arrow_vert_len# := 12.5u#; % length of vertical arrows arrow_diag_len# := 1/2(arrow_horiz_len# + arrow_vert_len#); arrow_spread# := 1.6equal_spread#; delim_height# := 4.9pt#; % half the height of normal delimiters bigop_height# := 10.7pt#; % height of big operators accent_height# := x_height# + 1.u#; % height of accents accent_thickness# := 4/5line_thickness#; rule_thickness# := line_thickness#; mode_setup; define_pixels(u, asc_height, cap_height, desc_depth, delim_height, bigop_height, x_height); define_whole_pixels(dot_size, small_op_size, med_op_size, large_op_size, plus_size, order_width, turnstile_width, equal_spread, greater_spread, arrow_horiz_len, arrow_vert_len, arrow_diag_len, arrow_spread); if known ps_output: define_pixels(math_axis, line_thickness, letter_line_thickness, rule_thickness, side_bearing, accent_height, accent_thickness); else: math_axis := good.y(math_axis# * hppp); line_thickness := ceiling(line_thickness# * hppp); letter_line_thickness := ceiling(letter_line_thickness# * hppp); rule_thickness := ceiling(rule_thickness# * hppp); side_bearing := ceiling(side_bearing# * hppp); accent_height := ceiling(accent_height# * hppp); accent_thickness := ceiling(accent_thickness# * hppp); fi stroke_through_thickness := 4/5line_thickness; bop_thickness_fac := 1.; % make big operators that much thicker % (including sum and integral) % Macros def ppos_cut(suffix $)(expr a, b) = ppos_cut_linethick($)(line_thickness, a, b); enddef; def ppos_cut_linethick(suffix $)(expr lt, a, b) = if sind(a-b) = 0 : penpos$(lt,0); else: penpos$(lt/abs(sind(a-b)),b); fi enddef; % Redefine clockwise and counterclockwise (turningnumber seems more stable) if known ps_output: vardef counterclockwise primary p = (if turningnumber p>0: p else: (reverse p) fi) enddef; vardef clockwise primary p = (if turningnumber p<0: p else: (reverse p) fi) enddef; fi % Selects the n-th element of a list def select(expr n)(text values) = begingroup; i := 0; for v = values: result := v; exitif i = n; i := i + 1; endfor; result endgroup enddef; % Splits a length at the math axis def vcentre(expr size) = size/2 + math_axis#, size/2 - math_axis# enddef; current_char := -1; def beginsymbol(expr width, height, depth) = current_char := current_char + 1; beginchar(current_char, width, height, depth); if not known ps_output: proofrule((side_bearing, math_axis),(w - side_bearing, math_axis)); proofrule((side_bearing, h),(side_bearing, -d)); proofrule((w - side_bearing, h),(w - side_bearing, -d)); fi enddef; def beginoperator(expr size, ratio) = beginsymbol(size + 2side_bearing#, vcentre(ratio * size)); pair centre; centre := (w/2, (h-d)/2); radius := w/2 - side_bearing - 1/2line_thickness; enddef; def beginbigop(expr xscale, yscale) = beginsymbol(xscale * 3/2order_width# + 2side_bearing#, vcentre(yscale * bigop_height#)); pair centre; centre := (w/2, (h-d)/2); op_width := xscale * 3/2order_width; op_height := yscale * bigop_height; enddef; def beginsquarebigop(expr xscale, yscale) = beginsymbol(xscale * bigop_height# + 2side_bearing#, vcentre(yscale * bigop_height#)); pair centre; centre := (w/2, (h-d)/2); op_width := xscale * bigop_height; op_height := yscale * bigop_height; enddef; def beginarrow(expr angle, scale, spread) = arrow_len# := scale * if angle mod 180 = 0: arrow_horiz_len# elseif angle mod 180 = 90: arrow_vert_len# else: arrow_diag_len# fi; arrow_len := scale * if angle mod 180 = 0: arrow_horiz_len elseif angle mod 180 = 90: arrow_vert_len else: arrow_diag_len fi; beginsymbol(arrow_len# * abs(cosd(angle)) + (spread + line_thickness#) * abs(sind(angle)) + 2side_bearing#, vcentre(arrow_len# * abs(sind(angle)) + (spread + line_thickness#) * abs(cosd(angle)))); pair centre, head, head_ex, foot, foot_ex; centre := (w/2, (h-d)/2); head := centre + (arrow_len - line_thickness)/2 * dir angle; head_ex := centre + arrow_len/2 * dir angle; foot := centre - (arrow_len - line_thickness)/2 * dir angle; foot_ex := centre - arrow_len/2 * dir angle; enddef; def beginorder(expr sign, width, spread) = beginsymbol(width + 2side_bearing#, vcentre(spread + line_thickness#)); pair centre, left_ex, right_ex, left_point, right_point; centre := (w/2, (h-d)/2); left_ex := centre - sign * (w/2 - side_bearing) * right; left_point := centre - sign * (w/2 - side_bearing - line_thickness/2) * right; right_ex := centre + sign * (w/2 - side_bearing) * right; right_point := centre + sign * (w/2 - side_bearing - line_thickness/2) * right; enddef; def beginturnstile(expr angle, scale) = beginsymbol(abs(sind(angle) + scale * cosd(angle)) * turnstile_width# + 2side_bearing#, abs(min(scale, 1 + (scale - 1)/2) * sind(angle) + cosd(angle)) * cap_height#, abs(max(0, (scale - 1)/2) * sind(angle)) * cap_height#); pair foot; if angle mod 180 = 0: len := scale * turnstile_width; spread := cap_height - line_thickness; else: len := scale * cap_height; spread := turnstile_width - line_thickness;; fi foot = (w/2, (h - d)/2) - (len - line_thickness)/2 * dir angle; enddef; def beginaccent(expr width, addheight) = thick := accent_thickness; beginsymbol(width, accent_height# + addheight, 0); enddef; % Strokes a pen path vardef stroke text t = forsuffixes e = l, r: path_.e := t; endfor path_.r -- reverse path_.l -- cycle enddef; % Shapes def circle(expr centre, radius) = (centre + radius * right){up} ... (centre + radius * dir 45){dir 135} ... (centre + radius * up){left} ... (centre + radius * dir 135){dir 225} ... (centre + radius * left){down} ... (centre + radius * dir 225){dir 315} ... (centre + radius * down){right} ... (centre + radius * dir 315){dir 45} ... cycle enddef; def square(expr centre, radius, angle) = (centre + sqrt(2) * radius * dir (angle + 45)) -- (centre + sqrt(2) * radius * dir (angle + 135)) -- (centre + sqrt(2) * radius * dir (angle + 225)) -- (centre + sqrt(2) * radius * dir (angle + 315)) -- cycle enddef; def triangle(expr centre, radius, angle) = (centre + radius * dir angle) -- (centre + radius * dir (angle + 120)) -- (centre + radius * dir (angle + 240)) -- cycle enddef; def reg_poly_points(suffix $)(expr n, centre, radius, angle) = for i = 0 upto n-1: z$[i] = centre + radius * dir (angle + i/n * 360); endfor; enddef; def dot(expr centre, radius) = circle(centre, radius) enddef; % Draw macros def draw_straight(expr orig, dest, thick, extend) = begingroup; pair p[].l, p[].r; theta := angle (dest - orig); if extend: 1/2[p1.l,p1.r] = orig - 1/2thick * dir theta; 1/2[p2.l,p2.r] = dest + 1/2thick * dir theta; else: 1/2[p1.l,p1.r] = orig; 1/2[p2.l,p2.r] = dest; fi p1.l - p1.r = p2.l - p2.r = thick * dir (theta + 90); fill stroke p1.e -- p2.e; endgroup; enddef; def draw_line(expr orig, dest, extend) = draw_straight(orig, dest, line_thickness, extend); enddef; def draw_line_linethick(expr orig, dest, lt, extend) = draw_straight(orig, dest, lt, extend); enddef; def draw_line_cut_linethick(suffix $, $$)(expr lt)= if (abs(angle(z$-z$$))<45) or (abs(angle(z$-z$$))>135) : ppos_cut_linethick($)(lt,angle(z$-z$$),90); ppos_cut_linethick($$)(lt,angle(z$-z$$),90); else: ppos_cut_linethick($)(lt,angle(z$-z$$),0); ppos_cut_linethick($$)(lt,angle(z$-z$$),0); fi penstroke z$e .. z$$e; penlabels($,$$); enddef; def draw_line_cut(suffix $, $$)= draw_line_cut_linethick($,$$)(line_thickness); enddef; def draw_circle(expr centre, radius, thick) = fill circle(centre, radius + 1/2thick); unfill circle(centre, radius - 1/2thick); enddef; def filldraw_circle(expr centre, radius, thick) = fill circle(centre, radius + 1/2thick); enddef; def draw_square(expr centre, radius, angle, thick) = fill square(centre, radius + 1/2thick, angle); unfill square(centre, radius - 1/2thick, angle); enddef; def filldraw_square(expr centre, radius, angle, thick) = fill square(centre, radius + 1/2thick, angle); enddef; def draw_triangle(suffix $)(expr centre, radius, angle, thick) = fill triangle(centre, radius + thick, angle); unfill triangle(centre, radius - thick, angle); enddef; def filldraw_triangle(suffix $)(expr centre, radius, angle, thick) = fill triangle(centre, radius + thick, angle); enddef; def draw_sim(suffix $)(expr lc, rc, spread, thick) = theta := angle (length(rc - lc), 10spread); signum := cosd (angle (rc - lc)) + sind (angle (lc - rc)); z0$.l = lc; z4$.r = rc; z2$ = 1/2[lc, rc]; z4$.r = rc; 1/2[z1$,z3$] = z2$; z1$ = 1/4[lc, rc] + 1/6thick * dir (angle (rc - lc)) + signum * spread * dir (angle (rc - lc) + 90); penpos0$(thick, angle(rc - lc) - signum * (90 - theta)); penpos1$(thick, angle(rc - lc) - signum * 90); penpos2$(thick, angle(rc - lc) - signum * (theta + 90 - 5)); penpos3$(thick, angle(rc - lc) - signum * 90); penpos4$(thick, angle(rc - lc) - signum * (90 - theta)); fill stroke z0$.e{dir (angle(rc - lc) + signum * theta)} .. {dir angle(rc - lc)}z1$.e .. {dir (angle(rc - lc) - signum * (theta - 5))}z2$.e .. {dir angle(rc - lc)}z3$.e .. {dir (angle(rc - lc) + signum * theta)}z4$.e; penlabels(0$,1$,3$,4$); enddef; def draw_bump(suffix $)(expr sign, lc, rc, rad, thick) = z0$ = lc; z1$ = rc; z2$ = 1/2[lc, rc] + sign * rad * dir (angle (rc - lc) + 90); z3$ = 1/2[lc, rc] - rad * dir (angle (rc - lc)); 1/2[z3$,z4$] = 1/2[lc, rc]; penpos0$(thick, angle (rc - lc) + sign * 90); penpos1$(thick, angle (rc - lc) + sign * 90); penpos2$(thick, angle (rc - lc) + sign * 90); penpos3$(thick, angle (rc - lc)); penpos4$(thick, angle (rc - lc)); z5$ = z3$.r; z6$ = z4$.l; penpos5$(thick, angle (rc - lc) + sign * 90); penpos6$(thick, angle (rc - lc) + sign * 90); path p$, q$; numeric s$, t$; p$ = z3$.l{dir (angle(rc - lc) + sign * 90)} .. {rc - lc}z2$.r; q$ = z2$.r{rc - lc} .. {dir (angle(rc - lc) - sign * 90)}z4$.r; s$ = xpart (p$ intersectiontimes (z0$.r -- z1$.r)); t$ = xpart (q$ intersectiontimes (z0$.r -- z1$.r)); fill z0$.r -- point s$ of p$ & subpath (s$,1) of p$ & subpath (0,t$) of q$ & point t$ of q$ -- z1$.r -- z1$.l -- z6$l. -- z6${dir (angle (rc - lc) + sign * 90)} .. z2$.l{lc - rc} .. {dir (angle (rc - lc) - sign * 90)}z5$ -- z5$.l -- z0$.l -- cycle; penlabels(0$,1$,2$,3$,4$,5$,6$); enddef; def draw_less(suffix $)(expr lc, rc, spread, thick, closed, straight) = put_less($)(lc, rc, spread, thick, closed, straight); fill z0$.l -- z3$.l -- z4$.l -- z1$.l -- z1$.r -- z5$ -- z0$.r -- cycle; if closed: fill z0$.l -- z6$.l -- z7$.l -- z1$.l -- z7$.r -- z6$.r -- cycle; fi; enddef; def put_less(suffix $)(expr lc, rc, spread, thick, closed, straight) = theta := angle((length(rc - lc) - thick/2) * right + spread/2 * up); z2$ = lc + 1/2thick * dir (angle (rc - lc)); 1/2[z0$.r,z1$.r] = rc; z0$ = z2$ + whatever * dir (angle (rc - lc) + theta); z1$ = z2$ + whatever * dir (angle (rc - lc) - theta); if straight: penpos0$(thick/cosd(theta), angle(rc - lc) - 90); penpos1$(thick/cosd(theta), angle(rc - lc) + 90); else: penpos0$(thick, angle(rc - lc) - 90 + theta); penpos1$(thick, angle(rc - lc) + 90 - theta); fi; penpos3$(thick, angle(rc - lc) - 90 + theta); penpos4$(thick, angle(rc - lc) + 90 - theta); z3$.l = z0$.l + whatever * (z2$ - z0$); z4$.l = z1$.l + whatever * (z2$ - z1$); 1/2[z3$.l,z4$.l] = lc; z5$ = z0$.r + whatever * (z2$ - z0$); z5$ = z1$.r + whatever * (z2$ - z1$); if closed: penpos6$(thick, angle(rc - lc)); penpos7$(thick, angle(rc - lc)); z6$.l = whatever[z0$.l,z3$.l]; z6$.r = whatever[z0$.r,z1$.r]; z7$.l = whatever[z1$.l,z4$.l]; z7$.r = whatever[z0$.r,z1$.r]; fi; penlabels(0$,1$,3$,4$,5$,6$,7$); enddef; def draw_prec(suffix $)(expr lc, rc, spread, thick, closed) = theta := 43; z0$ - z1$ = spread * dir (angle (rc - lc) + 90); 1/2[z0$.r,z1$.l] = rc; z2$ = lc; z2$' = lc + 1/2thick * dir angle(rc - lc); penpos0$(thick, angle(rc - lc) - theta); penpos1$(thick, angle(rc - lc) + 180 + theta); penpos2$(thick, angle(rc - lc) - 90); penpos2$'(thick, angle(rc - lc) - 90); fill stroke z2$.e -- z2$'.e{dir angle(rc - lc)} .. {dir (angle (rc - lc) + 90 - theta)}z0$.e; fill stroke z2$.e -- z2$'.e{dir angle(rc - lc)} .. {dir (angle (rc - lc) - 90 + theta)}z1$.e; if closed: z3$ = point 1/2 of (z0${dir (angle (rc - lc) - 90 - theta + 10)} .. {dir (angle (rc - lc) - 90 + theta - 10)}z1$); penpos3$(thick, angle(rc - lc)); fill z0$.l .. z3$.l .. z1$.r -- z1$.l .. z3$.r .. z0$.r -- cycle; fi; penlabels(0$,1$,2$,3$); enddef; def draw_subset(suffix $)(expr lc, rc, spread, thick) = 1/2[z0$,z1$] = rc; 1/2[z2$,z3$] = (4spread / 9abs(rc - lc))[z4$, rc]; z0$ - z1$ = z2$ - z3$ = spread * dir (angle (rc - lc) + 90); z4$ = lc + 1/2thick * dir (angle (rc - lc)); penpos0$(thick, angle(rc - lc) - 90); penpos1$(thick, angle(rc - lc) + 90); penpos2$(thick, angle(rc - lc) - 90); penpos3$(thick, angle(rc - lc) + 90); penpos4$(thick, angle(rc - lc)); fill stroke z0$.e -- z2$.e{lc - rc} .. z4$.e .. {rc - lc}z3$.e -- z1$.e; penlabels(0$,1$,2$,3$,4$) enddef; def draw_smile(suffix $)(expr sign, lc, rc, spread, thick, round) = z0$ = lc + sign * 1/2spread * dir (angle(rc - lc) + 90) + whatever * (rc - lc); z0$.l = lc + whatever * dir (angle(rc - lc) + 90); z1$ = rc + sign * 1/2spread * dir (angle(rc - lc) + 90) + whatever * (rc - lc); z1$.l = rc + whatever * dir (angle(rc - lc) + 90); z2$ = 1/2[lc,rc] - sign * 1/2spread * dir (angle(rc - lc) + 90); if round: theta := angle (length(lc - rc), 5spread); else: theta := angle (length(lc - rc), 2spread); fi; penpos0$(thick, angle(rc - lc) + sign * (90 - theta)); penpos1$(thick, angle(rc - lc) + sign * (90 + theta)); if round: penpos2$(thick, angle(rc - lc) + sign * 90); fill stroke z0$.e{dir (angle(rc - lc) - sign * theta)} .. {rc - lc}z2$.e{rc - lc} .. {dir (angle(rc - lc) + sign * theta)}z1$.e; else: penpos2$(thick / cosd theta, angle(rc - lc) + sign * 90); fill stroke z0$.e -- z2$.e -- z1$.e; fi; penlabels(0$, 1$, 2$); enddef; def stroke_through_angle(expr pos, spread, angle) = begingroup; stroke_len := 1/2spread / cosd (90 - angle); z100 = pos + stroke_len * dir angle; z101 = pos - stroke_len * dir angle; draw_line_cut_linethick(100,101)(stroke_through_thickness); endgroup; enddef; def stroke_through(expr pos, spread) = stroke_through_angle(pos, spread, 75); enddef; def stroke_through_arrow(expr pos, alpha, spread)(text angles) = begingroup; stroke_dir := alpha + select(alpha / 45)(angles); stroke_len := 1/2spread / sind (stroke_dir - alpha); z102 = pos + stroke_len * dir stroke_dir; z103 = pos - stroke_len * dir stroke_dir; draw_line_cut_linethick(102,103)(stroke_through_thickness); endgroup; enddef; def put_product_points(expr centre, width, height, sign, thick) = thin := thick; z1r - z0r = z3r - z2r = width * right; z2r - z0r = sign * (height - thin) * up; 1/2[1/2[z0l,z1l], 1/2[z2r,z3r]] = centre; z4 = z0 + min(5thin, 2/5width) * right; z5 = z1 + min(5thin, 2/5width) * left; z6 = 1/2[z0l,z4l]; z7 = 1/2[z1l,z5l]; x8 = 1/2[x0,x4]; x9 = 1/2[x1,x5]; y8 = y9 = y2l; penpos0(thin, sign * 90); penpos1(thin, sign * 90); penpos2(thin, sign * 90); penpos3(thin, sign * 90); penpos4(thin, sign * 90); penpos5(thin, sign * 90); penpos6(thick, 0); penpos7(thick, 0); penpos8(thick, 0); penpos9(thick, 0); y10 = y11 = y2r - sign * 1/2[thin,thick]; x10 = x6r; x11 = x7l; penlabels(0,1,2,3,4,5,6,7,8,9,10,11); enddef; def draw_product(expr centre, width, height, sign, thick) = put_product_points(centre, width, height, sign, thick) fill z6r -- z8r -- z9l -- z7l -- z7r -- z9r -- z3l -- z3r -- z2r -- z2l -- z8l -- z6l --cycle; enddef; def draw_productintegral(expr centre, width, height, sign, thick) = put_product_points(centre, width, height, sign, thick); z8''=0.3[z2l,z3l]; z9''=0.7[z2l,z3l]; x6'=x6; y6'-y6=sign*(x6-x0+1/2thick); penpos6'(sign*thick/sind(angle(z8''-z0)),0); penpos8''(thick, 0); penpos9''(thick, 0); z0r = z0'r; penpos0'(thick,sign*76); z2 - z2' = sign* 1/35height * up; penpos2'(thin,sign*90); z8''l = z8'l; penpos8'(thick,sign*90); x7'=x7; y7'-y7=sign*(x1-x7+1/2thick); penpos7'(sign*thick/sind(angle(z9''-z1)),0); z7'' = z7' + whatever*(z1-z9''); y7'' = y7; penpos7''(sign*thick/sind(angle(z7'-z7'')),0); fill z8''r -- z9''l{sign*down} .. {z1-z9''}z7'l -- z7''l -- z7''r -- z7'r{z9''-z1} .. {sign*up}z9''r -- z3l -- z3r -- z8'r{left} .. z2'r -- z2'l .. {right}z8''l{sign*down} ... {z0-z8''}z6'l{z0-z8''} ... {left}z0r -- z0'l{left} .. {right}z0l{right} ... {z8''-z0}z6'r{z8''-z0} ... {sign*up}cycle; penlabels(0',2',6',7',7'',8',8'',9''); enddef; def draw_sum(suffix $)(expr centre, width, height, thick) = thin := 4/5thick; z1$l - z0$l = z3$l - z2$l = width * right; z2$l - z0$l = height * up; 1/2[1/2[z0$l,z1$l], 1/2[z2$l,z3$l]] = centre = z4$; penpos0$(thin, 90); penpos1$(thick, 90); penpos2$(thin, -90); penpos3$(thick, -90); penpos4$(thick/sind(angle(z4$-z0$)), 0); y5$r = y0$l + thick; y6$r = y2$l - thick; z5$r = whatever[z0$r,z4$l]; z6$r = whatever[z2$r,z4$l]; penpos5$(thick/sind(angle(z4$-z0$)), 180); penpos6$(thick/sind(angle(z4$-z0$)), 180); fill z1$r -- z1$l -- z0$l -- z0$r -- z4$l -- z2$r -- z2$l -- z3$l -- z3$r -- z6$l -- z4$r -- z5$l -- cycle; penlabels(0$,1$,2$,3$,4$,5$,6$); enddef; def draw_integral(suffix $)(expr scale, centre, thick) = penpos0$(thick, 0); penpos1$(thick, 0); penpos2$(6/7thick, -90); penpos3$(thick, 0); penpos4$(6/7thick, -90); z0$ = 1/2[z1$,z3$] = 1/2[z2$,z4$]; z1$ - z3$ = whatever * dir 79; z2$ - z4$ = whatever * dir 70; x0$ = xpart centre; y2$l = h; y4$r = -d; y1$ = 1/2[y0$,y2$]; penpos5$(1.05*6/7thick/sind 70,-105); penpos6$(1.05*6/7thick/sind 70,-105); y5$l = y2$l - 0.2thick; x5$r = 5/4[x1$, x2$] + 0.2thick; y6$r = y4$r + 0.2thick; x6$r = 6/4[x3$, x4$] - 0.2thick; ucorr := max (x2$r, x1$r + 1/4thick) - x2$r; x2$ := x2$ + ucorr; x2$l := x2$l + ucorr; x2$r := x2$r + ucorr; x5$ := x5$ + ucorr; x5$r := x5$r + ucorr; x5$l := x5$l + ucorr; lcorr := min (x4$l, x1$l - 1/4thick) - x4$l; x4$ := x4$ + lcorr; x4$l := x4$l + lcorr; x4$r := x4$r + lcorr; x6$ := x6$ + lcorr; x6$r := x6$r + lcorr; x6$l := x6$l + lcorr; fill z5$l .. {left}z2$l{left} .. {dir angle(z0$-z1$)}z1$l -- z3$l{dir angle(z0$-z1$)} ... z4$l{left} .. z6$l -- z6$r .. {right}z4$r{right} .. {dir angle(z1$-z0$)}z3$r -- z1$r{dir angle(z1$-z0$)} ... z2$r{right} .. z5$r -- cycle; penlabels(0$,1$,2$,3$,4$,5$,6$); enddef; def draw_arrowhead_left(expr pos, angle, spread, thick) = begingroup; pair p[], p[].l, p[].r; p1 = pos; p2 = pos + sqrt(2) * (spread + thick)/2 * dir (angle + 135); 1/2[p1.l, p1.r] = p1; 1/2[p2.l, p2.r] = p2; p1.r - p1 = thick/(2 * sind 45) * dir angle; p2.r - p2 = thick/(2 * sind 45) * dir angle; p3.l = whatever[p2.l,p1.l]; p3.l = pos + 1/2thick * dir (angle - 90) + whatever * dir angle; p3.r - p1.r = whatever * dir (angle - 90); p3.r = pos + 1/2thick * dir (angle - 90) + whatever * dir angle; fill p1.r -- p2.r -- p2.l -- p3.l -- p3.r -- cycle; endgroup; enddef; def draw_arrowhead_right(expr pos, angle, spread, thick) = begingroup; pair p[], p[].l, p[].r; p1 = pos; p2 = pos + sqrt(2) * (spread + thick)/2 * dir (angle - 135); 1/2[p1.l, p1.r] = p1; 1/2[p2.l, p2.r] = p2; p1.r - p1 = thick/(2 * sind 45) * dir angle; p2.r - p2 = thick/(2 * sind 45) * dir angle; p3.l = whatever[p2.l,p1.l]; p3.l = pos + 1/2thick * dir (angle + 90) + whatever * dir angle; p3.r - p1.r = whatever * dir (angle + 90); p3.r = pos + 1/2thick * dir (angle + 90) + whatever * dir angle; fill p1.r -- p3.r -- p3.l -- p2.l -- p2.r -- cycle; endgroup; enddef; def draw_arrowhead(expr pos, angle, spread, thick) = begingroup; pair p[], p[].l, p[].r; p1 = pos; p2 = pos + sqrt(2) * (spread+thick)/2 * dir (angle + 135); p3 = pos + sqrt(2) * (spread+thick)/2 * dir (angle - 135); 1/2[p1.l, p1.r] = p1; 1/2[p2.l, p2.r] = p2; 1/2[p3.l, p3.r] = p3; p1.r - p1 = thick/(2 * sind 45) * dir angle; p2.r - p2 = thick/(2 * sind 45) * dir (angle); p3.r - p3 = thick/(2 * sind 45) * dir (angle); fill p1.r -- p2.r -- p2.l -- p1.l -- p3.l -- p3.r -- cycle; endgroup; enddef; % intersect the arrowhead curve with a path def arrowhead_intersection(expr pos, angle, spread, p) = (p intersectionpoint ((pos + sqrt(2) * spread/2 * dir (angle + 135)) -- pos -- (pos + sqrt(2) * spread/2 * dir (angle - 135))) ) enddef; def draw_bracket(expr sign, thick, draw_top, draw_mid, draw_bot, draw_double) = penpos0(thick, 90 - sign * 90); penpos1(thick, 90 - sign * 90); penpos2(thick, 90); penpos3(thick, 90); penpos4(thick, 90); penpos5(thick, 90); penpos6(thick, 0); penpos7(thick, 0); x3 - x2 = x5 - x4 = sign * (w - 2side_bearing); 1/2[x2,x3] = w/2; if draw_top: y1 = h; else: y1 = h + 1/2line_thickness; fi; if draw_bot: y0 = -d; else: y0 = -d - 1/2line_thickness; fi; x1 = x0; z6 = 1/2[z2l,z3l] + sign * 1/2thick * right; z7 = 1/2[z4r,z5r] + sign * 1/2thick * right; y2l = y3l; y4r = y5r; z2l = z0l; z4r = z1l; if draw_mid: fill stroke z0e -- z1e; else: if draw_bot: fill stroke z0e -- z0e + (w - 2side_bearing) * up; fi; if draw_top: fill stroke z1e -- z1e + (w - 2side_bearing) * down; fi; fi; if draw_top: fill stroke z4e -- z5e; fi; if draw_bot: fill stroke z2e -- z3e; fi; if draw_double: fill stroke z6e -- z7e; fi; enddef; def draw_angle(suffix $)(expr shift, sign, thick) = x0$ = x1$ = x2$ + sign * (w - 2side_bearing -2abs shift - thick); top y1$ = h; bot y0$ = -d; 1/2[y0$,y1$] = y2$; 1/2[x0$,x2$] = w/2 + shift; theta := angle(z0$ - z2$); penpos0$ (thick, 0); penpos1$ (thick, 0); penpos2$ (thick / abs(sind theta), 0); fill stroke z0$e -- z2$e -- z1$e; penlabels(0$, 1$, 2$); enddef; def draw_paren(expr sign, thick) = penpos0(thick, 90 - sign * 90); penpos1(thick, -90 + sign * 90); penpos2(1.1thick, 90 - sign * 90); if sign = 1: x2l = side_bearing; x1r = x0r = w - side_bearing; else: x1r = x0r = side_bearing; x2l = w - side_bearing; fi y1.l = h; y0.l = -d; 1/2[y0,y1] = y2; fill stroke z0e .. z2e .. z1e; penlabels(0,1,2); enddef; def draw_brace(expr centre, size, width, alpha, thick, top_size, mid_size, bot_size) = penpos1(5/6thick, alpha + 90); penpos2(thick, alpha); penpos2'(thick,alpha); penpos3(thick, alpha); penpos3'(thick,alpha); penpos4(11/12thick, alpha+90); penpos5(thick, alpha+180); penpos5'(thick, alpha+180); penpos6(thick, alpha+180); penpos6'(thick, alpha+180); penpos7(5/6thick, alpha+90); z1r - z7l = size * dir (alpha + 90); centre - 1/2[z1,z7] = z4 - centre = width/2 * dir alpha; z0 = centre; z3 = z0 + (1/3width + 1/2thick) * dir (alpha + 90); z5 = z0 - (1/3width + 1/2thick) * dir (alpha + 90); z2 = z0 + (size/2 - 1/3width - thick) * dir (alpha + 90); z6 = z0 - (size/2 - 1/3width - thick) * dir (alpha + 90); z3' = z0 + (mid_size/2 + 1/2line_thickness) * dir (alpha + 90); z5' = z0 - (mid_size/2 + 1/2line_thickness) * dir (alpha + 90); z2' = z0 + (size/2 - top_size - 1/2line_thickness) * dir (alpha + 90); z6' = z0 - (size/2 - bot_size - 1/2line_thickness) * dir (alpha + 90); beta := 0; if top_size > 0: fill stroke z1e{dir alpha} .. {dir (alpha - 90)}z2e -- z2'e; penlabels(1,2,2'); elseif bot_size > 0: fill stroke z7e{dir alpha} .. {dir (alpha + 90)}z6e -- z6'e; penlabels(6',6,7); elseif mid_size > 0: fill stroke z3'e -- z3e{dir (alpha - 90)} .. {dir alpha}z4e; fill stroke z5'e -- z5e{dir (alpha + 90)} .. {dir alpha}z4e; penlabels(3',3,4,5,5'); else: fill stroke z1e{dir alpha} .. z2e{dir (alpha - 90)} -- z3e{dir (alpha - 90)} .. z4e{dir alpha}; fill stroke z7e{dir alpha} .. {dir (alpha + 90)}z6e -- z5e{dir (alpha + 90)} .. {dir alpha}z4e; penlabels(1,2,3,4,5,6,7); fi; enddef; def draw_root(expr thick) = penpos0(rule_thickness, -90); penpos0'(rule_thickness, -90); y0l = h; x0 = w; z0' = z0 + 1/2line_thickness * right; y1 = -d; x1 = 4/9w; x2r = 2/9w + 1/2thick; y2r = 1/2[y0, y1]; z1' = z1 + thick * right; y6 = h; z6 = z0r + thick/sind(angle(z0r - z1')) * left + whatever * (z0r - z1'); penpos2(thick/abs(sind(angle(z1'-z2r))), 0); penpos3(1/2thick, angle (z1 - z2l)); z1'' = z1' - thick/abs(sind(angle(z1' - z2r))) * right; z3l = z2r + 3/2thick * dir (angle (z1 - z2l) - 90); z4 = z6 + whatever * (z0r - z1') = z2r + whatever * (z2r - z1'); z5 = whatever[z2l, z1''] = z3r + whatever * dir (angle (z1'' - z2l) - 90); fill z3r -- z5 -- z1'' -- z1' -- z0r -- z0'r -- z0'l -- z6 -- z4 -- z2r -- z3l -- cycle; penlabels (0,0',1,1',1'',2,3,4,5,6); enddef; def draw_root_top(expr thick) = y0 = h - 1/2rule_thickness; x0 = w; y1 = -d; x1 = x2 = 4/9w + 1/2thick; y2 = h - 1/2thick; draw_straight(z1, z2, thick, true); draw_straight((x1,y0), z0, rule_thickness, true); enddef; def draw_root_bot(expr thick) = penpos0(thick, 0); penpos0'(thick, -90); y0 = h + 1/2thick; x0l = x1; y1 = -d; x1 = 4/9w; x2r = 2/9w + 1/2thick; y2r = 1/2[y0, y1]; z1' = z1 + whatever * right; x1' = x0r; penpos2(thick/abs(sind(angle(z1'-z2r))), 0); penpos3(1/2thick, angle (z1 - z2l)); z1'' = z1' - thick/abs(sind(angle(z1' - z2r))) * right; z3l = z2r + 3/2thick * dir (angle (z1 - z2l) - 90); z4 = z0l + whatever * up = z2r + whatever * (z2l - z1); z5 = whatever[z2l, z1''] = z3r + whatever * dir (angle (z1'' - z2l) - 90); fill z3r -- z5 -- z1 -- z1' -- z0r -- z0l -- z4 -- z2r -- z3l -- cycle; penlabels (0,1,1',1'',2,3,4,5); enddef; % Weierstrass macros def ellipse_set(suffix $,@,@@,$$) = % given |z$,x@,z$$|, find |y@| and |z@@| % such that the path |z${x@-x$,0}..z@{0,y@-y$}..{z$$-z@@}z@@| % is consistent with an ellipse % and such that the line |z@@--z$$| has a given |slope| alpha_ := slope * (x@ - x$); beta_ := y$$ - y$ - slope * (x$$ - x$); gamma_ := alpha_ / beta_; y@ - y$ = .5(beta_ - alpha_ * gamma_); x@@ - x$ = -2gamma_ * (x@ - x$) / (1 + gamma_ * gamma_); y@@ - y$$ = slope * (x@@ - x$$) enddef; vardef super_arc.r(suffix $,$$) = % outside of super-ellipse pair centre, corner; if y$ = y$r: centre = (x$$r, y$r); corner = (x$r, y$$r); else: centre = (x$r, y$$r); corner = (x$$r, y$r); fi z$.r{corner - z$.r} ... superness[centre,corner]{z$$.r - z$.r} ... {z$$.r - corner}z$$.r enddef; vardef super_arc.l(suffix $,$$) = % inside of super-ellipse pair centre, corner; if y$ = y$r: centre = (x$$l, y$l); corner = (x$l, y$$l); else: centre = (x$l, y$$l); corner = (x$$l, y$l); fi z$l{corner - z$l} ... superness[centre,corner]{z$$l - z$l} ... {z$$l - corner}z$$l enddef; vardef pulled_super_arc.r(suffix $,$$)(expr superpull) = pair centre, corner; if y$ = y$r: centre = (x$$r, y$r); corner = (x$r, y$$r); else: centre = (x$r, y$$r); corner = (x$$r, y$r); fi z$r{corner - z$r} ... superness[centre,corner]{z$$r - z$r} ... {z$$r - corner}z$$r enddef; vardef pulled_super_arc.l(suffix $,$$)(expr superpull) = pair centre, corner, outer_point; if y$ = y$r: centre = (x$$l, y$l); corner = (x$l, y$$l); outer_point = superness[(x$$r, y$r), (x$r, y$$r)]; else: centre = (x$l, y$$l); corner = (x$$l, y$l); outer_point = superness[(x$r, y$$r), (x$$r, y$r)]; fi z$l{corner - z$l} ... superpull[superness[centre,corner], outer_point]{z$$l - z$l} ... {z$$l - corner}z$$l enddef; vardef pulled_arc@#(suffix $,$$) = pulled_super_arc@#($,$$)(superpull) enddef;