Hammered crash: an option to scatter the dents at random

randomDents = 1 places the marks at random with uniform density over the bow, from a seeded congruential generator in the script, so that a seed always gives the same cymbal; the default stays the spiral.

Jeremy Magland <jmagland@flatironinstitute.org> committed 1 month ago commit 149833c43ed7 parent 0b50660 Browse files

1 changed file+24−10

src/presets.tsmodified+24−10View file

@@ -190,16 +190,20 @@ end

190190 `;

191191

192192 const crashHammered16 = `% The 16 inch crash with bell, hammered: 160 shallow dents of 0.4 mm on

193-% the bow, laid out on a sunflower spiral so that no two align. A hammered

194-% cymbal is no longer axisymmetric, so its degenerate mode pairs split and

195-% its modes mix, which is part of what makes a cymbal sound like one. The

196-% dents here are what a script can express, a change of the rest shape;

197-% the residual stresses of real hammering are not modeled.

193+% the bow, laid out on a sunflower spiral so that no two align, or, with

194+% randomDents set to 1, scattered at random over the bow (dentSeed picks the

195+% pattern, and the same seed gives the same cymbal). A hammered cymbal is

196+% no longer axisymmetric, so its degenerate mode pairs split and its modes

197+% mix, which is part of what makes a cymbal sound like one. The dents here

198+% are what a script can express, a change of the rest shape; the residual

199+% stresses of real hammering are not modeled.

198200 inch = 0.0254; mm = 1e-3;

199201 D = 16*inch; R = D/2;

200202 bellR = 55*mm; bellH = 8*mm; bowH = 10*mm;

201203 tCenter = 1.2*mm; tEdge = 0.7*mm;

202204 nDents = 160; dentR = 12*mm; dentDepth = 0.4*mm;

205+randomDents = 0; % 0: the spiral; 1: random places, overlapping as hammer marks do

206+dentSeed = 1; % any positive integer; changes the random pattern

203207

204208 design.name = '16 inch hammered crash';

205209 design.material.E = 110e9;

@@ -213,7 +217,7 @@ design.bounds.width = D;

213217 design.bounds.height = D;

214218 design.inside = @(x, y, r, theta) r <= R;

215219 design.thickness = @(x, y, r, theta) tCenter + (tEdge - tCenter) * ramp(bellR, R, r);

216-design.profile = @(x, y, r, theta) bowH * (1 - (r/R).^2) + dome(r, bellR, bellH) + dents(x, y, bellR + dentR, R - dentR, nDents, dentR, dentDepth);

220+design.profile = @(x, y, r, theta) bowH * (1 - (r/R).^2) + dome(r, bellR, bellH) + dents(x, y, bellR + dentR, R - dentR, nDents, dentR, dentDepth, randomDents, dentSeed);

217221

218222 function v = ramp(a, b, x)

219223 v = min(max((x - a) ./ (b - a), 0), 1);

@@ -225,15 +229,25 @@ function v = dome(d, radius, height)

225229 v = 0.5 * height * (1 + cos(pi * d / radius)) .* (d < radius);

226230 end

227231

228-function v = dents(x, y, r0, r1, n, rd, depth)

232+function v = dents(x, y, r0, r1, n, rd, depth, random, seed)

229233 % n hammer marks between the radii r0 and r1: Gaussian dents of 1/e radius

230234 % rd, placed on a sunflower spiral (equal area per mark, golden-angle

231-% spacing) so that the pattern has no symmetry.

235+% spacing) so that the pattern has no symmetry, or at random with uniform

236+% density over the annulus, from a small congruential generator so that a

237+% seed always gives the same pattern.

232238 v = 0 * x;

233239 ga = pi * (3 - sqrt(5));

240+s = seed;

234241 for k = 1:n

235- rk = sqrt(r0^2 + (r1^2 - r0^2) * (k - 0.5) / n);

236- tk = k * ga;

242+ if random

243+ s = mod(s * 1664525 + 1013904223, 4294967296); u = s / 4294967296;

244+ s = mod(s * 1664525 + 1013904223, 4294967296); w = s / 4294967296;

245+ rk = sqrt(r0^2 + (r1^2 - r0^2) * u);

246+ tk = 2 * pi * w;

247+ else

248+ rk = sqrt(r0^2 + (r1^2 - r0^2) * (k - 0.5) / n);

249+ tk = k * ga;

250+ end

237251 dx = x - rk * cos(tk); dy = y - rk * sin(tk);

238252 v = v - depth * exp(-(dx.^2 + dy.^2) / rd^2);

239253 end