Flowers of mathematical graphics

A few days ago, I published an article about how to generate a curve. For more information, see

Mathematical graphics (1.11) Rose Line

Mathematical graphics (1.27) flowers

In this section, the two-dimensional curve is converted into a three-dimensional curve, which looks much more beautiful.

For related software, see: Mathematical graphics visualization tool. Use script code with custom syntax to generate mathematical graphics.

 

(1) rose Wire

vertices = D1:4000 D2:6n = 8u = from 0 to (n*PI) D1v = from 0 to 1 D2a = rand_int2(2, 16)r = 10*sin(a*u)*vk = u/n/2x = r*cos(u)*cos(k)z = r*sin(u)*cos(k)y = GOLD* abs(r)*sin(k)

(2) Double rose

vertices = D1:4000 D2:6n = rand_int2(3, 16)u = from 0 to (n*PI) D1v = from 0 to 1 D2r = 10*(1 + 3*sin(n*u))*vk = u/n/2x = r*cos(u)*cos(k)z = r*sin(u)*cos(k)y = GOLD* abs(r)*sin(k)

(3) Super rose

#http://www.2dcurves.com/roulette/rouletters.htmlvertices = D1:8000 D2:6n = 16u = from 0 to (n*PI) D1v = from 0 to 1 D2a = rand_int2(1, 100) / 8b = rand_int2(1, 100) / 8c = rand_int2(-10, 100) / 8d = rand_int2(1, 100) / 8f = rand_int2(1, 100) / 8w = pow(abs(cos(d*u)), a) + pow(abs(sin(d*u)), b)r = 10*v*sin(f*u)*pow(w, c)w = u/n/2x = r*sin(u)*cos(w)z = r*cos(u)*cos(w)y = GOLD*abs(r)*sin(w)

(4) n leaf grass

#http://www.mathcurve.com/courbes2d/biquartic/biquartic.shtmlvertices = D1:4000 D2:6m = 8u = from (-PI) to (m*PI) D1v = from 0 to 1 D2n = rand_int2(3, 10)p = (1 + cos(n*u) + sin(n*u)^2) * vk = u/m/2x = p*cos(u)*cos(k)z = p*sin(u)*cos(k)y = abs(p)*sin(k)

(5) folioide

vertices = D1:6 D2:4000m = 32u = from (-PI/2) to (m*PI) D2v = from 0 to 1 D1e = rand2(0.1, 10)a = 10 / ei = rand_int2(2, 10)j = rand_int2(1, 10)n = i/jp = a*(e*cos(n*u) + sign(u)*e*sqrt(1 - pow(cos(n*u), 2)))*vw = u/m/2x = p*cos(u)*cos(w)z = p*sin(u)*cos(w)y = GOLD * abs(p)*sin(w)

(6) Botanic

#http://www.2dcurves.com/roulette/rouletteb.htmlvertices = D1:8000 D2:6n = 32u = from 0 to (n*PI) D1v = from 0 to 1 D2r = 10*vc = rand2(0.1, 10)d = rand2(1, 10)p = r*(1 + d*sin(c*u))w = u/n/2x = p*cos(u)*cos(w)z = p*sin(u)*cos(w)y = 0.6*abs(p)*sin(w)