前幾天看科幻小說<三體>,講到有種武器叫水滴,是三體人用於對付地球人的.這一節將介紹幾種水滴形的數學公式.
<三體>書中對水滴的描述如下:
當全世界第一次看到探測器的影像時，所有人都陶醉於它那絕美的外形。這東西真的是太美了，它的形狀雖然簡潔，但造型精妙絕倫，曲面上的每一個點都恰到好處，使這滴水銀充滿着飄逸的動感，仿佛每時每刻都在宇宙之夜中沒有盡頭地滴落着。它給人一種感覺：即使人類藝術家把一個封閉曲面的所有可能形態平滑地全部試完，也找不出這樣一個造型。它在所有的可能之外，即使柏拉圖的理想國中也沒有這樣完美的形狀，它是比直線更直的線，是比正圓更圓的圓，是夢之海中躍出的一只鏡面海豚，是宇宙間所有愛的結晶...美總是和善聯在一起的，所以，如果宇宙中真有一條善惡分界線的話，它一定在善這一面。
使用自己定義語法的腳本代碼生成數學圖形.相關軟件參見:數學圖形可視化工具,該軟件免費開源.QQ交流群: 367752815
我之前寫過有關水滴線的文章,數學圖形(1.15) 水滴線,那是講的二維曲線,而這一節給大家帶來的是三維水滴形.當然水滴形就是由一個水滴線旋轉180度,或半個水滴線旋轉360度而生成的.
(1)水滴
vertices = D1:100 D2:100 u = from 0 to (PI) D1 v = from 0 to (2*PI) D2 a = 10 b = rand2(0.25, 1) m = a/2*(1 + cos(u)) n = a*a/64*(sin(2*u) + 2*sin(u))*b x = n*cos(v) z = n*sin(v) y = array_max(m)-m
(2)Ding-Dong
#http://mathworld.wolfram.com/Ding-DongSurface.html # x^2+y^2=(1-z)z^2 vertices = 360 v = from -1 to 1 D2 x = v*sqrt(0.5 - v/2) y = v a = 10 x = x*a y = y*a
#http://mathworld.wolfram.com/Ding-DongSurface.html # x^2+y^2=(1-z)z^2 vertices = D1:100 D2:100 u = from 0 to (PI*2) D1 v = from -1 to 1 D2 x = v*sqrt(0.5 - v/2)*cos(u) y = v z = v*sqrt(0.5 - v/2)*sin(u) a = 10 x = x*a y = y*a z = z*a
(3)kiss
#http://mathworld.wolfram.com/KissSurface.html # x^2+y^2=(1-z)z^4 vertices = 360 v = from -1 to 1 x = v*v*sqrt(0.5 - v/2) y = v a = 10 x = x*a y = y*a
#http://mathworld.wolfram.com/KissSurface.html # x^2+y^2=(1-z)z^4 vertices = D1:100 D2:100 u = from 0 to (PI*2) D1 v = from -1 to 1 D2 x = v*v*sqrt(0.5 - v/2)*cos(u) y = v z = v*v*sqrt(0.5 - v/2)*sin(u) a = 10 x = x*a y = y*a z = z*a
(4)Larme
#http://www.mathcurve.com/courbes2d/larme/larme.shtml vertices = D1:100 D2:100 u = from 0 to (PI) D1 v = from 0 to (2*PI) D2 n = rand2(1, 10) m = 10*cos(u) n = 10*sin(u)*pow(sin(u/2), n) x = n*cos(v) z = n*sin(v) y = m
(5)Pear
#http://www.2dcurves.com/quartic/quarticp.html#pearshapedcurve vertices = D1:100 D2:100 u = from 0 to (2*PI) D1 v = from 0 to (PI) D2 m = -1 - sin(u) n = 0.5*(1 + sin(u))*cos(u) x = n*cos(v) z = n*sin(v) y = array_max(m)-m
(6)Teardrop
#http://mathworld.wolfram.com/TeardropCurve.html vertices = D1:100 D2:100 u = from 0 to (PI) D1 v = from 0 to (2*PI) D2 m = rand2(0, 10) n = 10*sin(u)*pow(sin(u/2), m) y = 10*cos(u) x = n*cos(v) z = n*sin(v)
