數學圖形之球面,橢球面,膠囊體,刺球.

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球與圓很相關,一個是三維,一個是二維,可以參考下:圓,橢圓

 

(1)sphere的第一種寫法

vertices = D1:100 D2:100t = from 0 to (PI*2) D1r = from 0 to 1 D2x = 2*r*sin(t)*sqrt(1-r^2)y = 2*r*cos(t)*sqrt(1-r^2)z = 1-2*(r^2)

 

球的網格線:

(2)sphere的另兩種寫法

vertices = dimension1:36 dimension2:72u = from 0 to (2*PI) dimension1v = from (-PI*0.5) to (PI*0.5) dimension2r = 10.0x = r*cos(v)*sin(u)y = r*sin(v)z = r*cos(v)*cos(u)

vertices = dimension1:36 dimension2:72u = from 0 to (2*PI) dimension1v = from 0 to (PI) dimension2r = 10.0x = r*sin(v)*sin(u)y = r*cos(v)z = r*sin(v)*cos(u)

兩種寫法產生的圖形是一樣的

 

(3)彩色球

在指令碼中給rgb變數設值,就能設定頂點色.

vertices = dimension1:72 dimension2:72u = from 0 to (2*PI) dimension1v = from (-PI*0.5) to (PI*0.5) dimension2x = cos(v)*sin(u)y = sin(v)z = cos(v)*cos(u)a = 10.0r = (x+1.0)/2g = (y+1.0)/2b = (z+1.0)/2x = a*xy = a*yz = a*z

(4)圓弧面

將球的第二維度範圍減小,即得到圓弧面

vertices = dimension1:36 dimension2:72u = from 0 to (2*PI) dimension1v = from (PI*0.1) to (PI*0.5) dimension2r = 10.0x = r*cos(v)*sin(u)y = r*sin(v)z = r*cos(v)*cos(u)

 

(5)橢球面

#http://www.mathcurve.com/surfaces/ellipsoid/ellipsoid.shtmlvertices = D1:100 D2:100u = from 0 to (2*PI) D1v = from (-PI*0.5) to (PI*0.5) D2a = rand2(1, 10)b = rand2(1, 10)c = rand2(1, 10)x = a*cos(v)*sin(u)y = b*sin(v)z = c*cos(v)*cos(u)

 

(6)膠囊體

將球面向上下兩頭展開,即得到膠囊體

 

(7)刺球

將球面上頂點到球心的距離,有規律地變化,可以得到多變的球,如刺球

vertices = dimension1:129 dimension2:65u = from 0 to (2*PI) dimension1v = from (-PI*0.5) to (PI*0.5) dimension2n =4a = from 0 to 128 D1b = from 0 to 64 D2t = (mod(a, n) + mod(b, n))/n*4r = 10.0 + tx = r*cos(v)*sin(u)y = r*sin(v)z = r*cos(v)*cos(u)