Sphere of mathematical graphics, elliptical sphere, capsule body, and spam.

The ball is closely related to the circle. One is three-dimensional and the other is two-dimensional. For details, see circle and elliptical.

 

(1) method 1 of Sphere

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)

 

Gridlines of the ball:

(2) Two other ways of writing sphere

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)

The two statements generate the same image.

 

(3) colored balls

You can set the vertex color by setting values for the RGB variable in the script.

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) Arc Surface

Reduce the range of the second dimension of the ball to obtain the Arc Surface.

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) elliptical sphere

#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) Capsules

Stretch the sphere up and down to get the capsule body.

 

(7) spam

The distance from the vertices on the sphere to the ball center can be changed regularly to get a changeable ball, such as a prickly ball.

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)