Spiral surface of mathematical graphics

Spiral surface of mathematical graphics
This section describes how to generate spiral surfaces. for related software, see: Mathematical graphics visualization tool. Use script code with custom syntax to generate mathematical graphics. I have previously written a C ++ program for generating a ring. The code is published on the Generation Algorithm of the Spire graph (1) the positive spiral surface is to make the initial position of a straight line l overlap with the X axis, and then let the line l side rotate at a constant speed around the Z axis, while the side moves at a constant speed along the Z axis, then the surface scanned by a straight line under the synthesis of the two motion is the positive spiral surface. Obviously, the positive spiral surface can be seen as a straight line, that is, it is a straight surface. Why is it called Zheng ?. According to the formula, the circle is pulled up and then rotated several more times. copy the code vertices = D1: 32 D2: 360 u = from 0 to 3 D1v = from 0 to (8 * PI) D2 x = u * cos (v) y = v * 0.5z = u * sin (v) Copy code (2) positive spiral surface random (helicoiddroit) plus positive spiral surface of random parameters, and stretch outward. copy the code vertices = D1: 32 D2: 360 u = from 0 to 3 D1v = from 0 to (8 * PI) D2 a = rand2 (0.1, 1) B = rand2 (1, 5) x = (B + u) * cos (v) y = v * az = (B + u) * sin (v) copy the code (3) Check the formula of the Archimedes spiral plane. The Archimedes spiral plane is the positive spiral plane that changes the height parameter. Copy the Code # http: // 202.113.29.3/nankaisourc E/graphics/differential % 20 geometry/t060307.htm # http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/ vertices = D1: 100 D2: 360 u = from 0 to (2) D1v = from 0 to (8 * PI) d2 x =-u/SQRT2 * cos (v) y = u/SQRT2 + v/PI/2z =-u/SQRT2 * sin (v) Copy code (4) sincos spiral copy code vertices = D1: 720 D2: 72 p = from 0 to (8 * PI) D1q = from 0 to (PI) d2 a = 5 h = rand2 (0.5, 5) x = a/2 * (cos (p) + cos (q) y = h * (p + q) /2z = a/2 * (sin (p) + sin (q) u = Pv = q * 3 copy code (5) Progressively Open Spiral copy Code # http: // 202.113.29.3/nankaisource/graphics/differential % 20 geometry/t060306.htm # http://www.bb.ustc.edu.cn/jpkc/xiaoji/wjf/kj/ vertices = D1: 100 D2: 360 u = from 0 to (4 * PI) D1v = from 0 to (8 * PI) D2 x = 2 * [cos (u + v) + u * sin (u + v)] y = vz = 2 * [sin (u + v)-u * cos (u + v)] Copy code (6) hyperbolic sine spiral surface copy code vertices = D1: 360 D2: 72u = from 0 to (5 * PI) D1v = from 0 to (4 * PI) d2 a = 5 h = rand2 (5, 20) X = a * sh (u-v) * cos (u + v) y = h * (u + v) z = a * sh (u-v) * sin (u + v) w = 50x = limit (x,-w, w) z = limit (z,-w, w) Copy code (7) developable helicoid copy Code # http://www.mathcurve.com/surfaces/helicoiddeveloppable/helicoiddeveloppable.shtml vertices = dimension1: 1000 dimension2: 72 u = from 0 to (18 * PI) dimension1v = from 0 to (2 * PI) dimension2 a = rand2 (1, 10) B = rand2 (1, 10) x = a * (cos (u)-v * sin (u )) z = a * (sin (u) + V * cos (u) y = B * (u + v) Copy code (8) Helicoid_wiki a spiral surface found on the Wiki: copy Code # http://en.wikipedia.org/wiki/Catenoid vertices = D1: 400 D2: 100 u = from (0) to (PI * 16) D1v = from (0) to (4) d2 t = rand2 (-PI, PI) s = sin (t) c = cos (t) x = c * sinh (v) * sin (u) + s * cosh (v) * cos (u) z = u * c + v * sy =-c * sinh (v) * cos (u) + s * cosh (v) * sin (u) Copy code (9) helicoidcercle copy Code # http://www.mathcurve.com/surfaces/helicoidcercle/helicoidcercle.s Html vertices = D1: 72 D2: 1200 u = from 0 to (PI) D1v = from 0 to (36 * PI) D2 a = 1 h = 1/(2 * PI) x = a * cos (u) * cos (v) z = a * cos (u) * sin (v) y = B * sin (u) + h * v copies the code and returns to the first script. In the positive spiral plane, the code is generated as follows: "Then, the l side of the line rotates at a constant speed around the Z axis, one side moves at a constant speed along the Z axis. "If one side rotates at a constant speed around the Z axis and one side moves at a constant speed along the Z axis, what kind of surface will it generate? In this way, each curve can generate a spiral surface. here are two examples: (10) power spiral surface copy code vertices = D1: 32 D2: 360 u = from 0 to 2 D1v = from 0 to (8 * PI) d2 a = rand2 (-2, 2) w = pow (u, a) x = u * cos (v) y = v * 0.5 + wz = u * sin (v) copy code (11) refers to the Code vertices = D1: 32 D2: 360 u = from 0 to 2 D1v = from 0 to (8 * PI) d2 a = rand2 (0, 2) w = pow (a, u) x = u * cos (v) y = v * 0.5 + wz = u * sin (v)