21.14 scherk.input

Scherk’s minimal surface, defined by: Scherk’s minimal surface ezcos(x)=cos(y). See: A Comprehensive Introduction to Differential Geometry, Vol. 3, by Michael Spivak, Publish Or Perish, Berkeley, 1979, pp. 249-252.

(xOffset, yOffset):DFLOAT                                   Offsets for a single piece

                                                            of Scherk’s minimal surface

drawScherk(m,n) ==                                          Draw Scherk’s minimal surface

  free xOffset, yOffset                                     on an m by n patch

space := createThreeSpace() for i in 0..m-1 repeat   xOffset := i*%pi   for j in 0 .. n-1 repeat

      rem(i+j, 2) = 0 => ‘iter                              Draw only odd patches

yOffset := j*%pi

      drawOneScherk(space)                                  Draw a patch

makeViewport3D(space, “Scherk’s Minimal Surface”)

scherk1(u,v) ==                                             The first patch that makes

  x := cos(u)/exp(v)                                        up a single piece of

  point [xOffset + acos(x), yOffset + u, v, abs(v)]         Scherk’s minimal surface

scherk2(u,v) ==                                             The second patch

x := cos(u)/exp(v) point [xOffset - acos(x), yOffset + u, v, abs(v)]

scherk3(u,v) ==                                             The third patch

x := exp(v) * cos(u) point [xOffset + u, yOffset + acos(x), v, abs(v)]

scherk4(u,v) ==                                             The fourth patch

x := exp(v) * cos(u) point [xOffset + u, yOffset - acos(x), v, abs(v)]

drawOneScherk(s) ==                                         Draw the surface by

                                                            breaking it into four

                                                            patches and then drawing

                                                          the patches makeObject(scherk1,-%pi/2..%pi/2,0..%pi/2,space==s,            var1Steps == 28, var2Steps == 28) makeObject(scherk2,-%pi/2..%pi/2,0..%pi/2,space==s,            var1Steps == 28, var2Steps == 28) makeObject(scherk3,-%pi/2..%pi/2,-%pi/2..0,space==s,            var1Steps == 28, var2Steps == 28) makeObject(scherk4,-%pi/2..%pi/2,-%pi/2..0,space==s,            var1Steps == 28, var2Steps == 28) void()