6.4.8 Repeat Warp

From [pov:6.7.12.6.2]:
The repeat warp causes a section of the pattern to be repeated over and over. It takes a slice out of the pattern and makes multiple copies of it side-by-side. The warp has many uses but was originally designed to make it easy to model wood veneer textures. Veneer is made by taking very thin slices from a log and placing them side-by-side on some other backing material. You see side-by-side nearly identical ring patterns but each will be a slice perhaps 1/32th of an inch deeper.

The syntax for a repeat warp is

REPEAT_WARP:
    warp { repeat <Direction> [REPEAT_ITEMS...] }

REPEAT_ITEMS:
    offset <Amount> | flip <Axis>

The repeat vector specifies the direction in which the pattern repeats and the width of the repeated area. This vector must lie entirely along an axis. In other words, two of its three components must be 0. For example

pigment {
  wood
  warp { repeat 2*x }
}

which means that from x=0 to x=2 you get whatever the pattern usually is. But from x=2 to x=4 you get the same thing exactly shifted two units over in the x-direction. To evaluate it you simply take the x-coordinate modulo 2. Unfortunately you get exact duplicates which isn't very realistic. The optional offset vector tells how much to translate the pattern each time it repeats. For example

pigment {
    wood
    warp {repeat x*2  offset z*0.05}
  }

means that we slice the first copy from x=0 to x=2 at z=0 but at x=2 to x=4 we offset to z=0.05. In the 4 to 6 interval we slice at z=0.10. At the n-th copy we slice at 0.05 n z. Thus each copy is slightly different. There are no restrictions on the offset vector.

Finally the flip vector causes the pattern to be flipped or mirrored every other copy of the pattern. The first copy of the pattern in the positive direction from the axis is not flipped. The next farther is, the next is not, etc. The flip vector is a three component x, y, z vector but each component is treated as a boolean value that tells if you should or should not flip along a given axis. For example

pigment {
    wood
    warp {repeat 2*x  flip <1,1,0>}
	}

means that every other copy of the pattern will be mirrored about the x- and y- axis but not the z-axis. A non-zero value means flip and zero means do not flip about that axis. The magnitude of the values in the flip vector doesn't matter.