## Introduction

Interlacing is the primary digital process used to make a lenticular picture. It converts a lenticular sequence to a printable image suitable for picture fabrication.

Interlacing is done in two steps:

Creation of the pure interlace,

Rendering the pure interlace to print.

This is illustrated in the figure below.

Each step has its parameters and algorithms.

## The pure interlace

The pure interlace is made from vertical cells. The height of each cell is equal to the height of the sequence image, and the number of cells is equal to the number of lenticules in the picture.

Each cell is made from columns. The column's height equals the cell's height. The number of columns in each cell is equal to the sequence length.

The unit length of the pure interlace is a pixel. The sizes of the pure interlace elements are whole numbers (of pixels). In Grape, the column width is derived from the following formula:

(column width) = [(printing density) / pitch / (sequence length)]

where [x] denotes the nearest integer to x when x > 1, and 1 when x < 1. For example, if the printing density is 720 pixels/inch, the pitch is 40.15lpi, and the sequence length is 9, then the column width is 2 pixels. The pixel width of the pure interlace is (number of cells)*(sequence length)*(column width).

Each column is filled with a sample from a sequence image, the width of which is the column width. A special algorithm, called the "sampling algorithm," is in charge of this sample preparation. Several sampling algorithms are used in image processing science. Common sampling algorithms are "nearest neighbor," "linear," and "spline." In most cases, sampling involves loss of information.

## Rendering

Rendering is converting the pure interlace to an image that will be printed and used to make the lenticular picture. The rendered image is a resized version of the pure interlace.

The vertical resizing is applied to match the printed image height with the required picture height. The horizontal resizing matches the printed cell size to the lenticular pitch.

Image resizing is accomplished with a resampling algorithm. The word "resampling" is a combination of "reconstruction" and "sampling," which implies that a resampling algorithm is a combination of sampling and reconstruction algorithms. Several resampling algorithms are used in image processing science.

In general, rendering reduces the resolution of the pure interlace. The resolution reduction is not uniform across the image area. In singular cases where the ratio on the right-hand side of the column width equation happens to be a whole number, rendering can be skipped, and the pure and the rendered interlaces become identical. In such a case, there will be no reduction in the pure interlace resolution.

## Raster versus vector representation

In computer science, images are represented in raster or vector formats. In the raster format, the image is an array of numbers, where each number represents a pixel color value. In the vector format, the image is represented by mathematical formulas.

One can make the pure interlace in a vector format. If the sequence images are also given in a vector format, this can be done without sampling, thus preserving the information in the sequence. However, to print the vector interlace, it must be rasterized, which requires a resampling algorithm. In the bottom line, the raster and vector representations will yield similar, if not identical, visual results.

The concept of the vector interlace was proposed to me recently by Rob Noy (private correspondence).

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