Apparatus and method for printing on articles having a non-planar surface

1. A method for printing on an article having a non-planar surface, the method comprising:

obtaining coordinates or a geometry for a non-planar surface of an article;

determining a tangent orientation for a print head using a sabre angle based upon a specified or desired print density (dpi) and calculations of a tangent/slope for a range of points on the non-planar surface that are within an intended print region or area;

measuring or determining offset distances between successive points along or about the sabre line;

using the tangent orientation and positioning the print head relative to the non-planar surface of the article; and

printing on the intended print region or area of said article.

2. The method of claim 1 , wherein said article is a plastic container.

3. The method of claim 2 , wherein the plastic container is a plastic bottle.

4. The method of claim 1 , wherein the positioning of the print head relative to the non-planar surface of said article involves a sabre angle, a process direction angle, and a cross process direction angle.

5. The method of claim 4 , wherein the process direction and the cross process direction angles are determined from or using the sabre angle.

6. The method of claim 1 , wherein a minimum or specified number of points are selected or picked along or about the sabre line.

7. The method of claim 6 , wherein the minimum or specified number of points are used to determine additional tangent points on the surface.

8. The method of claim 6 , an iterative process is employed to increase the number of points selected or picked along or about the sabre line to provided improved numerical convergence.

9. The method of claim 1 , wherein the range of points on the non-planar surface that are within an intended print region or area are, at least in part, based on a specified or determined print width associated with a printing surface or substrate.

10. The method of claim 1 , wherein the geometry of the non-planar surface is identified from or provided by three-dimensional drafting or modeling software.

11. The method of claim 1 , wherein the determination of offset distances involves using a least-squares analysis or a line-fitting calculation.

12. The method of claim 1 , including assessing a line placement on the non-planar surface with respect to the sabre line; calculating a distance between coordinates; and applying trigonometric functions between distances calculated between coordinates and the offset distances between each coordinate point to provide a print angle for that point.

13. The method of claim 12 , including providing print angles for a plurality of points.