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 in three dimensions; and

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

wherein the positioning of the print head involves a sabre angle, a cross process angle, and a process angle; and the sabre angle is used to calculate the cross process angle and the process angle; and based on the desired print resolution, sabre angle, and print dimensions, points are selected along or about a sabre line; and a minimum or specified number of points are used to refine tangents at one or more points on the non-planar surface.

2. The method of claim 1 , including selecting a range of points based on specified or determined print width associated with a printing surface or substrate.

3. The method of claim 1 , wherein the geometry of the non-planar surface is identified from or provided by a common reference entity.

4. The method of claim 3 , wherein the common reference entity is provided by three-dimensional drafting or modeling software.

5. A method for priming 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 in three dimensions; and

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

wherein the positioning of the print head involves a sabre angle, a cross process angle, and a process angle; and the sabre angle is used to calculate the cross process angle and the process angle; and based on the desired print resolution, sabre angle, and print dimensions, points are selected along or about a sabre line; and offset distances between successive points are determined.

6. The method of claim 5 , wherein the determination of offset distances involves using a least-squares analysis or a line-fitting calculation.

7. The method of claim 1 , wherein the coordinates or geometry for the non-planar surface are determined prior to calculating one or more angles associated with the positioning of the print head.

8. The method of claim 1 , including:

providing an article with a non-planar surface having a print area or print region;

providing or obtaining a desired print resolution and an associated sabre line;

selecting or identifying a number of points near the sabre line that are on or within the print area or print region;

determining a tangent for the non-planar surface; and positioning a print head relative to said article using information associated with the tangent.

9. The method of claim 1 , including:

providing a plurality of points in two dimensions, the plurality of points representing points selected or identified in connection with a print surface/substrate;

providing a sabre line with a sabre angle;

selecting a plurality of points on the print surface and identifying three-dimensional coordinates at the print surface for the plurality of points;

providing a minimum number of points along or about the sabre line;

measuring the offset distances between successive points;

assessing a line placement on the surface with respect to the sabre line;

calculating the 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.

10. The method of claim 9 , including providing print angles for a plurality of points.

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

(a) selecting a plurality of points based on a print width on an identified printing surface;

(b) identifying coordinates with respect to a common reference point;

(c) selecting a plurality of points along a sabre line, the sabre line having a sabre angle;

(d) obtaining an offset distance between successive points along the sabre line;

(e) selecting a coordinate that describes the curvature of the printing surface;

(f) determining a print angle based on the selected coordinate;

(g) using a distance equation to determine the distances between identified coordinates; and

(h) using trigonometric functions between the determined distance between identified coordinates and the offset distance to provide a print angle for a specific point.

12. The method of claim 11 , including repeating one or more steps (d) through (h) for a plurality of the points selected in step (a).

13. The method of claim 11 , including plotting a plurality of points describing the nature of point deviation or the tangent/slope at points at the reference sabre angle.

14. The method of claim 13 , including using line fitting techniques to find an average angle for the slope associated with the plotted points.

15. The method of claim 11 , wherein one or more steps of the method are repeated for a non-sabre angle.

16. An apparatus for printing on an article having a non-planar surface, the apparatus comprising:

a print head including a plurality of nozzles;

a means for determining a tangent for a print surface or print substrate on a non-planar print surface of said article; and

a means for positioning the print head relative to the non-planar surface based on the determined tangent using a sabre angle, a cross process angle, and a process angle;

wherein the apparatus is configured to use the sabre angle to calculate the cross process angle and the process angle; the apparatus is configured to select points along or about a sabre line based on the desired print resolution, sabre angle, and print dimensions; and the apparatus is configured to use a minimum or specified number of points to refine tangents at one or more points on the non-planar surface.

17. The apparatus of claim 16 , wherein the means for positioning the print head comprises a mechanical arm providing at least two degrees of rotational freedom.