Build a repeating tiled watermark layout at any angle

Build a complete repeating watermark grid without guessing how many copies are needed beyond the visible edges. Provide the image canvas dimensions, watermark tile dimensions, horizontal and vertical spacing, and a rotation angle. The calculator returns stable center coordinates for every rotated tile that touches the canvas, including partial tiles at its boundaries. The layout is centered on the canvas, uses consistent row and column identifiers, and can be passed directly to an image, SVG, PDF, or canvas rendering pipeline.

Define the canvas and watermark tile

Start with the width and height of the destination canvas, then provide the unrotated width and height of one watermark tile. All dimensions use the same unit, which will usually be pixels but can also be points or another coordinate unit when a renderer uses a different system. The tile must fit within the canvas in both dimensions.

That validation catches accidental swaps, incorrect unit conversions, and requests that would produce a single oversized stamp instead of a repeating pattern. Next, set horizontal and vertical spacing. These values are gaps between tile edges along the grid's own axes, not absolute distances on the screen after rotation.

Zero creates edge-to-edge tiles, while larger values create a lighter pattern with more empty space. The returned origin is the canvas center. Row zero and column zero identify the tile centered at that origin, giving downstream code a stable anchor even when the canvas dimensions, spacing, or angle later change.

Understand rotation and edge coverage

The angle rotates the entire lattice clockwise around the center of the canvas. Any finite degree value is accepted and normalized into one revolution, so minus thirty degrees and three hundred thirty degrees produce the same layout. Rotation expands the region that the grid must cover: a tile whose center lies outside the image can still have a corner visible inside it.

The calculator therefore projects the canvas onto the rotated grid axes, creates a bounded set of candidate rows and columns, and tests each rotated tile rectangle against the canvas rectangle. A position is returned whenever those rectangles touch or overlap. This exact intersection rule avoids missing corner tiles and avoids emitting distant tiles that a simple oversized bounding box would include.

Coordinates describe tile centers because center-based rotation is supported consistently by raster libraries, SVG transforms, CSS transforms, and canvas APIs. Partial boundary tiles are intentional; let the destination renderer clip them to the canvas.

Render and reproduce the layout

Process the positions in their returned order, from lower row identifiers to higher ones and then from lower columns to higher columns. The row and column identifiers are useful for debugging, alternating opacity, or selecting every other tile, but they do not replace the coordinates. Numeric coordinates are rounded to six decimal places so serialized results remain stable across calls while retaining subpixel precision for high-resolution output.

If you need a staggered brick pattern, random jitter, individually rotated marks, or text measurement, apply those transformations after receiving this regular grid or use a specialized compositor.