Both Bézier curves and splines are mathematical representations used to define smooth curves in graphics, including for manipulating text. However, they differ in their underlying structure:

• Bézier Curves: These are defined by a set of control points that influence the shape of the curve. The curve does not necessarily pass through the control points, but they dictate its direction and curvature. The more control points, the more complex and precise the curve can be.
• Splines: Splines are piecewise polynomial curves that are joined together smoothly. They are typically defined by a set of control points and constraints that ensure continuity between different segments of the spline. Common types include Bezier splines and B-splines.

Advantages and Disadvantages:

In summary, Bézier curves are easier to learn and use for basic text effects, while splines offer greater control and smoothness for more advanced and intricate designs.

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Path operations are functions that allow you to combine or modify vector paths. They are essential for creating complex shapes from simpler ones, reducing file size, and streamlining the design process.

Here are four common path operations:

1. Union: Combines two or more paths into a single path. The overlapping areas are merged.
2. Intersection: Creates a new path that consists only of the overlapping area of two or more paths.
3. Difference: Subtracts one path from another. The result is a new path that is the area of the first path excluding the overlapping area with the second path.
4. Exclusion: Similar to difference, but the roles of the paths are reversed. The result is a new path that is the area of the second path excluding the overlapping area with the first path.

Example: Creating a shape with a hole

You could create a circle and then use the difference operation to subtract that circle from a square, resulting in a square with a circular hole in the middle. This is a common technique for creating logos and other designs.

To create a text effect where letters flow along a curved path, a designer would typically follow these steps:

1. Create a Path: The first step is to define the curved path along which the text will flow. This is usually done using a drawing tool within the graphics package, such as a Bézier curve tool. The designer will click to create anchor points that define the shape of the curve.
2. Apply the Text Object: The text object containing the desired words is then created.
3. Link Text to Path: The text object needs to be linked to the path. This is typically done using a "path" or "curve" option within the text properties. This links the text's baseline and character positions to the curve's geometry.
4. Adjust Anchor Points: The anchor points of the curve can be adjusted to fine-tune the flow of the text. Moving these points will alter the curve's shape and, consequently, the way the text follows it. The designer can also add or remove anchor points to create more complex curves.
5. Refine Appearance: The appearance of the text can be further refined by adjusting font style, size, colour, and adding effects like shadows or outlines to enhance the visual impact.
6. Consider Kerning and Leading: It's important to review kerning and leading to ensure the text remains readable when flowing along the curve. Adjustments may be necessary to prevent letters from overlapping or becoming too compressed.

Key terminology used in this process includes path (the curved line), anchor points (the points that define the curve's shape), and Bézier curves (the type of curve used to create the path). The linking of the text to the path is crucial for maintaining the desired visual effect.