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Is a path the set of points from a to b? And is the stroke the "definition" (i.e. the color, shape, etc.) of the path?
And, how can you have a path with no stroke? Is this only because it is a computer drawing program? In the real world you can't have a path without a stroke can you?
If it matters, I am using Inkscape.
A path, as you said, is a set of points. It is a set of coordinates that define a shape. The path itself is only a set of numbers, a mathematical definition, nothing more. Anything you see on your screen is a visual representation of that path.
A stroke is a visual attribute that you can apply to a path. A stroke can have a defined width, color or a number of other properties. A stroke is a visual effect that is attached to the path.
You can have a path without a stroke, but you can't have a stroke without a path.
You're on the right track, but missing the mark a bit. Adobe defines paths as follows:
A path consists of segments and vertices. Segments are the lines or curves that connect vertices. Vertices define where each segment of a path starts and ends. Some Adobe applications use the terms anchor point and path point to refer to a vertex.
Essentially, a path is a line that connects anchor points. Paths can be open (e.g. a straight line) or they can be closed, to make a shape. Closed paths do not need to be filled with color, I think this is where you are confusing stroke with fill.
A stroke, on the other hand, is simply a line that follows your path. Strokes can be set to the inside, middle, or outside of your path and may vary in thickness, color, style, etc.
To answer your question about paths in the real world: no, they don't exist in the same sense as they do in computer graphics.
The best example I could give you of a real-world representation of paths would be to imagine your path as a stencil. You can either trace around the edge of that stencil (stroke) or you can color the stencil in completely (fill).
As far as stroke is concerned – from an artist’s vocabulary it is the real world that has substance – a brush/pen with paint/ink (substance of colour and thickness) will produce a ‘stroke’. Lines, vectors and paths can be plotted on a graph in mathematics and are computational.
The path is the shape. The stroke is the thickness of the line of the shape. Stroke can be zero… Which means the object doesn’t appear in preview mode but you would see it in outline mode.
Think of walking from point a (the front door of your home)to point b (your car assuming you have one!). Pt a is the start, pt b is the end. The path is a mathematical description of the shape of your walk from the door to your car. Maybe it’s a straight line, maybe it’s a c shaped walk, maybe it’s s shaped. If the walk has lots of twists and turns it’s easier to break it up into multiple paths each with its own start and end point. So the mathematical formula or path might sound like “start at pt a. Walk perfectly straight for 10 feet to pt b the turn 90 degreesAnd walk 20 feet in a right handed curve. You have arrived at pt c, your car” A to b is one segment and b to c is a second segment of your Path.
The path does not describe the walkway. The Stroke does. So the Stroke might say, “Your walkway is a red path that is initially 4 feet wide at point a but narrows to 2 feet wide at point b”. Now visualize the segment from a to b. It's a polygon wider at point then point b. Everything in Inkscape is described mathematically, so to describe the path, Inkscape will actually describe a set of 4 lines identifying the perimeter of the polygon and the angle between the end points of each vertex of the polygon. All together the formulas for the perimeter and the color that fills the polygon describes the Stroke. The Stroke is described by 4 line segments (the perimeter of the polygon) and the fill color. AND, each of the 4 line segments is a Path!
Finally, think of a c shaped stroke. The inside curve of the c is shorter than the outside curve. The path describing the inside curve is shorter than the path describing the outside curve. If you made the c shaped curve infinitely narrow, the inside and outside curve would be the same length. But for it to be a stroke you’d still need to describe both the inside and outside curves. And you’d still need to say what color fills between the curves for it to be a stroke.
A path has no width or color. It’s just directions from point a to point b. A stroke adds width and color to a path.
