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This is a very nice tutorial. One small point. Coordinates are expressed in a "X/Y" format which was very confusing to me because I was thinking of them as rati

by kghose 12y ago

This is a very nice tutorial. One small point. Coordinates are expressed in a "X/Y" format which was very confusing to me because I was thinking of them as ratios. It might be better to print them the commonly used tuple convention (X,Y)

TheRealPomax 12y ago
nice, file it and I'll see how easily I can get on that.
TuringTest 12y ago
The tutorial doesn't work for me. It provides a thorough explanation of the polynomials, but it fails to explain the very basics of how the curves are laid out on the plane. It does a nice work of explaining how a circle is drawn, but its explanation of how x and y are calculated for a Bézier curve doesn't make sense to me: "Bézier curves use the "binomial polynomial" for both x and y." If the same function on "t" is used for both x and y, they would always have the same value, and the "curve" is always a diagonal with 45 degrees. What am I missing? I can't infer it from the tutorial. Also, it introduces the idea of a "control point" and starts using it, but never manages to define what it is, or how it is represented in the equation or graphically. It merely labels some curves as "P1", "P2"... in the graphs and telss that these somehow change the shape of the curves, and tells us that they have an associated linear "wi" weight; but again, the way in which the (x1, y1) pairs are connected to the binomial and polynomial term is never spelled out, and left as an exercise to the reader. Things are further complicated by the mysterious "strength" parameter "S" in the graphs, which is also unexplained, never used again, and appears right when we're trying to understand the difficult concept of a control point to further confuse things. I had followed the tutorial quite well up to that point, but that section lost me completely.
- colomon 12y ago
  Haven't read the article, but I do know a bit about these curves. Bézier curves do indeed use the "binomial polynomial" for both x and y. That polynomial defines how the control points are used (with t) to calculate the point on the curve. So for the simplest example, a linear Bézier curve, the curve is a straight line from the first control point to the second.

by kghose 12y ago

TheRealPomax 12y ago

nice, file it and I'll see how easily I can get on that.

TuringTest 12y ago

The tutorial doesn't work for me. It provides a thorough explanation of the polynomials, but it fails to explain the very basics of how the curves are laid out on the plane. It does a nice work of explaining how a circle is drawn, but its explanation of how x and y are calculated for a Bézier curve doesn't make sense to me: "Bézier curves use the "binomial polynomial" for both x and y." If the same function on "t" is used for both x and y, they would always have the same value, and the "curve" is always a diagonal with 45 degrees. What am I missing? I can't infer it from the tutorial. Also, it introduces the idea of a "control point" and starts using it, but never manages to define what it is, or how it is represented in the equation or graphically. It merely labels some curves as "P1", "P2"... in the graphs and telss that these somehow change the shape of the curves, and tells us that they have an associated linear "wi" weight; but again, the way in which the (x1, y1) pairs are connected to the binomial and polynomial term is never spelled out, and left as an exercise to the reader. Things are further complicated by the mysterious "strength" parameter "S" in the graphs, which is also unexplained, never used again, and appears right when we're trying to understand the difficult concept of a control point to further confuse things. I had followed the tutorial quite well up to that point, but that section lost me completely.

colomon 12y ago
Haven't read the article, but I do know a bit about these curves. Bézier curves do indeed use the "binomial polynomial" for both x and y. That polynomial defines how the control points are used (with t) to calculate the point on the curve. So for the simplest example, a linear Bézier curve, the curve is a straight line from the first control point to the second.