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phiby
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I have been reading about B-Splines for a couple of days now, but I just can't get what a knot is! I have referred multiple books & websites. Can someone explain knots to me a in a simple language?
Assume a B-spline with n+1 control points (0 to n) & d control points per curve(polynomial of degree (d-1)). The text says that B-Splines are defined only in the interval from knot value ud-1 to un+1. So what are the extra knots at the beginning and end of the knot vector for?HallsofIvy said:"Knots" are the points where the "pieces" change. That is, where the formula changes.
Knots are points on a curve or surface that define its shape. B-splines, or basis splines, are mathematical functions that are used to create smooth curves or surfaces between these knots.
Knots and B-splines are commonly used in computer graphics and animation to create smooth, realistic curves and surfaces. They are also used to control the shape and movement of objects in 3D animations.
Uniform knots are evenly spaced along a curve or surface, while non-uniform knots have varying spacing. Non-uniform knots allow for more flexibility in shaping the curve or surface, but can also lead to more complex calculations.
B-splines allow for more control over the shape of a curve or surface compared to Bezier curves. B-splines also have a greater ability to represent complex shapes and can be easily extended to higher dimensions.
One limitation of using knots and B-splines is that they can be computationally intensive, especially when using non-uniform knots. Additionally, the placement of knots can greatly affect the resulting curve or surface, so careful consideration must be taken when choosing knot locations.