Klockan3 said:A smooth curve is a curve for which all of its derivatives exists, which gives that all derivatives must be continuous and smooth. A piecewise smooth curve is a curve for which there exists a set of intervals where the curve is smooth on each of those intervals. As an example, a curve might not be smooth on [a,b] but it is still piecewise smooth if it is smooth on both [a,c] and (c,b].
A smooth curve is a continuous mathematical function that has no sharp corners or breaks. This means that the slope of the curve changes gradually and continuously at all points.
A smooth curve is defined as a function that is infinitely differentiable, meaning that it has derivatives of all orders. This ensures that the curve is continuous and has no sharp corners or breaks.
A smooth curve has derivatives of all orders, while a non-smooth curve may have sharp corners or breaks and does not have derivatives at these points. This means that a smooth curve is continuously differentiable, while a non-smooth curve is not.
A piecewise smooth curve is a curve that is composed of multiple smooth segments, with each segment having a different mathematical definition. This means that the curve may have sharp corners or breaks at the points where the segments meet, but each individual segment is smooth.
A piecewise smooth curve may have sharp corners or breaks at the points where the segments meet, while a smooth curve is continuous and has no sharp corners or breaks. Additionally, a piecewise smooth curve is composed of multiple smooth segments, while a smooth curve is defined by a single mathematical function.