Contents
How do you construct a closed curve?
A closed curve is any design that has no end points drawn on a flat surface . In other words, if you draw a design, without lifting your pencil, and end at the point you began, it would be a closed curve. There is no way in or out of the shape.
Which spline curve generate closed curves?
The open B-spline curve C(u) of degree p defined on the above constructed n+1 control points and n+p+2 knots is a closed curve with Cp-1 continuity at the joining point C(u0) = C(un+1).
Who is simple closed curve?
In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves. A curve which starts and ends at the same point without crossing itself is called a simple closed curve. A circle is a simple closed curve.
How to generate closed curves for a B-spline curve?
There are many ways to generate closed curves. The simple ones are either wrapping control points or wrapping knot vectors. Suppose we want to construct a closed B-spline curve C ( u) of degree p defined by n +1 control points P0 , P1., Pn.
When does a curve become a closed on?
The shape of the curve does not change very much. Then, control points 1 and 8 are made identical as shown in Figure (c). It is clear that the gap between the first and last points of the curve is closer. Finally, the curve becomes a closed on when control points 2 and 9 are made identical as shown in Figure (d).
How are control points made identical in a closed curve?
In the figure, control point pairs 0 and 7, 1 and 8, and 2 and 9 are placed close to each other to illustrate the construction. Figure (b) shows the result of making control points 0 and 7 identical. The shape of the curve does not change very much. Then, control points 1 and 8 are made identical as shown in Figure (c).
How to make a closed curve with p + 2 knots?
Add p +2 knots and wrap around the first p +2 knots: un+1 = u0 , un+2 = u1 , …, un+p = up-1 , un+p+1 = up , un+p+2 = up+1 as shown in the following diagram. In this way, we have n + p +2 = ( n +1) + p + 1 knots.