6
votes
Accepted
Determining Rational Quadratic Bezier Curve Weights for Circle
Check out the section on Circular Arcs and Circles, from Ching-Kuang Shene's excellent computational geometry course notes:
[G]iven three control points P0, P1 and P2 such that P0P1 = P1P2 holds, if ...
- 881
5
votes
Accepted
NURBS topology classification
Before we begin, let us differentiate between two things:
The shape of a sphere,
and the topology of a sphere.
A NURBS surface can make the shape of a sphere. In a typical configuration, it will be '...
- 8,397
4
votes
Accepted
How do CAD programs render non-polygonal 3D objects?
Depends on the CAD program. But yes basically they do just what you describe they triangulate the model into a mesh/lines on demand and then display that. How they chose to do this depends on the CAD, ...
- 8,397
3
votes
How to sample 3D points to visualize a B-spline surface?
Based on your linked question, the problem appears to be that you don't get enough samples in highly curved areas of the surface. You could increase the sample density everywhere, but then you ...
- 24.7k
2
votes
Accepted
B spline curve generation in Python
In line 15 use the half-open interval, i.e.,
if u>=t[0][i] and u<t[0][i+1]:
Otherwise, at knot values, you evaluate two basis functions at the k=1 basis ...
- 166
2
votes
Problems with Subdivision Surfaces
Both T-splines and subdivision surfaces are capable of handling an arbitrary topology input mesh, whereas NURBS can only handle meshes with regular topology.
Complex NURBS objects are therefore made ...
- 1,188
2
votes
Accepted
Sweeping cross section along nurbs curve
Unfortunately, there are no real answers for this. The problem is called 'offsetting'. It is often investigated in the context of typefaces / fonts. There is no analytical or exact solution for ...
- 136
1
vote
Matrix form of an open uniform cubic b-spline
If you want to determine those matrices you have to use the knot vector $[0, 0, 0, 0, 4, 5, 6,...]$ and write out the expressions using the Cox-DeBoor algorithm. I believe you will need to compute the ...
- 1,188
1
vote
drawing NURBS: knots, multiplicity, divide by zero?
Your edit is correct. In this context 0/0=0. This definition is repeated by David F. Rogers on page 45 of An Introduction to NURBS with Historical Perspective. Even luckier the page is available on ...
1
vote
Accepted
How does the Lane Riesenfeld algorithm work?
What you're looking for is called de Boor's algorithm. It lets you compute a point on a b-spline curve by doing a series of linear interpolation (LERP) calculations. So, it works very much like the de ...
- 338
1
vote
Accepted
Normalize NURBS knot vector
The relative size of the spacing of knots is irrelevant for the NURBS curve. The only thing that matters is that they keep the relation. Note this may not be wise as parametrization may have other ...
- 8,397
1
vote
NURBS curve offset
Quickly Googling produces:
This related question on StackOverflow
"Computing offsets of NURBS curves and surfaces" (paper)
Discussions of 2.
To summarize them:
Suggests that this is impossible to ...
- 1,950
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