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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 ...
• 901
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, ...
• 8,437

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 ...
• 25k
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

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 ...
• 1,283
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 ...
• 156
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 ...
• 1,283
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 ...
• 348
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 ...
• 8,437

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