# Questions tagged [nurbs]

NonUniform B-Spline (NURBS) is a method to describe parametric curves/surfece. TYpically used as base poriniteves in CAD modelling.

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### How to remove a control point from a NURBS curve?

I am trying to write an algorithm to remove a control point from a NURBS curve, similarly to what can be achieved using the CVREMOVE command in AutoCAD. I searched online but I was unable to find a ...
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### How can I determine ideal NURBS surface control points for a multi-patch sphere?

I would like to know how to "parameterize" the control points for the 6 faces of the commonly used NURBS mutli-patch sphere ("Cobb sphere"), for an arbitrary-size control point ...
103 views

### Can STEP files contain polygon data? How do I get a smoother mesh out of a STEP file?

I am trying to work with a .STEP file I have received. Upon opening it in CAD Assistant, I find its surface as jagged lines, like a low poly model. When I export it as OBJ from there, the edges and ...
1 vote
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### Matrix form of an open uniform cubic b-spline

I'm trying to find the matrix form for the equation of a cubic b-spline. More specifically, the "middle" part, S_i(t), is pretty straightforward and available everywhere: ...
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### Sweeping cross section along nurbs curve

I have a nurb/b-spline curve in 2d, and I want to sweep a cross section along it. Here is the curve and resulting "tube" (green points are control points): However, as you can see, the ...
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1 vote
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### Geodesic approximation algorithms for minimal geodesic curvature

Introduction I am building an application in which given a surface and a pair of points on it, an analytic expression of some geodesic arc (preferably the one with the shortest length), between them ...
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### Determining Rational Quadratic Bezier Curve Weights for Circle

I am trying to create a spherical interpolation with 3 points. I'm currently using Quadratic Bezier Interpolation but have been told I should use Rational Quadratic Bezier Curve in order to get a ...
43 views

### Projecting a point on a Freefrom surface

My first issue is getting a set of planes and a set of points as input, an find the projection of the those points on the nearest plane. That was pretty easy, where i just calculate the normal of the ...
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### Problems with Subdivision Surfaces

It sounds like Subdivision Surfaces are better than NURBS but not as good as T-splines. I would like to know some of the disadvantages of Subdivision Surfaces, what they can't do or what they do ...
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### drawing NURBS: knots, multiplicity, divide by zero?

I'm trying to grasp how NURBS curves work. I think I understand the principle, but I'm unsure about the formula. Here, I base myself on this course. From a DXF file, I got the following parameters: <...
• 131
1 vote
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### B spline curve generation in Python

I am using the de boors algorithm to generate B splines in python. However I am getting spikes in the final figure. I do not understand why this happens. I am posting my code here for reference <...
1 vote
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### How does the Lane Riesenfeld algorithm work?

I understand de Casteljau's algorithm and I am familiar although not fully experienced with B-Splines. I am trying to understand the geometric interpretation of B-splines through the algorithm (just ...
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### Normalize NURBS knot vector

I have NURBS surface data. I have a list of control points, knot vectors in U and V params and the degree. The U knot vector lies in range -3.14 to 3.14 and the knot V vector lies in range -100 to 100....
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### How do CAD programs render non-polygonal 3D objects?

How CAD programs handle displaying B-Reps and NURBS/T-Splines in their viewports? Assuming viewport uses OpenGL API - are those programs transform every object into triangles and creating/deleting ...
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### How to sample 3D points to visualize a B-spline surface?

Given that I have implemented a function called calc_bspline_surf() in C, and that function has the following declaration: ...
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### Making surface with common parametrization from bunch of other surfaces

I have bunch of surfaces, like in these two images: Currently to make single surface with common parametrization I sample points uniformly from all source surfaces, and fit single NURBS surface from ...
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### NURBS topology classification

In what sense is it true that a NURBS surface can only have the topology of a plane, cylinder or torus? For example I can do a NURBS sphere. Is the sphere homeomorphic to one of the above surfaces?
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### NURBS knot multiplicity

In Splitting of NURBS curves there the answer relied on "maximum knot multiplicity". In order not to mix-up different topics I would like to kindly ask to answer it in another question: what is this "...
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### Splitting of NURBS curves

Splitting Bezier curve into two parts at some parameter t is easy thanks to De Casteljau's algorithm. Is there a similar algorithm for NURBS curves? How to split a ...
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### NURBS curve drawing

How to draw a NURBS curve? Compared with Bezier curve, I just evaluate the Bernstein polynomial, multiply it with control point positions and that's it. Looking at the "General form of a NURBS curve"...
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### NURBS curve offset

One of the benefits of NURBS curve over, say Bezier curve, is the ability to create offset curves exactly. How to proceed with such computation? Do I just translate the control points?
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