nurbs | Non-Uniform Rational B-Splines of any dimensionality | 3D Animation library

I'm trying to calculate the centroid of a 3D mesh of triangles.

EDIT : it turns out I was not, I was trying to calculate the center of gravity, which is not the same

My code is made of bits and pieces, mainly :

• This nice paper by Cha Zhang and Tsuhan Chen
• SO : How to calculate the volume of a 3D mesh object the surface of which is made up triangles
• SO : How to compute the centroid of a mesh with triangular faces?

I compared my results to those provided by Rhino. I calculate the centroid and volume :

• of the reference NURBS volume with Rhino 7
• of a 27k triangle mesh with Rhino 7
• of a simplified 1k triangle mesh with Rhino 7
• of the same 1k triangle mesh with my code.

As you can see, it works great to calculate the volume, but not for the centroid, and i can't seem to know why. I need the error to be less than 0.01. I checked everything several times, but there must be something obvious.

I'm not great with numerical instability :

• should I work in milimeters instead of meters ?
• should I calculate the tetrahedrons signed volume with another point than the origin, as suggested by galinette in the second reference ? I tried and it didn't improve much.

MY CODE

Before calculationg anything, I check that my mesh is correct (code not provided) :

• closed mesh, no naked edges or any holes ;
• the vertices of all triangles are ordered consistently, i.e. triangles are correctly oriented towards the outside of the mesh.

I am wondering how you would model arbitrarily complex Bézier curves. I am not quite understanding the underlying abstraction yet of what a bezier curve is fundamentally composed of, as there are too many equations. I would like to have a generic struct that defines a bezier curve. The SVG path gives many examples of the types of curves you can create. They include linear, cubic, and quadratic bezier curves.

If a B-spline is a better generic model, then that would be fine to use too. I am not familiar with those yet tho. Difference between bezier segment and b-spline. I guess "a B-spline curve is a curve that consists of Bezier curves as segments", so that is what I am looking for.

SVG docs say:

Cubic Béziers take in two control points for each point.

Several Bézier curves can be stringed together to create extended, smooth shapes. Often, the control point on one side of a point will be a reflection of the control point used on the other side to keep the slope constant. In this case, a shortcut version of the cubic Bézier can be used, designated by the command S (or s).

The other type of Bézier curve, the quadratic curve called with Q, is actually a simpler curve than the cubic one. It requires one control point which determines the slope of the curve at both the start point and the end point. It takes two parameters: the control point and the end point of the curve.

Arcs and NURBS (non-uniform rational B-splines) are more complex than just plain bezier curves, but it would be nice if the model could be generalized enough to include these as well. Basically I would like a generic model of bezier curves/b-splines/nurbs to use in a drawing/graphics framework, and not sure what that would be.

• Must each bezier class be implemented separately, or can they be combined into one generic class?
• If separate, are they each basically just an array of control points?

So basically I start to think:

I am trying to parse autocad nurbs surface and draw with triangulation using webGL in javascript. I already looked for dxf parser by bjnortier. It supports majority entities like line,arc,3Dface, polyline, lwpolyline, etc., but doesn't support surfaces. Is there any library? Help, please!

I am trying to make Verb's Nurbs Surface to work with vanilla webGL (cheating a bit with webgl-utils though). PIXI.js also yields the same results, corners work, but not the control points.

I could do it using corners verb.geom.NurbsSurface.byCorners however when I try to use the controlPoints using verb.geom.NurbsSurface.byKnotsControlPointsWeights the surface gets messed up, most probably the indices are wrong!

There is an example of using verb with THREE.js but even when I try the same functions used in the example, the results are the same.

I have commented out the function based on the corners, you can see that it works. I console logged srf and from the _data object I could see Verb is generating those control points under the hood, but the same points would not work if I try them with byKnotsControlPointsWeights

Apart from a working solution, I also would like to understand why the code does not work, and which part in the THREE.js is different from my vanilla code that makes it work with THREE but not here.

To enforce my (weak) functional programming skills, I am studying The NURBS book by Piegl and Tiller converting all the algorithms to Haskell. It is a very nice and instructive process but I got stuck on algorithm 2.2, here is (a C-like reworked-by-me version of) the pseudo-code:

So I'm currently trying to take slices on a plane orthogonal to a spline. Direction doesn't really matter too much since I'm using the points to interpolate 3D scans

I'm mainly unsure about the rotmat method (this is a stripped down version of my class, technically a NURBS-Python surface derived class), where I'm rotating the plane mesh from a flat x/y plane (all z=0) to match the new normal vector (tangent of the spline, stored in the der variable).

Anyone have an idea how to rotate a set of points to go from one normal vector to another? The angle around the axis of the new vector doesn't matter than much to me.

(sorry for vg, kind of an obscure library but somewhat convenient actually):

Here is the spline without constraints:

I want to create a NURBS surface that is animated in oscillation with Three.js.

This is my initialization of the NURBS:

I'm looking to convert a series of ordered (pretty dense) 2D points describing arbitrary curves into a NURBS representation, which can be written into an IGES file.

I'm using scipy.interpolate's splprep to get a B-spline representation of the given series of points, and then I had presumed the NURBS definition would essentially be this plus saying all weights are equal to 1. However I think I am fundamentally misinterpreting the output of splprep, specifically the relation between 'B-spline coefficients' and the control points needed to manually recreate the spline in some CAD package (I am using Siemens NX11).

I've tried a simple example of approximating the function y = x^3 from a sparse set of points: