Whate is Spline Modelling

Support Modeling
1

I understand all types of modelling: polygonal representation, implicit surfaces, subdivision surfaces and volumetric modeling. However, there is one modeling type that I just don’t understand. I have been researching for hours and it is incredibly confusing. This last type of modeling is some mixture of splines, polynoms, curves, beziers, NURBS, patches… I have no idea how to array all those terms.

Please help me, since I would urgently need it to write my prescientific paper.

Thanks!

2

one thing
Nurbs surfaces have what is called Geometric continuity
and it is the only one in blender
so very powerful to keep surfaces smooth

with one of the spline curve you can loaf surface
which can do boat or plane hull !

happy bl

3

Hmm, not sure I understand what exactly you want to know, but to bring some order to the terms:

  • A spline is some kind of curve which is defined by a sequence of control points. There are different kinds, some interpolate between the control points (like c-spline interpolation), other do not (in general) pass through the control points directly (like b-splines).
  • A bezier curve is a different kind of curve representation. You probably have seen these in vector drawing software. In addition to control points they have ‘handles’ to control the tangent of the curve there.
  • NURBS curves (non-uniform rational b-splines) are an extended version of b-splines, which (of course) are a certain kind of splines. They have the additional feature of weights attached to control points.
  • Patches are the 2D generalization of (1D) curves. Typically they are created from the cartesian product of the curve basis functions. They are actually related to subdiv surfaces. For a square grid mesh the limit surface of Catmull-Clark subdiv (for an infinite number of subdivisions) is equivalent to the cubic b-spline patch with the same control points.
4

Thank you very much for your reply! I think I understand the majority. I can approximately imagine what patches are. Still, I wonder what cubic patches are? And is there a difference between ‘patches’ and ‘surface patches’?

TheRedWaxPolice 5
6

Splines can have different orders/degrees. Mathematically splines are expressed by polynomials, but these are used piecewise, meaning different polynomials are used between different control points. The degree of the polynomial determines how smooth a spline can be at the points where 2 polynomial curve pieces connect. Polynomials of degree 1 (linear) can only make the curve continuous. Degree 2 (quadratic) allows the tangents to be continuous/smooth, while degree 3 (cubic) also makes the curvature continuous. Cubic splines are the most common choice in graphics, as they provide the level of mathematical smoothness which makes the curve look smooth to the eye.

Cubic spline patches are then the 2d generalization of cubic splines. They behave in both directions like cubic splines. Same applies to bezier patches. (Bezier curves also can have different orders, but in graphics also cubic is used almost exclusively).

Not that I am aware of when used in the context of 3d graphics. Might be a difference in the precise mathematical definition, though. Don’t know.