RHINOCEROS AND NURBS MODELING

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1 Introduction RHINOCEROS AND NURBS MODELING There are three main ways to create a 3D computer model using 3D applications. Each has particular advantages and drawbacks, and the ability to create (or convert to) the right type in the right situation is a valuable professional skill. These model types and their properties are: Polygonal models are made from vertices, edges, and faces - there are no curves and so they have no accurate or measureable curvature higher accuracy for complex surfaces is only achieved at the expense of file size (lots of faces) poly models are easy to edit and animate poly models can be used for additive manufacturing (3D printing) Subdivision surfaces they are easy to edit and animate; subdivs are a single surface, so flow easily across a mesh if created from quads control cages are created using the same simple techniques as polygonal models subdivs can be infinitely increased to give smooth surfaces (though not in Blender) subdivs can be used to make 3D objects though they have small files sizes they cannot be precisely defined as their shape depends on the entire geometry of the surrounding control cage - ie, no accurate fillets or radii however, subdivision surfaces can be converted to NURBS in specialist software NURBS being defined by mathematical curves NURBS surfaces have perfect accuracy and control one surface, or part of one surface, can be changed without altering neighboring surfaces they are widely used for traditional subtractive manufacturing (machining; injection molding) however, NURBS surfaces are hard to edit and animate as the seams tend to split open it is often difficult to create smooth transitions between neighboring surfaces

2 NURBS models Let s look more closely at NURBS modeling. The acronym stands for Non-Uniform Rational B-Spline and the elements of this name give an idea of what makes it unique. There is a good introduction to the theory of NURBS (that author prefers NURB but either is acceptable) surfaces at articles/develop/issue_25/schneider.html (you may need to enter this URL manually into your browser). Starting from the end, a B-Spline is a basis spline, in other words a curve where each control point has a defined influence on the curve, and there is a point beyond which any particular control point has no influence at all. The points on the curve where control point influences stop and start are called knots, and it is a feature of splines that they are continuous through single knots. Double knots create sharp corners. Non-Uniform means that the knots along the curve can be unevenly spaced. They can even be in the same location, allowing sharp points to be created. Finally, Rational means that the control points do not all have the same influence on the curve - in other words they have a weight, or a ratio, compared to the normal value of 1.0. As a result the control points for a 3D surface have four values - X, Y, Z, and W, where W is the weight. A high weight pulls the surface towards the control point. These features of NURBS surfaces mean that very high quality surfaces can be produced that flow into one another. The four main types of surface boundary are illustrated above. The first boundary is sharp; in other words, the edges share a location value only. This is known as G0 (G zero). The second example has a simple fillet (radius) applied to the shared boundary. It looks smooth, but there is a instant transition between the flat and the curved parts. This is known as G1, and although it is acceptable in many cases it would not be appropriate in the case of a car body panel as reflections will not roll smoothly across the boundary. A transition curve is needed. To illustrate a transition curve, look at the illustration to the left. This show the transition from a straight section of railroad track to a curve. If the straight section led immediately into a curve the train would be jolted off the track by the immediate sideways force. A smooth transition curve gradually increases the force. Similarly, in roadbuilding, curves have to grad-

3 ually decrease in radius to allow drivers to rotate the steering wheel smoothly. An immediate constant curve would mean drivers having to jerk the wheel sharply to follow the road. The G2 transition in the boundary illustration shows this. It is a blend of the two surfaces, and its radius goes from matching the neighboring surfaces at the transitions to a maximum in the center. Finally, G3 continuity smooths the transition even more by softening the rate of change in the radius. Rhinoceros Blender is an excellent polygonal and subdivision surface modeler, but its NURBS implementation (as of version 2.76) is minimal. However Rhino, as it s generally known, is a well established and powerful NURBS modeler, and it s recommended for becoming familiar with NURBS modeling. You can download a fully functional trial version of Rhino for Windows or MacOS from This will save 25 times before removing that facility, but it will otherwise continue to function indefinitely. Rhinoceros is not open source or free, however. It s a commercial product that costs $995, but the educational version is remarkable value at $195. Rhino is also an excellent file format translator and indeed is worth the money for that function alone. There are useful tutorials on the Rhino site at Rhino is not parametric like Solidworks or Pro Engineer, but it has a free plug-in called Grasshopper that allows users to creat parametric node networks - similar to the Node Editor in Blender - which can be used to control the development of Rhino models. You can download Grasshopper free from Chris Yonge

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