Datt 2500 week 12
- 1. Datt 2500 Introduction to 3D Modelling Week 12
- 2. What are NURBS? Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. Nurbs are curves (B-splines) that are "influenced" by the positions of defining points called vertices. The designer changes the shape of the curve by changing the positions of the defining vertex points.
- 3. What are NURBS? Nurbs are a convenient way to define smooth curves and surfaces interactively on the computer screen The key benefit of NURBS is that it isn't an approximation of a smooth shape. The math calculates an accurate definition of the surface shape which is still smooth however closely the surface is examined. Think about it like you would approach working with Vectors in illustrator or photoshop
- 4. Origins of NURBS Before computers, designs were drawn by hand on paper with various drafting tools. Rulers were used for straight lines, compasses for circles, and protractors for angles. But many shapes, such as the freeform curve of a ship's bow, could not be drawn with these tool. shipbuilders often needed a life-size version which could not be done by hand. Such large drawings were done with the help of flexible strips of wood, called splines. The splines were held in place at a number of predetermined points, called "ducks“ The elasticity of the spline material caused the strip to take the shape that minimized the energy of bending, thus creating the smoothest possible shape that fit the constraints. source: http://www.alatown.com/spline/
- 5. Traditional Modeling Nurbs Modeling Material Long, thin pieces of wood, plastic or metal Mathematics called NURBS - Non- Uniform Rational B-Splines Controls Heavy metal weights called 'ducks' Control Vertices - CV's - also known as Control Points Flexibility Depends on the stiffness of the material Depends on the Number of CVs, determined by the Degree and Spans Smoothness Created by the consistent density of the material Determined by the Degree and Spans of the NURBS curve Shape (1) Position of the weights along the curve... Position of the CVs along the curve... Shape (2) .... and by the distance it pulls the curve away from flat .... and the distance of the CVs away from the curve Controls connected by... No connection Lines called Hulls source: http://www.bluesmith.co.uk/nurbs1.htm
- 6. Origins of NURBS In 1946, mathematicians started studying the spline shape, and derived the piecewise polynomial formula known as the spline curve or spline function. I. J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen. As computers were introduced into the design process, the physical properties of such splines were investigated so that they could be modelled with mathematical precision and reproduced where needed.
- 7. Origins of NURBS Pioneering work was done in France by Renault engineer Pierre Bézier, and Citroën's physicist and mathematician Paul de Casteljau. Real-time, interactive rendering of NURBS curves and surfaces was first made commercially available on Silicon Graphics workstations in 1989. In 1993, the first interactive NURBS modeler for PCs, called NöRBS, was developed by CAS Berlin, a small startup company cooperating with the Technical University of Berlin.
- 8. Why use NURBS? Nurbs are mostly used for the creation of smooth 3D objects and are more prominent in fields like Industrial Design (Cars, ships and airplanes are mostly designed using Nurbs objects), Architecture & Engineering They are not very common in Animation, Games and Special Effects. On occasion, they will be used (for car rims for example) but they are far less common then polygons. NURBS are ideally suited to hard-surface modeling; objects such as vehicles, equipment, and commercial product designs benefit from the types of smooth surfacing produced by NURBS models.
- 9. They have a fast workflow, and can produce a finish product very quickly The results are smooth and precise They have fewer surfaces, which means fewer errors A smooth Nurbs surface require less computational data then a smooth Polygon surface The Advantages of Nurbs Modeling
- 10. They are not good for work that require a lot of details (which makes them unsuited for most organic shapes including character modeling). Since it doesn’t have UV Maps, complex texturing and shading doesn’t work Some programs (ie game engines) are just not built to compute Nurbs and might just crash or just not render the object In many respect they are obsolete. While some industries still use them, subdvid surfaces and 3D sculpting are becoming more popular due to their diversity The Disadvantages of Nurbs Modeling
- 11. NURBS Components
- 12. Nurbs Curves CV (Control Verticals) CVs (control vertices) control how the curve is “pulled” from a straight line between edit points. Hull To show the relationship between CVs, Maya can draw lines between them. These lines are called hulls. Edit Points Edit points appear as small Xs that marks connection points between spans.
- 13. Nurbs Surfuces CV (Control Verticals) They do not exist on the actual surface but are used to manipulate the shape of the surface. Hull The hull comprises straight lines that connect CVs. When you select a hull, you are actually selecting all of its associated CVs. The hull offers a better visual cue for the distribution of CVs in a crowded area. isoparms Isoparms are lines that represent cross-sections in the U and V directions
- 14. Nurbs Surfaces Spans Spans A span or segment is the space between isoparms at edit points. When creating surfaces using Revolve, Primitives, Loft or rebuilding, you can specify the number of segments or spans. Surface Point Surface Point You can select a Surface point that represents a measurement of U and V. The values at this point are dependent on the parameterization of the surface. Surfuce Patch Surface Patch A NURBS surface patch is defined by an enclosed span square. Several patches can be selected and duplicated to create individual NURBS surfaces.