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Rhino 4 Essential Training

Comparing Bezier curves, B-splines, and NURBS objects


From:

Rhino 4 Essential Training

with Dave Schultze

Video: Comparing Bezier curves, B-splines, and NURBS objects

In this video, we'll take a look at the foundation of organic modeling, the B-spline, and compare to it's far more well known cousin, the Bezier curve for which it is often mistaken. The Bezier is the curve widely used in 2D applications like Illustrator and Photoshop, and let's you draw or edit using points connected to handlebars, which are then used to adjust the shape of the curve. Let's first take a look at a Bezier and note the handles that make it easy to draw and edit. So, Bezier curves, first and foremost, are formula-based for infinite smoothness.
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  1. 4m 13s
    1. Welcome
      1m 1s
    2. Using the exercise files
      28s
    3. Recommended hardware
      2m 44s
  2. 19m 8s
    1. Understanding the three types of entities: curves, surfaces, and solids
      5m 51s
    2. Comparing Bezier curves, B-splines, and NURBS objects
      3m 35s
    3. Comparing isocurve surfaces and mesh surfaces
      4m 50s
    4. Setting measurement units and tolerance
      4m 52s
  3. 18m 16s
    1. Introducing the viewport
      3m 20s
    2. Using construction planes to anchor model design
      5m 27s
    3. Changing the way a model is viewed using shading modes
      3m 11s
    4. Navigating the viewport with pan, zoom, rotate, and reset controls
      3m 24s
    5. Exploring help options
      2m 54s
  4. 29m 48s
    1. Understanding Rhino's command philosophy
      3m 10s
    2. Using toolbars and docking buttons to a toolbar
      3m 33s
    3. Navigating the geometry menus using a "department store" analogy
      3m 35s
    4. Using the command line and status bar to get feedback
      4m 56s
    5. Modifying the nudge control and setting other preferences
      6m 54s
    6. Using the Properties window
      3m 1s
    7. Opening and saving files
      4m 39s
  5. 14m 24s
    1. Creating basic objects: curves, surfaces, and solids
      4m 22s
    2. Performing basic transformations
      3m 14s
    3. Selecting objects
      3m 37s
    4. Organizing a project using layers
      3m 11s
  6. 21m 18s
    1. Understanding lines and polylines
      4m 10s
    2. Building rectangles and polygons
      5m 12s
    3. Creating arcs, circles, and ellipses
      7m 8s
    4. Drawing freeform curves
      4m 48s
  7. 47m 36s
    1. Comparing different types of 3D surfaces
      7m 11s
    2. Extruding surfaces to create features in a model
      8m 58s
    3. Creating surfaces with lofts
      7m 49s
    4. Using Revolve and Rail Revolve to create surfaces
      7m 42s
    5. Using Sweep Rail to create a 3D claw
      7m 49s
    6. Creating complex surface shapes using Network Surface
      8m 7s
  8. 46m 48s
    1. Introducing solids
      5m 42s
    2. Making solids with primitives
      5m 41s
    3. Extruding curves to create solids without primitives
      8m 59s
    4. Creating unique shapes with the union, difference, and intersection Boolean operators
      6m 46s
    5. Troubleshooting solids and Booleans
      8m 53s
    6. Editing with the solid edit tools
      6m 20s
    7. Creating and transforming holes in solids
      4m 27s
  9. 27m 8s
    1. Understanding Rhino's modeling aids
      3m 59s
    2. Working with the Grid Snap modeling aid
      2m 22s
    3. Using the Ortho modeling aid
      3m 4s
    4. Using the Planar modeling aid
      2m 4s
    5. Incorporating the Osnap modeling aid into your workflow
      6m 7s
    6. Understanding the Project and Smart Track modeling aids
      4m 42s
    7. Setting cursor constraints
      4m 50s
  10. 50m 14s
    1. Editing corners with Fillet and Chamfer
      7m 38s
    2. Trimming and splitting with curve Booleans
      5m 37s
    3. Moving and rotating objects with the Drag and Nudge tools
      7m 24s
    4. Copying and pasting objects
      4m 10s
    5. Understanding how Rhino uses Undo and Redo
      3m 42s
    6. Grouping objects
      3m 21s
    7. Scaling objects
      6m 40s
    8. Duplicating objects using the Mirror command
      6m 36s
    9. Making copies and structured sets using arrays
      5m 6s
  11. 20m 37s
    1. Using the Analysis toolbar to understand characteristics of a model
      6m 14s
    2. Defining degrees of curve and surfaces
      6m 6s
    3. Using Rebuild and Change Degree
      8m 17s
  12. 26m 21s
    1. Measuring and labeling values on a model using dimensioning
      5m 22s
    2. Creating screen captures for quick proofs
      5m 16s
    3. Creating 2D views of a 3D model
      6m 44s
    4. Rendering a project
      8m 59s
  13. 22m 5s
    1. Preparing a model for prototyping by confirming that all gaps are closed
      5m 17s
    2. Using the "shelling" technique to create wall thickness
      10m 54s
    3. Exporting to the STL format for 3D printing
      5m 54s
  14. 14s
    1. Goodbye
      14s

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Rhino 4 Essential Training
5h 48m Beginner Apr 08, 2010

Viewers: in countries Watching now:

In Rhino 4.0 Essential Training, author Dave Schultze shows how the 3D NURBS-based modeling tools in Rhino 4.0 are used to engineer products from toy robots to full-sized aircraft. This course concentrates on using Rhino 4.0 for industrial design and rapid prototyping, with a review of common 3D terminology using specific examples. Along with a comprehensive exploration of the Rhino interface, the course includes an introduction to building 3D objects with Rhino's three primary entities: the curve, the surface, and the solid. Exercise files are included with the course.

Topics include:
  • Understanding 3D terminology
  • Viewing a 3D model in Rhino 4.0
  • Manipulating objects with commands
  • Creating curves, surfaces, and solids
  • Applying transformations to 3D objects
  • Creating unique shapes with Boolean operators
  • Snapping to objects and planes
  • Defining curve and surface degree
  • Prototyping a 3D model
Subjects:
Architecture Modeling Product Design CAD 2D Drawing 3D Drawing
Software:
Rhino
Author:
Dave Schultze

Comparing Bezier curves, B-splines, and NURBS objects

In this video, we'll take a look at the foundation of organic modeling, the B-spline, and compare to it's far more well known cousin, the Bezier curve for which it is often mistaken. The Bezier is the curve widely used in 2D applications like Illustrator and Photoshop, and let's you draw or edit using points connected to handlebars, which are then used to adjust the shape of the curve. Let's first take a look at a Bezier and note the handles that make it easy to draw and edit. So, Bezier curves, first and foremost, are formula-based for infinite smoothness.

It has the handlebar controls, which we've mentioned, which are connected via center point, and the two end points of the handles. It's also extremely useful for 2D, like Illustrator and Photoshop as mentioned, but not so much for 3D. Let's take a look at the B-spline. Again, this curve is also formula- based, and generates infinite smoothness. However, it doesn't have handlebars on the curve. It uses a control cage. That cage is outside of the curve. It only touches at the very end points.

This curve was invented specifically for 3D for which it's excellent, but not so much for 2D. Now, let's take a look at the B-spline in 3D. Here is a Freeform Curve that has been drawn in Rhino. You can see the control points are highlighted there. So, if your curve does not display the control points, you can easily turn them on with the Control Point icon or using the F10 keyboard shortcut. You can see the cage, which allows editing. So, these can be moved back and forth changing the shape of the curve.

So, I am going to zoom out and let you see that we have three of these curves. Those were used to generate a 3D surface, so here's the resulting surface from those curves. This is the term you might have heard called N.U.R.B.S. The technical definition is Non Uniform Rational B-Spline, so that's what the B.S stands for. It means surfaces that have been generated from these Freeform Curves called B-splines. The surface has the advantage of being editable, just like the curves were.

So, I am going to select the surface. Let me turn on the control points for the surface. Here is a similar pattern from curves to the surface, as far as the location of these points. I am going to grab a couple of these guys and just pull them in one direction and see what happens. So, just like the curve that this generated from, this surface is infinitely smooth. I'll try one more little tweak here.

Check it out from the back side. So, this hopefully illustrates why we don't use the Bezier curves from 2D. Any handlebars that were on this surface would be way too difficult to navigate or manage. You would have not only the center point, but also both of the handlebar ends, which would then need to be both moved and rotated, which would be extremely difficult. So, note that these control points for the surface, can only move. There is no really rotation about them. We can also move them in groups and scale them.

So, the word B-spline does sound familiar to Bezier, but B-splines are mandatory and superior when you start working in 3D. B-Splines, with their cage of control points off of the line, do take a little getting used to, especially if you have loads of experience with 2D and Illustrator. But here is the good news. You can import an illustrator file, drawn with Beziers, and easily convert them to B-splines to generate 3D surfaces, as we have just seen.

Find answers to the most frequently asked questions about Rhino 4 Essential Training.


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Q: I'm noticing several differences between the options that author shows in the video and my copy of Rhino. For example, I can't select curves on the edge of a surface or turn on control point when vertically extruding a closed surface like an ellipse. Also, I do not get the Sweep option. I'm running on Mac OS X Snow Leopard.
A: This course was recorded on a Windows computer. As of February 2012, Rhino for Mac is still in beta, so it is not yet a full-fledged product. Wait until the full version comes out to see if these issues are resolved.
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