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ABSTRACT
Thanks to the growth of computational power and the development of new productiontechnologies, NURBS modeling has become the standard in many fields:Industrial Design, Architecture and, more recently, Engineering.Simplified Complexity is a method for learning NURBS modeling with Rhinoceros®.
Born as the synthesis of twenty years of professional experience and teaching,Simplified Complexity consists of a structured knowledge system allowing deepunderstanding of the software.
With this method the user can take advantage of Rhinoceros® full modeling potential.
The idea behind Simplified Complexity is that even if the software has a clear andintuitive interface, NURBS geometry remains quite complex.
In order to become aprofessional user, it is necessary to start from basic geometry knowledge: this willallow to foresee and avoid complexity or, if this is not possible, at least reduce it and optimize it.
TOPICS
1_vector geometry and differential geometry
2_NURBS topology
3_NURBS curves and surfaces
4_optimizing NURBS geometry
5_advanced modeling techniques
6_visualization and fabrication
INDEX
Acknowledgments
Foreword – Seamless
Introduction
1_Geometry basics
1.1 Reference systems and coordinates
1.2 Conic curves
1.3 Vector geometry and curve properties
1.4 Differential geometry of curves
1.5 Curvature of a surface
1.6 Interpolation
2_NURBS geometry
2.1 Bézier and spline
2.2 B-Spline
2.3 NURBS curve
2.3.1 Domain and parametric representation
2.3.2 Degree and order
2.3.3 Knot vector
2.3.4 Control points and weight
2.3.5 Edit points
2.3.6 Curve velocity
2.3.7 Curve orientation
2.4 Continuity
2.4.1 Internal continuity
2.4.2 Remarkable curves – the circle
2.4.3 Geometric continuity
3_Rhino Overview
3.1 Reference system in Rhino
3.1.1 Changing the local coordinate system (CPlane)
3.2 Units and tolerance
3.2.1 Absolute tolerance
3.3 Record History
3.4 Drawing curves around a line
4_Curves: interpolation vs. control
4.1 Interpolated curve
4.2 Conic curve
4.3 Control point curve
4.3.1 Degree and deformability
4.3.2 Three practical rules for drawing free-form curves
4.3.3 Tracing an organic sketch
4.4 Tutorial – Construction lines
4.4.1 Preparing the blueprints
4.4.2 Placing the blueprints
4.4.3 Tracing the construction lines
5_Working with curves
5.1 Join and tolerance
5.2 Extend
5.3 Offset
5.3.1 Offset distance and curvature
5.4 Complex connections: blend curves
5.4.1 Geometric continuity settings and editing
5.5 Curve from two views
5.6 Curve boolean
5.7 NURBS curve manipulation
5.7.1 Rebuild curve
5.7.2 Rebuild curve non-uniform
5.7.3 Refit curve
5.7.4 Fair curve
5.7.5 Criteria for the rebuild or refit of a curve
5.7.6 Insert control point
5.7.7 Insert knot
5.7.8 Insert kink
5.7.9 Control points weight
5.7.10 Change degree
5.8 Tutorial – Creating the 3D curves
5.8.1 Create 3D curves
6_NURBS topology
6.1 Rectangular topology
6.1.1 Topology of a sphere
6.2 Orientation of a surface
6.3 Parametric representation of a surface
7_NURBS surfaces
7.1 Deformable plane
7.2 Surface from 3-4 corner points
7.3 Extrusion
7.3.1 Extrusion and continuity
7.4 Revolve
7.4.1 Rail revolve
7.5 Surface from planar curves
7.5.1 Inconsistency
7.6 Surface from edges curves
7.6.1 Deformability
7.7 Loft
7.7.1 Selecting the cross-sections
7.7.2 Style of the loft
7.7.3 Cross-sections options
7.7.4 Twisted loft
7.7.5 Closed cross-sections and torsion
7.8 Sweep1 1657.8.1 Interpolation in Sweep1
7.8.2 Style: Freeform
7.8.3 Style: Roadlike (helical ramps)
7.8.4 Style: Align with surface
7.8.5 Torsion in Sweep1
7.8.6 Complex tubular shapes
7.9 Sweep2
7.9.1 Cross-section in middle position
7.9.2 Sweep2 topology
7.9.3 Add slash and regularity
7.9.4 Rails from surface edges
7.9.5 Significant surfaces with Sweep2
7.9.6 Sweep2 and complexity
7.9.7 Limits of the Sweep2
7.10 Network surface
7.10.1 Tolerance and complexity
7.10.2 Creating the network
7.10.3 Continuity
7.11 Patch
7.11.1 Attractor points
7.11.2 Digital Terrain Modeling
7.12 Heightfield from image
7.12.1 Heightmap
7.12.2 Command description
7.13 Tutorial – Modeling the wheels
8_Working with control points
8.1 NURBS surface manipulation
8.1.1 Deformable sphere
8.1.2 Inserting control points, knots and kinks
8.2 Selecting points
8.3 Setting coordinates
8.4 Smooth deformations
8.5 Free deformations
8.6 Tutorial – Modeling the body of the car
9_Surface analysis
9.1 Parametric directions of a surface
9.1.1 Command _Dir
9.2 Curvature of a surface
9.3 Geometric continuity
9.3.1 Zebra analysis
9.3.2 Environment analysis
10_Curve-surface interaction
10.1 Edge, border and isocurve
10.1.1 Working with edges
10.2 Intersections and sections
10.3 Projections
10.3.1 Project
10.3.2 Pull
10.4 Holes in thick objects
10.5 Projection with minimum deformation
10.6 Managing curves complexity
10.6.1 Rebuild of a curve on surface
10.6.2 Dynamic rebuild/refit
10.7 2D drawings
10.7.1 Make2D
10.7.2 Inclined projections
10.7.3 Sections
10.7.4 3D and perspective sections
11_Working with surfaces
11.1 Trim and split
11.1.1 Preservation of the control structure
11.1.2 Trim and split of a closed surface
11.2 Fillet and chamfer of surfaces
11.3 Surface Offset
11.4 Surface extension
11.5 Complex connections between surfaces
11.5.1 Sweep2
11.5.2 Network surface
11.5.3 Blend surface 11.6 Tutorial – Projections and trim objects
11.6.1 Trim curves
11.6.2 Details
11.6.3 Interiors
12_Deformations
12.1 Main deformations
12.2 Flow
12.2.1 Flow along curve
12.2.2 Flow along surface
12.3 Cage 300
12.3.1 Types of lattices
12.3.2 Global and local deformations
12.3.3 How to work with the lattice
12.4 Tutorial – Various edits
13_ Emboss and engraving
13.1 Drawing on surfaces
13.1.1 Curves on surface
13.1.2 Projections
13.1.3 UV curves
13.2 Engraving and embossing
13.2.1 Constant height embossing
13.2.2 Variable height embossing
13.2.3 Tubular embossing
13.2.4 Embossing with blend
13.2.5 Embossing with flow
13.3 Tutorial – Adding details
14_Modeling for production
14.1 Solid modeling
14.1.1 Joining surfaces
14.2 Connections
14.2.1 FilletEdge
14.2.2 BlendSrf
14.2.3 When to round off edges
14.2.4 Connections and complexity
14.3 Solid check
14.3.1 Naked edges
14.4 Mesh geometry
14.4.1 Mesh topology
14.4.2 Production: NURBS Mesh conversion
14.5 3D printing
14.5.1 Preparing the model for 3D printing
14.6 Cutting
14.6.1 Stereotomy and waffling
14.6.2 Developable surfaces
14.7 CNC milling
14.7.1 Preparing the model for CNC milling
14.7.2 Knots and curve velocity
15_Modeling for visualization
15.1 Render: NURBS Mesh conversion
15.2 High-resolution and optimization
15.3 Edges rounding
Drawing brazenly
ONO: Designing a revolution
Command Index
Decoded QR codes
Credits
