Lecture Autodesk inventor: Splines and surfaces

Lecture Autodesk inventor: Splines and surfaces. The main contents of the chapter consist of the following: Space curves and surfaces, half hull, ducks and splines, classes of CAD splines, cubic spline, bezier curves, B-spline, freeform curves in AutoCAD,...

Splines and Surfaces

Space Curves and Surfaces

Automobiles

Ship hulls

Aircraft fuselages and wings

Propeller blades

Ergonomic design

Freeform curves and surfaces used in  design and manufacture of:

Half Hull

Ducks and Splines

Ducks – lead weights

Spline ­ long, smooth flexible strip of wood or  plastic

Curves drawn using ducks and spline to fit (i.e.,  pass through) data points

Resulting curve mathematically described by  cubic polynomials

Classes of CAD Splines 

Cubic spline

Bezier curves

B­splines

 NURBS

Cubic Spline

Modeled after physical splines

Curve fits (i.e., interpolates) all data points

Boundary conditions: end points and tangent  vectors at endpoints

Single cubic spline segment

Bezier Curves

Control polygon

Interior data (control) points are approximated, not  interpolated

Curve is pulled by interior control points

Each point influences entire curve  no local 

control

Degree of equation one less than # of control 

points

B­spline

Generalization of Bezier

Blended piecewise polynomial curve

Polynomial degree independent of # of control  points

Curve divided into segments (knots)

Different segment shapes governed by 

different polynomials

A given control point only influences the curve  locally

Control points (not on the curve) pull curve into  shape

NURBS

Non­Uniform Rational B­Spline

Non­Uniform  irregular spacing between points Rational  weighted vertices

Can control how closely curve comes to 

approximating vertices

Freeform Curves in AutoCAD

PLine (2D “planar” polyline)

 PEdit

 Fit  cubic spline (interpolates data points)

 Spline  B­spline (approximates data points)

3DPOLY (3D “space” polyline)

 PEdit

 Spline (B­spline)

SPLINE  NURBS

 SPLINEDIT

Classes of Surfaces

Planar

Ruled

 Developable

Surface of Revolution

Tabulated Surface

Coons Patch

Bezier

B­spline

3D Surface Meshes in AutoCAD

Predefined surface meshes (e.g., Box,  Cone, Wedge, Pyramid, Dome, Dish,  etc)

RULESURF  ruled surface

REVSURF  surface of revolution

TABSURF  tabulated surface

EDGESURF  Coons surface patch 3DMESH

Ooitilshi

Splines and Surfaces