Lecture Autodesk inventor Splines and surfaces

Splines and Surfaces


Space Curves and Surfaces
Freeform curves and surfaces used in
design and manufacture of:
Automobiles
Ship hulls
Aircraft fuselages and wings
Propeller blades
Ergonomic design


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
B-splines


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


B-spline
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
Non-Uniform Rational B-Spline
Non-Uniform  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  B-spline (approximates data points)

3DPOLY (3D “space” polyline)


PEdit
 Spline (B-spline)

SPLINE  NURBS


SPLINEDIT


Classes of Surfaces
Planar
Ruled


Developable

Surface of Revolution
Tabulated Surface
Coons Patch
Bezier
B-spline


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