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 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 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     ...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. .. 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 ... REVSURF  surface of revolution TABSURF  tabulated surface EDGESURF  Coons surface patch 3DMESH     Ooitilshi     Splines and Surfaces