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 (., 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 (., 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 (., Box, Cone, Wedge, Pyramid, Dome, Dish, etc) RULESURF ruled surface REVSURF surface of revolution TABSURF tabulated surface EDGESURF Coons surface | 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 (., 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 (., 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
