Thiết kế flash - Splines and surfaces

Splines and SurfacesSpace Curves and SurfacesAutomobilesShip hullsAircraft fuselages and wingsPropeller bladesErgonomic designFreeform curves and surfaces used in design and manufacture of:Half HullDucks and SplinesDucks – lead weightsSpline - long, smooth flexible strip of wood or plasticCurves drawn using ducks and spline to fit (i.e., pass through) data pointsResulting curve mathematically described by cubic polynomialsClasses of CAD Splines Cubic splineBezier curvesB-splinesNURBSCubic SplineModeled after physical splinesCurve fits (i.e., interpolates) all data pointsBoundary conditions: end points and tangent vectors at endpointsSingle cubic spline segmentBezier CurvesControl polygonInterior data (control) points are approximated, not interpolatedCurve is pulled by interior control pointsEach point influences entire curve  no local controlDegree of equation one less than # of control pointsB-splineGeneralization of BezierBlended piecewise polynomial curvePolynomial degree independent of # of control pointsCurve divided into segments (knots)Different segment shapes governed by different polynomialsA given control point only influences the curve locallyControl points (not on the curve) pull curve into shapeNURBSNon-Uniform Rational B-SplineNon-Uniform  irregular spacing between pointsRational  weighted verticesCan control how closely curve comes to approximating verticesFreeform Curves in AutoCADPLine (2D “planar” polyline)PEditFit  cubic spline (interpolates data points)Spline  B-spline (approximates data points)3DPOLY (3D “space” polyline)PEditSpline (B-spline)SPLINE  NURBSSPLINEDITClasses of SurfacesPlanarRuledDevelopableSurface of RevolutionTabulated SurfaceCoons PatchBezierB-spline3D Surface Meshes in AutoCADPredefined surface meshes (e.g., Box, Cone, Wedge, Pyramid, Dome, Dish, etc)RULESURF  ruled surfaceREVSURF  surface of revolutionTABSURF  tabulated surfaceEDGESURF  Coons surface patch3DMESHOoitilshiSplines and Surfaces