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Classification of CAD surface entities

Short answer

CAD surface entities are divided into analytic (plane, ruled, tabulated cylinder, surface of revolution) and synthetic (Bezier, B-spline, Coons patch) surfaces. Synthetic surfaces model free-form shapes such as car bodies and aircraft wings.

List and classify the surface entities used in CAD systems. Briefly describe the plane, ruled, tabulated cylinder and surface of revolution, and state where synthetic surfaces are used.

CAD surface entities are divided into analytic and synthetic surfaces.

ClassSurfacesDefined by
AnalyticPlane, ruled surface, surface of revolution, tabulated cylinderStandard equations, few parameters
SyntheticBezier, B-spline (NURBS), Coons patch, Hermite bicubicControl points / boundary curves
DerivedFillet surface, offset surface, blend surfaceBuilt from other surfaces

Analytic surfaces

  • Plane surface: defined by three non-collinear points, or a point and a normal. Equation ax+by+cz=dax+by+cz=d.
  • Ruled (lofted) surface: generated by joining corresponding points of two boundary curves with straight lines: P(u,w)=(1−w)P1(u)+wP2(u)\mathbf P(u,w)=(1-w)\mathbf P_1(u)+w\mathbf P_2(u). Example: a cone or a twisted turbine-blade strip.
  • Tabulated cylinder: a planar curve (directrix) translated along a straight line of fixed direction and length: P(u,w)=C(u)+wL\mathbf P(u,w)=\mathbf C(u)+w\mathbf L. Example: an extruded profile.
  • Surface of revolution: a plane curve (generatrix) rotated through an angle about an axis: P(u,ϕ)\mathbf P(u,\phi) with the radius from the curve. Examples: bottles, vases, pulleys, domes.

Synthetic surfaces

These are free-form surfaces for shapes with no simple equation: car bodies, aircraft wings, ship hulls, helmets and plastic housings. They are built from a net of control points (Bezier, B-spline) or from four boundary curves (Coons patch).

Surfaces are stored in parametric form P(u,w)\mathbf P(u,w), 0≤u,w≤10\le u,w\le1, so normals, tangents and boundaries are easy to compute for display and machining.

✓ Answer checked by Claude Opus 5.5 (high effort)

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