In FRED, surface types fall into two categories, implicit and explicit. Implicit functions define a surface through the equation f(x, y, z) =0 where all (x, y, z) points which satisfy the equation lie on the surface. Explicit functions define a surface parametrically in the form (x(u,v), y(u,v), z(u,v)) where (u,v) are the parameter values. Several explicit functions are based upon curve types described below. It is also possible to deform a base surface with multiple other surfaces to create surfaces deformed by gravity, molding tools and more.
| Implicit Surface Types: | |
Plane
|
(flat surface) |
Conicoid
|
(spheroid, ellipsoid, hyperboloid, etc. – the classic optical surface) |
Standard
|
asphere (conicoid plus polynomial in even powers of radial distance) |
General
|
asphere (conicoid plus polynomial in even and odd powers of radial distance) |
|
Cylinder
|
(tube/cone) |
|
Ellipsoid/Hyperboloid
|
(constructed by specifying the location of the two foci) |
|
Toroidal asphere
|
(anamorphic aspheric “potato chip” surface with non-symmetric aspheric warping) |
|
XY Toroidal asphere
|
(X or Y toroid with even/odd polynomial aspheric terms) |
|
Polynomial asphere
|
(conicoid plus XY polynomial aspheric terms) |
|
Polynomial surface
|
(general 3D polynomial function in x, y, z) |
|
Zernike surface
|
(the first 66 Zernike polynomial terms) |
|
Scripted surface
|
(user-defined BASIC script) |
|
Sampled Mesh
surface
|
(Rectilinear mesh of sampled sag values with bicubic interpolation between sample points |
 |
|
|
Explicit Surface Types:
|
|
|
Tabulated cylinder
|
(straight line extruded curve) |
|
Spline
|
(collection of parametric polynomial patches) |
|
Ruled surface
|
(two curves connected together) |
|
Surface of revolution
|
(curve revolved around an arbitrary axis) |
|
NURB surface
|
(Non-Uniform Rational Basis-Spline surface) |
|
Trimmed parametric
|
(explicit surface trimmed by curves in parametric space) |
|
|
| Curve Types: | |
|
Circular arc
|
(segment of a circle – or the complete circle) |
|
Conic arc
|
(segment of a sphere, ellipse, hyperbola, etc.) |
|
Line segment
|
(single linear segment) |
|
NURB
|
(Non-Uniform Rational Basis-Spline curve) |
|
Spline
|
(polynomial segments) |
|
Segmented lines
|
(set of connected line segments user-defined or FRED-generated) |
|
Racetrack Curve |
(rectangle with rounded corners) |
|
Composite curve
|
(set of connected curve segments of arbitrary type) |
|
Aperture collection curve
|
(a special collection of closed curves that may be used for surface bounding, clear aperture/edge/hole/obscuration specification, and linear extrusion) |
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