Surface types
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Revision as of 21:46, 23 February 2016 by Jaakko Leppänen (Talk | contribs) (→Second-order quadratic surfaces)
Contents
Elementary surfaces
Notes:
- Elementary surfaces refer here to surfaces that can be represented by a single equation.
Planes
Notes:
- Parametric form of the general plane is assumed if four values are provided in the surface card. With six values the plane is assumed to be defined by three points.
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
py | x0 | Plane perpendicular to x-axis at x = x0 | |
pz | y0 | Plane perpendicular to y-axis at y = y0 | |
px | z0 | Plane perpendicular to z-axis at z = z0 | |
plane | A, B, C, D | General plane in parametric form | |
plane | x1, y1, y1, x2, y2, y2, x3, y3, y3 | General plane defined by three points |
Second-order quadratic surfaces
Notes:
- cyl is a shorthand notation for cylz
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
cylx | y0, z0, r | Infinite cylinder parallel to x-axis, centred at (y0,z0), radius r | |
cyly | x0, z0, r | Infinite cylinder parallel to y-axis, centred at (x0,z0), radius r | |
cylz, cyl | x0, y0, r | Infinite cylinder parallel to z-axis, centred at (x0,y0), radius r | |
cylv | x0, y0, z0, u0, v0, w0, r | Infinite cylinder, parallel to (u0,v0,w0), centred at (x0,y0,z0), radius r | |
sph | x0, y0, z0, r | Sphere, centred at (x0,y0,z0), radius r | |
quadratic | A, B, C, D, E, F, G, H, I, J, K | Sphere, centred at (x0,y0,z0), radius r |
Non-quadratic surfaces
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
inf | - | All space | |
torx | x0, y0, z0, r, R | Circular torus with major radius R perpendicular to x-axis, centred at (x0, y0, z0), minor radius r | |
tory | x0, y0, z0, r, R | Circular torus with major radius R perpendicular to y-axis, centred at (x0, y0, z0), minor radius r | |
torz | x0, y0, z0, r, R | Circular torus with major radius R perpendicular to z-axis, centred at (x0, y0, z0), minor radius r |
Derived surface types
Notes:
- Derived surfaces refer here to surfaces composed of two or more elementary types.
Truncated cylinders
Notes:
- Truncated cylinders use the same names as the infinite cylinders above, with two additional values determining the height.
Surface name | Parameters | Composed of | Description |
---|---|---|---|
cylx | y0, z0, r, z0, z1 | Infinite cylinder + two planes | Infinite cylinder parallel to x-axis, centred at (y0,z0), radius r, truncated between [z0, z1] |
cyly | x0, z0, r, z0, z1 | Infinite cylinder + two planes | Infinite cylinder parallel to y-axis, centred at (x0,z0), radius r, truncated between [z0, z1] |
cylz, cyl | x0, y0, r, z0, z1 | Infinite cylinder + two planes | Infinite cylinder parallel to z-axis, centred at (x0,y0), radius r, truncated between [z0, z1] |
Prisms
Notes:
- All prisms are parallel to z-axis, and they can be rotated using surface transformations.
Surface name | Parameters | Composed of | Description |
---|---|---|---|
sqc | x0, y0, d | four planes | Infinite square prism parallel to z-axis, centred at (x0,y0), half-width d |
rect | x0, x1, y0, y1 | four planes | Infinite rectangular prism parallel to z-axis, between [x0, x1] and [y0, y1] |
hexxc | x0, y0, d | six planes | Infinite hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to x-axis, half-width d |
hexxy | x0, y0, d | six planes | Infinite hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to y-axis, half-width d |
hexxprism | x0, y0, d, z0, z1 | eight planes | Truncated hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to x-axis, half-width d, truncated between [z0, z1] |
hexyprism | x0, y0, d, z0, z1 | eight planes | Truncated hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to y-axis, half-width d, truncated between [z0, z1] |
3D polyhedra
Surface name | Parameters | Composed of | Description |
---|---|---|---|
cube | x0, y0, z0, d | six planes | Cube, centred at (x0,y0,z0), half-width d |
cuboid | x0, x1, y0, y1, z0, z1 | six planes | Cuboid, between [x0, x1], [y0, y1] and [z0, z1] |