Difference between revisions of "Surface types"
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| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, u<sub>0</sub>, v<sub>0</sub>, w<sub>0</sub>, r'' | | ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, u<sub>0</sub>, v<sub>0</sub>, w<sub>0</sub>, r'' | ||
| <math>S(x,y,z) = (1-u_0^2)(x - x_0)^2 + (1-v_0^2)(y - y_0)^2 + (1-w_0^2)(z - z_0)-r^2</math> | | <math>S(x,y,z) = (1-u_0^2)(x - x_0)^2 + (1-v_0^2)(y - y_0)^2 + (1-w_0^2)(z - z_0)-r^2</math> | ||
− | | Infinite, centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), radius ''r'' | + | | Infinite, parallel to (''u<sub>0</sub>,v<sub>0</sub>,w<sub>0</sub>'') centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), radius ''r'' |
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Revision as of 12:03, 23 February 2016
Contents
Elementary surfaces
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, parallel to (u0,v0,w0) centred at (x0,y0,z0), radius r |