Difference between revisions of "Surface types"

Revision as of 11:48, 23 February 2016

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	$S(x) = x - x_0$	Plane perpendicular to x-axis at x = x₀
`pz`	y₀	$S(y) = y - y_0$	Plane perpendicular to y-axis at y = y₀
`px`	z₀	$S(z) = z - z_0$	Plane perpendicular to z-axis at z = z₀
`plane`	A, B, C, D	$S(x,y,z) = Ax+ By + Cz - D$	General plane in parametric form
`plane`	x₁, y₁, y₁, x₂, y₂, y₂, x₃, y₃, y₃		General plane defined by three points

Notes:

Surface name	Parameters	Surface equation	Description
`cylx`	y₀, z₀, r	$S(y,z) = (y - y_0)^2 + (z - z_0)^2 - r^2$	Infinite cylinder parallel to x-axis, centred at (y₀,z₀), radius r
`cyly`	x₀, z₀, r	$S(x,z) = (x - x_0)^2 + (z - z_0)^2 - r^2$	Infinite cylinder parallel to y-axis, centred at (x₀,z₀), radius r
`cylz, cyl`	x₀, y₀, r	$S(x,y) = (x - x_0)^2 + (y - y_0)^2 - r^2$	Infinite cylinder parallel to z-axis, centred at (x₀,y₀), radius r
`cylv`	x₀, y₀, z₀, u₀, v₀, w₀, r	$S(x,y) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - \left(u_0(x - x_0) + v_0(y - y_0) + w_0(z - z_0)\right)^2 - r^2$	Infinite cylinder parallel to z-axis, centred at (x₀,y₀), radius r

@@ Line 70: / Line 70: @@
 | <tt>cylv</tt>
 | ''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) =  (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 (u_0(x - x_0) + v_0(y - y_0) + w_0(z - z_0))^2 - r^2</math>
+| <math>S(x,y) =  (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - \left(u_0(x - x_0) + v_0(y - y_0) + w_0(z - z_0)\right)^2 - r^2</math>
 | Infinite cylinder parallel to z-axis, centred at (''x<sub>0</sub>,y<sub>0</sub>''), radius ''r''
 |-