Difference between revisions of "Surface types"

Revision as of 12:13, 23 February 2016

Notes:

Elementary surfaces refer here to surfaces that can be represented by a single equation.

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	$S(x,y,z) = (1-u_0^2)(x - x_0)^2 + (1-v_0^2)(y - y_0)^2 + (1-w_0^2)(z - z_0)-r^2$	Infinite cylinder, parallel to (u₀,v₀,w₀), centred at (x₀,y₀,z₀), radius r
`sph`	x₀, y₀, z₀, r	$S(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - r^2$	Sphere, centred at (x₀,y₀,z₀), radius r

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	Infinite cylinder + two planes	Infinite cylinder parallel to x-axis, centred at (y₀,z₀), radius r
`cyly`	x₀, z₀, r	Infinite cylinder + two planes	Infinite cylinder parallel to y-axis, centred at (x₀,z₀), radius r
`cylz, cyl`	x₀, y₀, r	Infinite cylinder + two planes	Infinite cylinder parallel to z-axis, centred at (x₀,y₀), radius r

@@ Line 78: / Line 78: @@
 | <tt>sph</tt>
 | ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r''
-| <math>S(x,y) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - r^2</math>
+| <math>S(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - r^2</math>
 | Sphere, centred at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), radius ''r''