Surface types

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	$S(x) = x - x_0$	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

Second-order quadratic surfaces

Notes:

• cyl is a shorthand notation for cylz

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

Non-quadratic surfaces

Surface name	Parameters	Surface equation	Description
inf		$S(y,x,z) = -\infty$	All space

Derived surface 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	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

Prisms

Surface name	Parameters	Composed of	Description
sqc	y0, z0, d	four planes	Infinite square prism, centred at (y0,z0), half-width d